8th Grade - Center For Teaching &...
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Transcript of 8th Grade - Center For Teaching &...
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8th Grade Energy of Objects of Motion
2015shy10shy28
wwwnjctlorg
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Energy of Objects in Motion
bull Energy and its Forms
Click on the topic to go to that section
bull Mechanical Energy
bull Types of Energy Resourcesbull Conservation of Energy
bull Energy of Motionbull Stored Energy
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In the previous units we have been studying the motion of objectsWe talked about how far and fast an object goes if a force is applied
to it
Why does a force cause an object to accelerate
Review from Last Unit
Answer
By applying a force onto an object energy is given to the object This energy is added to the amount of energy the object already possessed
If a resistive force is applied onto an object then the force is taking energy away from the object causing it to decelerate
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Energy and its Forms
Return to Tableof Contents
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What is Energy
Energy is a measurement of an objects ability to do work
How would you define work
How would you know if any work was being done
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What is Energy
Energy is a measurement of an objects ability to do work
Work is defined as applying a force in order to move an object in a given direction When work is done on an object by another object there is a transfer of energy between objects
Since energy is equal to work the unit for both is the same the Joule (J)
1 Joule = 1 Newtonshymeter
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Work can only be done to a system by an external force a force from something that is not a part of the system
Work
So lets say our system is a plane The gate assistance vehicle is not part of the system When the vehicle comes along and pushes back the plane it increases the energy of the plane
The assistance truck is an outside force doing work on the plane
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The amount of work done is the change in the amount of energy that the system will experience This is given by the equation
W = E final shy Einitial
Work
Fill in the blanks with positive or negative HINT Think about how these statements relate to acceleration
bull When a force is applied to an object that causes it to speed up and move a distance the work is _______________ bull When a resistive force is applied to an object that causes it to slow down over a distance or not move at all the work would be ____________
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If an object moves in the same direction as the direction of the force applied to it the energy of the system is increased
The work is positive W gt 0
Positive Work
They can push the truck to get it to move
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If an object moves in the direction opposite to the direction of the
force applied to it then the work is negative W lt 0
The energy of the system is reduced
Negative Work
The parachute moves downwards while air resistance acts upwards
on the parachute
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If an object does not move even when there is a force applied to it then no work is done on the object
W=0 J
Zero Work
The people exert a force onto the wall but the wall does not move
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NonshyMechanical Energy The energy of an object that is not due to its motion or position Nonshymechanical energy usually describes an object at its atomic level
Exampleselectrical energychemical energythermal energysound energy
Mechanical Energy shy The energy of an object due to its motion and position Mechanical energy is usually used to describe a large object
It is the sum of kinetic and potential energy
Mechanical vs NonshyMechanical EnergyEnergy exists in many forms but can be broken down into two major forms
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1 Which of the following is the unit for energy
A Meter
B Newton
C Second
D Joule Answer
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2 A wagon is rolling down a hill A man tries to stop the wagon by trying to push it back up the hill but he is unsuccessful Is the man doing positive or negative work
A positive
B negative
Answer
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3 A boy kicks a soccer ball into a net Did the boy do positive or negative work on the ball
A positive
B negative
Answer
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4 A woman walks across an icy sidewalk that has been covered in salt to help make it less slippery Is the salt doing positive or negative work on the womans shoes
A positive
B negative Answer
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5 Jill is waiting for the bus and she forgot her mittens She rubs her hands together to keep them warm In this situation there is ______________ energy due to the movement of her hands There is also _______________ energy due to the heat she generates by rubbing her hands together
A mechanical nonshymechanical
B nonshymechanical mechanical
Answer
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Mechanical Energy
Return to Tableof Contents
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__________ Energy
__________ Energy __________ Energy
Forms of Mechanical EnergyMechanical Energy can be broken down into two different types of Energy energy of motion which is called Kinetic Energy and stored energy which is called Potential Energy Potential Energy has two forms Gravitational and Elastic depending upon how the energy is stored
Write the underlined words into the correct
place in the diagram
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6 Which of the following is a form of mechanical energy
A Kinetic
B Thermal
C Chemical
D Solar
Answer
A shy Kinetic
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Energy of Motion
Return to Tableof Contents
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7 Which of the following is a type of energy which is used to describe the motion of an object
A Electrical Energy
B Nuclear Energy
C Kinetic Energy
D All of the above
Answer
C shy Kinetic
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Energy of Motion
In order for an object to move one of two scenarios has to occur
1 The object uses some of the potential energy that it had stored
2 Energy is transferred to the object from an outside source
In either case now that the object is in motion the object is experiencing kinetic energy
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An objects state of motion can be described by looking at the amount of kinetic energy that the object has at that moment in time
Kinetic Energy
Since the state of motion of an object can change with time the kinetic energy of an object can also change with time
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velocitymass
The amount of kinetic energy that an object possesses is dependent on two factors
Kinetic Energy
Both of these factors are directly proportional to the kinetic energy We talked about this mathematical relationship in the
last chapter What did directly proportional mean
and
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Kinetic Energy Mass Velocity
Since kinetic energy is the energy of motion
the object has to have a velocity to have kinetic energy The larger the
velocity the __________________ the kinetic energy
The larger the mass the more energy is needed to move the object
therefore the _______________ the kinetic energy
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How Does Kinetic Energy Depend on MassIf two identical objects are moving at the same velocity they will have the same kinetic energy
v = 5 ms
v = 5 ms
A tennis ball and a bowling ball are both shown above The bowling ball is heavier than the tennis ball Which ball would have more kinetic energy
However if one object has more mass than the other the heavier object will have more kinetic energy
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Velocity vs Speed
Remember that velocity is another way to measure motion V elocity is the speed of an object with direction Speed does not have a direction so we call speed a scalar quantity
Since velocity has both magnitude and direction it is a vector quantity
Runners speed 10 kmhr
Runners velocity 10 kmhr to the East
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How Does Kinetic Energy Depend on Velocity
In this picture the hare is moving faster than the tortoise at this point
If we assumed that they had the same mass who would have more kinetic energy Why Discuss this with a partner
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v = 5 ms
v = 10 ms
How Does Kinetic Energy Depend upon Velocity
If two identical objects are moving at the same velocity then they will have the same kinetic energy However if one of the objects is moving faster the faster one will have more kinetic energy
In the diagram above two identical tennis balls are moving Which tennis ball has more kinetic energy and why
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8 Three different emergency vehicles are noticed driving on the highway at a speed of 25 ms Which of the following cars have the most kinetic energy at that moment
A a police car
B an ambulance
C a firetruck
D they all have the same kinetic energy
Answer
C
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9 Three different baseball pitchers had the speed of their fastball measured by a radar gun Which of the following pitchers fastball had the smallest amount of kinetic energy
A a little league pitcher (22 ms)
B a high school pitcher (33 ms)
C a major league pitcher (41ms)
D they all had the same kinetic energy
Answer
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10 Which of the following situations has the least kinetic energy Be ready to explain your answer
A a man sitting still on a park bench
B a child riding a bike
C a woman driving a car
D it is impossible to tell
Answer
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Calculating Kinetic Energy
Kinetic energy can be solved for by using the equation
12KE = mv2
Lets fill in the table below
variable unitsName
Kinetic Energy
mms
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Example shy Calculating Kinetic Energy
A car which has a mass of 1000 kg is moving with a velocity of 5 ms How much kinetic energy does the car possess Calculate the cars kinetic energy
KE = mv2KE = (05)(1000 kg)(5 ms)2
KE = (05)(1000 kg)(25 m2s2)KE = 125000 J
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Click on the box to see the solution
Teacher N
otes
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11 A 10 kg snowball is rolling down a hill Just before reaching the bottom its velocity is measured to be 10 ms What is the kinetic energy of the ball at this position
Answer
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12 A 100 kg running back in football is running with a velocity of 2 ms What is his kinetic energy
Answer
KE= 12 mv2KE= 12 (100 kg) (2 ms)2KE= 12 (100 kg) (4m2s2)KE= 200 J
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13 A 2000 kg car with a velocity of 20 ms slows down and stops at a red light What is the change in kinetic energy
Answer
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14 A 50 kg girl rode her 12 kg bicycle in a race She started from rest and peddled with a velocity of 10 ms What is the change in kinetic energy of the girl and her bicycle
Answer
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Thinking Mathematically
KE = mv212
We have already said that mass is directly proportional to kinetic energy
This means that if the mass of the object doubles the
kinetic energy ___________ If the mass of the object increases by a
factor of 5 then the kinetic energy___________ by ______________
If the mass of the object decreases by half then the kinetic
energy will ____________ by ___________
doubles
increases a factor of 5
decrease half
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15 If the mass of a wagon is doubled its kinetic energy
A increases
B decreases
Answer
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16 If the mass of a wagon is doubled by what factor does the kinetic energy increase
Answer
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Thinking Mathematically
Kinetic energy can be solved by using the equation
KE = mv212
From the equation we can see that the kinetic energy is also directly proportional to the square of the velocity
This means that if the velocity doubles the kinetic energy increases by a factor of 4
22=4
If the velocity is quadrupled then the kinetic energy increases by a factor of 16
42= 16
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17 If the velocity of a wagon is tripled its kinetic energy
Answer
A increases
B decreases
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18 If the velocity of a wagon is tripled by what factor does the kinetic energy increase
Answer
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19 Two balls are moving with the same velocity ball A has a mass of 10 kg and ball B has a mass of 40 kg How much more kinetic energy does ball B have
Answer
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20 A cart halves its mass and at the same time doubles its speed Does the kinetic energy increase or decrease By what factor does the kinetic energy change
A increase 2
B increase 4
C decrease 2
D decrease 4
Answer
bull half the mass gives 12 the KEbull double the speed gives 4 x KEbull therefore (12)(4)= 2
A
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Stored Energy
Return to Tableof Contents
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Where does Kinetic Energy Come From
Imagine a roller coaster car that is at the top of the first hill and is stopped
Does the car stay stopped at the top of the hill for the entire ride
What happens
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Where does Kinetic Energy Come From
Once the car leans over the edge gravity pulls it down The ride is taking advantage of the gravitational attraction between the car and Earth to give the car kinetic energy and make it go faster as it falls
The kinetic energy the car is receiving is coming from another type of energy called potential energy
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Where does Kinetic Energy Come From
Potential energy is energy stored in an object due to the objects position The roller coaster car on the previous slide had stored energy due to its height above the ground
There are two forms of potential energy that we will be looking at in this unit
Gravitational Potential Energy
and
Elastic Potential Energy
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Gravitational Potential Energy
The potential energy due to elevated positions is called gravitational potential energy
Gravitational potential energy is stored energy and it can be used at a later time to cause an object to moveOnce the person steps off the diving board the gravitational potential energy is converted into kinetic energy and the person falls (moves)
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Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
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Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
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h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
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h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
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h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
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h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
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21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
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22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
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Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
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Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
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23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
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24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
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GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
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25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
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26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
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27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
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28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
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Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
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Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
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Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
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What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
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What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
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How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
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29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
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Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
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Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
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Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
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Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
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30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
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31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
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32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
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Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
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Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
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33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
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34 If the spring constant k is halved by what factor does the EPE decrease
Answer
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35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
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Conservation of Energy
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What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
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This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
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When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
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When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
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Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
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At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
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At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
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At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
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36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
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37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
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38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
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Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
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Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
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Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
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Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
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Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
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39 In which position of the block would the system have only EPE
A B C Answer
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40 In which position of the block would the system have both KE and EPE
A B C Answer
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41 In which position of the block would the system have only KE
A B C
Answer
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If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
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v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
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Types of Energy Resources
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Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
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Types of Energy Resources
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Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
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Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
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Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
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Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
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Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
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42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
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8th Grade Energy of Objects of Motion
2015shy10shy28
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Energy of Objects in Motion
bull Energy and its Forms
Click on the topic to go to that section
bull Mechanical Energy
bull Types of Energy Resourcesbull Conservation of Energy
bull Energy of Motionbull Stored Energy
4
In the previous units we have been studying the motion of objectsWe talked about how far and fast an object goes if a force is applied
to it
Why does a force cause an object to accelerate
Review from Last Unit
Answer
By applying a force onto an object energy is given to the object This energy is added to the amount of energy the object already possessed
If a resistive force is applied onto an object then the force is taking energy away from the object causing it to decelerate
5
Energy and its Forms
Return to Tableof Contents
6
What is Energy
Energy is a measurement of an objects ability to do work
How would you define work
How would you know if any work was being done
7
What is Energy
Energy is a measurement of an objects ability to do work
Work is defined as applying a force in order to move an object in a given direction When work is done on an object by another object there is a transfer of energy between objects
Since energy is equal to work the unit for both is the same the Joule (J)
1 Joule = 1 Newtonshymeter
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Work can only be done to a system by an external force a force from something that is not a part of the system
Work
So lets say our system is a plane The gate assistance vehicle is not part of the system When the vehicle comes along and pushes back the plane it increases the energy of the plane
The assistance truck is an outside force doing work on the plane
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The amount of work done is the change in the amount of energy that the system will experience This is given by the equation
W = E final shy Einitial
Work
Fill in the blanks with positive or negative HINT Think about how these statements relate to acceleration
bull When a force is applied to an object that causes it to speed up and move a distance the work is _______________ bull When a resistive force is applied to an object that causes it to slow down over a distance or not move at all the work would be ____________
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If an object moves in the same direction as the direction of the force applied to it the energy of the system is increased
The work is positive W gt 0
Positive Work
They can push the truck to get it to move
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If an object moves in the direction opposite to the direction of the
force applied to it then the work is negative W lt 0
The energy of the system is reduced
Negative Work
The parachute moves downwards while air resistance acts upwards
on the parachute
12
If an object does not move even when there is a force applied to it then no work is done on the object
W=0 J
Zero Work
The people exert a force onto the wall but the wall does not move
13
NonshyMechanical Energy The energy of an object that is not due to its motion or position Nonshymechanical energy usually describes an object at its atomic level
Exampleselectrical energychemical energythermal energysound energy
Mechanical Energy shy The energy of an object due to its motion and position Mechanical energy is usually used to describe a large object
It is the sum of kinetic and potential energy
Mechanical vs NonshyMechanical EnergyEnergy exists in many forms but can be broken down into two major forms
14
1 Which of the following is the unit for energy
A Meter
B Newton
C Second
D Joule Answer
15
2 A wagon is rolling down a hill A man tries to stop the wagon by trying to push it back up the hill but he is unsuccessful Is the man doing positive or negative work
A positive
B negative
Answer
16
3 A boy kicks a soccer ball into a net Did the boy do positive or negative work on the ball
A positive
B negative
Answer
17
4 A woman walks across an icy sidewalk that has been covered in salt to help make it less slippery Is the salt doing positive or negative work on the womans shoes
A positive
B negative Answer
18
5 Jill is waiting for the bus and she forgot her mittens She rubs her hands together to keep them warm In this situation there is ______________ energy due to the movement of her hands There is also _______________ energy due to the heat she generates by rubbing her hands together
A mechanical nonshymechanical
B nonshymechanical mechanical
Answer
19
Mechanical Energy
Return to Tableof Contents
20
__________ Energy
__________ Energy __________ Energy
Forms of Mechanical EnergyMechanical Energy can be broken down into two different types of Energy energy of motion which is called Kinetic Energy and stored energy which is called Potential Energy Potential Energy has two forms Gravitational and Elastic depending upon how the energy is stored
Write the underlined words into the correct
place in the diagram
21
6 Which of the following is a form of mechanical energy
A Kinetic
B Thermal
C Chemical
D Solar
Answer
A shy Kinetic
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Energy of Motion
Return to Tableof Contents
23
7 Which of the following is a type of energy which is used to describe the motion of an object
A Electrical Energy
B Nuclear Energy
C Kinetic Energy
D All of the above
Answer
C shy Kinetic
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Energy of Motion
In order for an object to move one of two scenarios has to occur
1 The object uses some of the potential energy that it had stored
2 Energy is transferred to the object from an outside source
In either case now that the object is in motion the object is experiencing kinetic energy
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An objects state of motion can be described by looking at the amount of kinetic energy that the object has at that moment in time
Kinetic Energy
Since the state of motion of an object can change with time the kinetic energy of an object can also change with time
26
velocitymass
The amount of kinetic energy that an object possesses is dependent on two factors
Kinetic Energy
Both of these factors are directly proportional to the kinetic energy We talked about this mathematical relationship in the
last chapter What did directly proportional mean
and
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Kinetic Energy Mass Velocity
Since kinetic energy is the energy of motion
the object has to have a velocity to have kinetic energy The larger the
velocity the __________________ the kinetic energy
The larger the mass the more energy is needed to move the object
therefore the _______________ the kinetic energy
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How Does Kinetic Energy Depend on MassIf two identical objects are moving at the same velocity they will have the same kinetic energy
v = 5 ms
v = 5 ms
A tennis ball and a bowling ball are both shown above The bowling ball is heavier than the tennis ball Which ball would have more kinetic energy
However if one object has more mass than the other the heavier object will have more kinetic energy
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Velocity vs Speed
Remember that velocity is another way to measure motion V elocity is the speed of an object with direction Speed does not have a direction so we call speed a scalar quantity
Since velocity has both magnitude and direction it is a vector quantity
Runners speed 10 kmhr
Runners velocity 10 kmhr to the East
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How Does Kinetic Energy Depend on Velocity
In this picture the hare is moving faster than the tortoise at this point
If we assumed that they had the same mass who would have more kinetic energy Why Discuss this with a partner
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v = 5 ms
v = 10 ms
How Does Kinetic Energy Depend upon Velocity
If two identical objects are moving at the same velocity then they will have the same kinetic energy However if one of the objects is moving faster the faster one will have more kinetic energy
In the diagram above two identical tennis balls are moving Which tennis ball has more kinetic energy and why
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8 Three different emergency vehicles are noticed driving on the highway at a speed of 25 ms Which of the following cars have the most kinetic energy at that moment
A a police car
B an ambulance
C a firetruck
D they all have the same kinetic energy
Answer
C
33
9 Three different baseball pitchers had the speed of their fastball measured by a radar gun Which of the following pitchers fastball had the smallest amount of kinetic energy
A a little league pitcher (22 ms)
B a high school pitcher (33 ms)
C a major league pitcher (41ms)
D they all had the same kinetic energy
Answer
34
10 Which of the following situations has the least kinetic energy Be ready to explain your answer
A a man sitting still on a park bench
B a child riding a bike
C a woman driving a car
D it is impossible to tell
Answer
35
Calculating Kinetic Energy
Kinetic energy can be solved for by using the equation
12KE = mv2
Lets fill in the table below
variable unitsName
Kinetic Energy
mms
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Example shy Calculating Kinetic Energy
A car which has a mass of 1000 kg is moving with a velocity of 5 ms How much kinetic energy does the car possess Calculate the cars kinetic energy
KE = mv2KE = (05)(1000 kg)(5 ms)2
KE = (05)(1000 kg)(25 m2s2)KE = 125000 J
12
Click on the box to see the solution
Teacher N
otes
37
11 A 10 kg snowball is rolling down a hill Just before reaching the bottom its velocity is measured to be 10 ms What is the kinetic energy of the ball at this position
Answer
38
12 A 100 kg running back in football is running with a velocity of 2 ms What is his kinetic energy
Answer
KE= 12 mv2KE= 12 (100 kg) (2 ms)2KE= 12 (100 kg) (4m2s2)KE= 200 J
39
13 A 2000 kg car with a velocity of 20 ms slows down and stops at a red light What is the change in kinetic energy
Answer
40
14 A 50 kg girl rode her 12 kg bicycle in a race She started from rest and peddled with a velocity of 10 ms What is the change in kinetic energy of the girl and her bicycle
Answer
41
Thinking Mathematically
KE = mv212
We have already said that mass is directly proportional to kinetic energy
This means that if the mass of the object doubles the
kinetic energy ___________ If the mass of the object increases by a
factor of 5 then the kinetic energy___________ by ______________
If the mass of the object decreases by half then the kinetic
energy will ____________ by ___________
doubles
increases a factor of 5
decrease half
42
15 If the mass of a wagon is doubled its kinetic energy
A increases
B decreases
Answer
43
16 If the mass of a wagon is doubled by what factor does the kinetic energy increase
Answer
44
Thinking Mathematically
Kinetic energy can be solved by using the equation
KE = mv212
From the equation we can see that the kinetic energy is also directly proportional to the square of the velocity
This means that if the velocity doubles the kinetic energy increases by a factor of 4
22=4
If the velocity is quadrupled then the kinetic energy increases by a factor of 16
42= 16
45
17 If the velocity of a wagon is tripled its kinetic energy
Answer
A increases
B decreases
46
18 If the velocity of a wagon is tripled by what factor does the kinetic energy increase
Answer
47
19 Two balls are moving with the same velocity ball A has a mass of 10 kg and ball B has a mass of 40 kg How much more kinetic energy does ball B have
Answer
48
20 A cart halves its mass and at the same time doubles its speed Does the kinetic energy increase or decrease By what factor does the kinetic energy change
A increase 2
B increase 4
C decrease 2
D decrease 4
Answer
bull half the mass gives 12 the KEbull double the speed gives 4 x KEbull therefore (12)(4)= 2
A
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Stored Energy
Return to Tableof Contents
50
Where does Kinetic Energy Come From
Imagine a roller coaster car that is at the top of the first hill and is stopped
Does the car stay stopped at the top of the hill for the entire ride
What happens
51
Where does Kinetic Energy Come From
Once the car leans over the edge gravity pulls it down The ride is taking advantage of the gravitational attraction between the car and Earth to give the car kinetic energy and make it go faster as it falls
The kinetic energy the car is receiving is coming from another type of energy called potential energy
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Where does Kinetic Energy Come From
Potential energy is energy stored in an object due to the objects position The roller coaster car on the previous slide had stored energy due to its height above the ground
There are two forms of potential energy that we will be looking at in this unit
Gravitational Potential Energy
and
Elastic Potential Energy
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Gravitational Potential Energy
The potential energy due to elevated positions is called gravitational potential energy
Gravitational potential energy is stored energy and it can be used at a later time to cause an object to moveOnce the person steps off the diving board the gravitational potential energy is converted into kinetic energy and the person falls (moves)
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Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
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Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
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h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
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Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
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3
Energy of Objects in Motion
bull Energy and its Forms
Click on the topic to go to that section
bull Mechanical Energy
bull Types of Energy Resourcesbull Conservation of Energy
bull Energy of Motionbull Stored Energy
4
In the previous units we have been studying the motion of objectsWe talked about how far and fast an object goes if a force is applied
to it
Why does a force cause an object to accelerate
Review from Last Unit
Answer
By applying a force onto an object energy is given to the object This energy is added to the amount of energy the object already possessed
If a resistive force is applied onto an object then the force is taking energy away from the object causing it to decelerate
5
Energy and its Forms
Return to Tableof Contents
6
What is Energy
Energy is a measurement of an objects ability to do work
How would you define work
How would you know if any work was being done
7
What is Energy
Energy is a measurement of an objects ability to do work
Work is defined as applying a force in order to move an object in a given direction When work is done on an object by another object there is a transfer of energy between objects
Since energy is equal to work the unit for both is the same the Joule (J)
1 Joule = 1 Newtonshymeter
8
Work can only be done to a system by an external force a force from something that is not a part of the system
Work
So lets say our system is a plane The gate assistance vehicle is not part of the system When the vehicle comes along and pushes back the plane it increases the energy of the plane
The assistance truck is an outside force doing work on the plane
9
The amount of work done is the change in the amount of energy that the system will experience This is given by the equation
W = E final shy Einitial
Work
Fill in the blanks with positive or negative HINT Think about how these statements relate to acceleration
bull When a force is applied to an object that causes it to speed up and move a distance the work is _______________ bull When a resistive force is applied to an object that causes it to slow down over a distance or not move at all the work would be ____________
10
If an object moves in the same direction as the direction of the force applied to it the energy of the system is increased
The work is positive W gt 0
Positive Work
They can push the truck to get it to move
11
If an object moves in the direction opposite to the direction of the
force applied to it then the work is negative W lt 0
The energy of the system is reduced
Negative Work
The parachute moves downwards while air resistance acts upwards
on the parachute
12
If an object does not move even when there is a force applied to it then no work is done on the object
W=0 J
Zero Work
The people exert a force onto the wall but the wall does not move
13
NonshyMechanical Energy The energy of an object that is not due to its motion or position Nonshymechanical energy usually describes an object at its atomic level
Exampleselectrical energychemical energythermal energysound energy
Mechanical Energy shy The energy of an object due to its motion and position Mechanical energy is usually used to describe a large object
It is the sum of kinetic and potential energy
Mechanical vs NonshyMechanical EnergyEnergy exists in many forms but can be broken down into two major forms
14
1 Which of the following is the unit for energy
A Meter
B Newton
C Second
D Joule Answer
15
2 A wagon is rolling down a hill A man tries to stop the wagon by trying to push it back up the hill but he is unsuccessful Is the man doing positive or negative work
A positive
B negative
Answer
16
3 A boy kicks a soccer ball into a net Did the boy do positive or negative work on the ball
A positive
B negative
Answer
17
4 A woman walks across an icy sidewalk that has been covered in salt to help make it less slippery Is the salt doing positive or negative work on the womans shoes
A positive
B negative Answer
18
5 Jill is waiting for the bus and she forgot her mittens She rubs her hands together to keep them warm In this situation there is ______________ energy due to the movement of her hands There is also _______________ energy due to the heat she generates by rubbing her hands together
A mechanical nonshymechanical
B nonshymechanical mechanical
Answer
19
Mechanical Energy
Return to Tableof Contents
20
__________ Energy
__________ Energy __________ Energy
Forms of Mechanical EnergyMechanical Energy can be broken down into two different types of Energy energy of motion which is called Kinetic Energy and stored energy which is called Potential Energy Potential Energy has two forms Gravitational and Elastic depending upon how the energy is stored
Write the underlined words into the correct
place in the diagram
21
6 Which of the following is a form of mechanical energy
A Kinetic
B Thermal
C Chemical
D Solar
Answer
A shy Kinetic
22
Energy of Motion
Return to Tableof Contents
23
7 Which of the following is a type of energy which is used to describe the motion of an object
A Electrical Energy
B Nuclear Energy
C Kinetic Energy
D All of the above
Answer
C shy Kinetic
24
Energy of Motion
In order for an object to move one of two scenarios has to occur
1 The object uses some of the potential energy that it had stored
2 Energy is transferred to the object from an outside source
In either case now that the object is in motion the object is experiencing kinetic energy
25
An objects state of motion can be described by looking at the amount of kinetic energy that the object has at that moment in time
Kinetic Energy
Since the state of motion of an object can change with time the kinetic energy of an object can also change with time
26
velocitymass
The amount of kinetic energy that an object possesses is dependent on two factors
Kinetic Energy
Both of these factors are directly proportional to the kinetic energy We talked about this mathematical relationship in the
last chapter What did directly proportional mean
and
27
Kinetic Energy Mass Velocity
Since kinetic energy is the energy of motion
the object has to have a velocity to have kinetic energy The larger the
velocity the __________________ the kinetic energy
The larger the mass the more energy is needed to move the object
therefore the _______________ the kinetic energy
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How Does Kinetic Energy Depend on MassIf two identical objects are moving at the same velocity they will have the same kinetic energy
v = 5 ms
v = 5 ms
A tennis ball and a bowling ball are both shown above The bowling ball is heavier than the tennis ball Which ball would have more kinetic energy
However if one object has more mass than the other the heavier object will have more kinetic energy
29
Velocity vs Speed
Remember that velocity is another way to measure motion V elocity is the speed of an object with direction Speed does not have a direction so we call speed a scalar quantity
Since velocity has both magnitude and direction it is a vector quantity
Runners speed 10 kmhr
Runners velocity 10 kmhr to the East
30
How Does Kinetic Energy Depend on Velocity
In this picture the hare is moving faster than the tortoise at this point
If we assumed that they had the same mass who would have more kinetic energy Why Discuss this with a partner
31
v = 5 ms
v = 10 ms
How Does Kinetic Energy Depend upon Velocity
If two identical objects are moving at the same velocity then they will have the same kinetic energy However if one of the objects is moving faster the faster one will have more kinetic energy
In the diagram above two identical tennis balls are moving Which tennis ball has more kinetic energy and why
32
8 Three different emergency vehicles are noticed driving on the highway at a speed of 25 ms Which of the following cars have the most kinetic energy at that moment
A a police car
B an ambulance
C a firetruck
D they all have the same kinetic energy
Answer
C
33
9 Three different baseball pitchers had the speed of their fastball measured by a radar gun Which of the following pitchers fastball had the smallest amount of kinetic energy
A a little league pitcher (22 ms)
B a high school pitcher (33 ms)
C a major league pitcher (41ms)
D they all had the same kinetic energy
Answer
34
10 Which of the following situations has the least kinetic energy Be ready to explain your answer
A a man sitting still on a park bench
B a child riding a bike
C a woman driving a car
D it is impossible to tell
Answer
35
Calculating Kinetic Energy
Kinetic energy can be solved for by using the equation
12KE = mv2
Lets fill in the table below
variable unitsName
Kinetic Energy
mms
36
Example shy Calculating Kinetic Energy
A car which has a mass of 1000 kg is moving with a velocity of 5 ms How much kinetic energy does the car possess Calculate the cars kinetic energy
KE = mv2KE = (05)(1000 kg)(5 ms)2
KE = (05)(1000 kg)(25 m2s2)KE = 125000 J
12
Click on the box to see the solution
Teacher N
otes
37
11 A 10 kg snowball is rolling down a hill Just before reaching the bottom its velocity is measured to be 10 ms What is the kinetic energy of the ball at this position
Answer
38
12 A 100 kg running back in football is running with a velocity of 2 ms What is his kinetic energy
Answer
KE= 12 mv2KE= 12 (100 kg) (2 ms)2KE= 12 (100 kg) (4m2s2)KE= 200 J
39
13 A 2000 kg car with a velocity of 20 ms slows down and stops at a red light What is the change in kinetic energy
Answer
40
14 A 50 kg girl rode her 12 kg bicycle in a race She started from rest and peddled with a velocity of 10 ms What is the change in kinetic energy of the girl and her bicycle
Answer
41
Thinking Mathematically
KE = mv212
We have already said that mass is directly proportional to kinetic energy
This means that if the mass of the object doubles the
kinetic energy ___________ If the mass of the object increases by a
factor of 5 then the kinetic energy___________ by ______________
If the mass of the object decreases by half then the kinetic
energy will ____________ by ___________
doubles
increases a factor of 5
decrease half
42
15 If the mass of a wagon is doubled its kinetic energy
A increases
B decreases
Answer
43
16 If the mass of a wagon is doubled by what factor does the kinetic energy increase
Answer
44
Thinking Mathematically
Kinetic energy can be solved by using the equation
KE = mv212
From the equation we can see that the kinetic energy is also directly proportional to the square of the velocity
This means that if the velocity doubles the kinetic energy increases by a factor of 4
22=4
If the velocity is quadrupled then the kinetic energy increases by a factor of 16
42= 16
45
17 If the velocity of a wagon is tripled its kinetic energy
Answer
A increases
B decreases
46
18 If the velocity of a wagon is tripled by what factor does the kinetic energy increase
Answer
47
19 Two balls are moving with the same velocity ball A has a mass of 10 kg and ball B has a mass of 40 kg How much more kinetic energy does ball B have
Answer
48
20 A cart halves its mass and at the same time doubles its speed Does the kinetic energy increase or decrease By what factor does the kinetic energy change
A increase 2
B increase 4
C decrease 2
D decrease 4
Answer
bull half the mass gives 12 the KEbull double the speed gives 4 x KEbull therefore (12)(4)= 2
A
49
Stored Energy
Return to Tableof Contents
50
Where does Kinetic Energy Come From
Imagine a roller coaster car that is at the top of the first hill and is stopped
Does the car stay stopped at the top of the hill for the entire ride
What happens
51
Where does Kinetic Energy Come From
Once the car leans over the edge gravity pulls it down The ride is taking advantage of the gravitational attraction between the car and Earth to give the car kinetic energy and make it go faster as it falls
The kinetic energy the car is receiving is coming from another type of energy called potential energy
52
Where does Kinetic Energy Come From
Potential energy is energy stored in an object due to the objects position The roller coaster car on the previous slide had stored energy due to its height above the ground
There are two forms of potential energy that we will be looking at in this unit
Gravitational Potential Energy
and
Elastic Potential Energy
53
Gravitational Potential Energy
The potential energy due to elevated positions is called gravitational potential energy
Gravitational potential energy is stored energy and it can be used at a later time to cause an object to moveOnce the person steps off the diving board the gravitational potential energy is converted into kinetic energy and the person falls (moves)
54
Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
55
Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
56
h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
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91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
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4
In the previous units we have been studying the motion of objectsWe talked about how far and fast an object goes if a force is applied
to it
Why does a force cause an object to accelerate
Review from Last Unit
Answer
By applying a force onto an object energy is given to the object This energy is added to the amount of energy the object already possessed
If a resistive force is applied onto an object then the force is taking energy away from the object causing it to decelerate
5
Energy and its Forms
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6
What is Energy
Energy is a measurement of an objects ability to do work
How would you define work
How would you know if any work was being done
7
What is Energy
Energy is a measurement of an objects ability to do work
Work is defined as applying a force in order to move an object in a given direction When work is done on an object by another object there is a transfer of energy between objects
Since energy is equal to work the unit for both is the same the Joule (J)
1 Joule = 1 Newtonshymeter
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Work can only be done to a system by an external force a force from something that is not a part of the system
Work
So lets say our system is a plane The gate assistance vehicle is not part of the system When the vehicle comes along and pushes back the plane it increases the energy of the plane
The assistance truck is an outside force doing work on the plane
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The amount of work done is the change in the amount of energy that the system will experience This is given by the equation
W = E final shy Einitial
Work
Fill in the blanks with positive or negative HINT Think about how these statements relate to acceleration
bull When a force is applied to an object that causes it to speed up and move a distance the work is _______________ bull When a resistive force is applied to an object that causes it to slow down over a distance or not move at all the work would be ____________
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If an object moves in the same direction as the direction of the force applied to it the energy of the system is increased
The work is positive W gt 0
Positive Work
They can push the truck to get it to move
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If an object moves in the direction opposite to the direction of the
force applied to it then the work is negative W lt 0
The energy of the system is reduced
Negative Work
The parachute moves downwards while air resistance acts upwards
on the parachute
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If an object does not move even when there is a force applied to it then no work is done on the object
W=0 J
Zero Work
The people exert a force onto the wall but the wall does not move
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NonshyMechanical Energy The energy of an object that is not due to its motion or position Nonshymechanical energy usually describes an object at its atomic level
Exampleselectrical energychemical energythermal energysound energy
Mechanical Energy shy The energy of an object due to its motion and position Mechanical energy is usually used to describe a large object
It is the sum of kinetic and potential energy
Mechanical vs NonshyMechanical EnergyEnergy exists in many forms but can be broken down into two major forms
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1 Which of the following is the unit for energy
A Meter
B Newton
C Second
D Joule Answer
15
2 A wagon is rolling down a hill A man tries to stop the wagon by trying to push it back up the hill but he is unsuccessful Is the man doing positive or negative work
A positive
B negative
Answer
16
3 A boy kicks a soccer ball into a net Did the boy do positive or negative work on the ball
A positive
B negative
Answer
17
4 A woman walks across an icy sidewalk that has been covered in salt to help make it less slippery Is the salt doing positive or negative work on the womans shoes
A positive
B negative Answer
18
5 Jill is waiting for the bus and she forgot her mittens She rubs her hands together to keep them warm In this situation there is ______________ energy due to the movement of her hands There is also _______________ energy due to the heat she generates by rubbing her hands together
A mechanical nonshymechanical
B nonshymechanical mechanical
Answer
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Mechanical Energy
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__________ Energy
__________ Energy __________ Energy
Forms of Mechanical EnergyMechanical Energy can be broken down into two different types of Energy energy of motion which is called Kinetic Energy and stored energy which is called Potential Energy Potential Energy has two forms Gravitational and Elastic depending upon how the energy is stored
Write the underlined words into the correct
place in the diagram
21
6 Which of the following is a form of mechanical energy
A Kinetic
B Thermal
C Chemical
D Solar
Answer
A shy Kinetic
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Energy of Motion
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7 Which of the following is a type of energy which is used to describe the motion of an object
A Electrical Energy
B Nuclear Energy
C Kinetic Energy
D All of the above
Answer
C shy Kinetic
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Energy of Motion
In order for an object to move one of two scenarios has to occur
1 The object uses some of the potential energy that it had stored
2 Energy is transferred to the object from an outside source
In either case now that the object is in motion the object is experiencing kinetic energy
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An objects state of motion can be described by looking at the amount of kinetic energy that the object has at that moment in time
Kinetic Energy
Since the state of motion of an object can change with time the kinetic energy of an object can also change with time
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velocitymass
The amount of kinetic energy that an object possesses is dependent on two factors
Kinetic Energy
Both of these factors are directly proportional to the kinetic energy We talked about this mathematical relationship in the
last chapter What did directly proportional mean
and
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Kinetic Energy Mass Velocity
Since kinetic energy is the energy of motion
the object has to have a velocity to have kinetic energy The larger the
velocity the __________________ the kinetic energy
The larger the mass the more energy is needed to move the object
therefore the _______________ the kinetic energy
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How Does Kinetic Energy Depend on MassIf two identical objects are moving at the same velocity they will have the same kinetic energy
v = 5 ms
v = 5 ms
A tennis ball and a bowling ball are both shown above The bowling ball is heavier than the tennis ball Which ball would have more kinetic energy
However if one object has more mass than the other the heavier object will have more kinetic energy
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Velocity vs Speed
Remember that velocity is another way to measure motion V elocity is the speed of an object with direction Speed does not have a direction so we call speed a scalar quantity
Since velocity has both magnitude and direction it is a vector quantity
Runners speed 10 kmhr
Runners velocity 10 kmhr to the East
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How Does Kinetic Energy Depend on Velocity
In this picture the hare is moving faster than the tortoise at this point
If we assumed that they had the same mass who would have more kinetic energy Why Discuss this with a partner
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v = 5 ms
v = 10 ms
How Does Kinetic Energy Depend upon Velocity
If two identical objects are moving at the same velocity then they will have the same kinetic energy However if one of the objects is moving faster the faster one will have more kinetic energy
In the diagram above two identical tennis balls are moving Which tennis ball has more kinetic energy and why
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8 Three different emergency vehicles are noticed driving on the highway at a speed of 25 ms Which of the following cars have the most kinetic energy at that moment
A a police car
B an ambulance
C a firetruck
D they all have the same kinetic energy
Answer
C
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9 Three different baseball pitchers had the speed of their fastball measured by a radar gun Which of the following pitchers fastball had the smallest amount of kinetic energy
A a little league pitcher (22 ms)
B a high school pitcher (33 ms)
C a major league pitcher (41ms)
D they all had the same kinetic energy
Answer
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10 Which of the following situations has the least kinetic energy Be ready to explain your answer
A a man sitting still on a park bench
B a child riding a bike
C a woman driving a car
D it is impossible to tell
Answer
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Calculating Kinetic Energy
Kinetic energy can be solved for by using the equation
12KE = mv2
Lets fill in the table below
variable unitsName
Kinetic Energy
mms
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Example shy Calculating Kinetic Energy
A car which has a mass of 1000 kg is moving with a velocity of 5 ms How much kinetic energy does the car possess Calculate the cars kinetic energy
KE = mv2KE = (05)(1000 kg)(5 ms)2
KE = (05)(1000 kg)(25 m2s2)KE = 125000 J
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Click on the box to see the solution
Teacher N
otes
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11 A 10 kg snowball is rolling down a hill Just before reaching the bottom its velocity is measured to be 10 ms What is the kinetic energy of the ball at this position
Answer
38
12 A 100 kg running back in football is running with a velocity of 2 ms What is his kinetic energy
Answer
KE= 12 mv2KE= 12 (100 kg) (2 ms)2KE= 12 (100 kg) (4m2s2)KE= 200 J
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13 A 2000 kg car with a velocity of 20 ms slows down and stops at a red light What is the change in kinetic energy
Answer
40
14 A 50 kg girl rode her 12 kg bicycle in a race She started from rest and peddled with a velocity of 10 ms What is the change in kinetic energy of the girl and her bicycle
Answer
41
Thinking Mathematically
KE = mv212
We have already said that mass is directly proportional to kinetic energy
This means that if the mass of the object doubles the
kinetic energy ___________ If the mass of the object increases by a
factor of 5 then the kinetic energy___________ by ______________
If the mass of the object decreases by half then the kinetic
energy will ____________ by ___________
doubles
increases a factor of 5
decrease half
42
15 If the mass of a wagon is doubled its kinetic energy
A increases
B decreases
Answer
43
16 If the mass of a wagon is doubled by what factor does the kinetic energy increase
Answer
44
Thinking Mathematically
Kinetic energy can be solved by using the equation
KE = mv212
From the equation we can see that the kinetic energy is also directly proportional to the square of the velocity
This means that if the velocity doubles the kinetic energy increases by a factor of 4
22=4
If the velocity is quadrupled then the kinetic energy increases by a factor of 16
42= 16
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17 If the velocity of a wagon is tripled its kinetic energy
Answer
A increases
B decreases
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18 If the velocity of a wagon is tripled by what factor does the kinetic energy increase
Answer
47
19 Two balls are moving with the same velocity ball A has a mass of 10 kg and ball B has a mass of 40 kg How much more kinetic energy does ball B have
Answer
48
20 A cart halves its mass and at the same time doubles its speed Does the kinetic energy increase or decrease By what factor does the kinetic energy change
A increase 2
B increase 4
C decrease 2
D decrease 4
Answer
bull half the mass gives 12 the KEbull double the speed gives 4 x KEbull therefore (12)(4)= 2
A
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Stored Energy
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50
Where does Kinetic Energy Come From
Imagine a roller coaster car that is at the top of the first hill and is stopped
Does the car stay stopped at the top of the hill for the entire ride
What happens
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Where does Kinetic Energy Come From
Once the car leans over the edge gravity pulls it down The ride is taking advantage of the gravitational attraction between the car and Earth to give the car kinetic energy and make it go faster as it falls
The kinetic energy the car is receiving is coming from another type of energy called potential energy
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Where does Kinetic Energy Come From
Potential energy is energy stored in an object due to the objects position The roller coaster car on the previous slide had stored energy due to its height above the ground
There are two forms of potential energy that we will be looking at in this unit
Gravitational Potential Energy
and
Elastic Potential Energy
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Gravitational Potential Energy
The potential energy due to elevated positions is called gravitational potential energy
Gravitational potential energy is stored energy and it can be used at a later time to cause an object to moveOnce the person steps off the diving board the gravitational potential energy is converted into kinetic energy and the person falls (moves)
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Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
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Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
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h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
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h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
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Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
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Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
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23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
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GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
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Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
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Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
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What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
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What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
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How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
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29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
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Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
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Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
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Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
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Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
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91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
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When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
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At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
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113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
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5
Energy and its Forms
Return to Tableof Contents
6
What is Energy
Energy is a measurement of an objects ability to do work
How would you define work
How would you know if any work was being done
7
What is Energy
Energy is a measurement of an objects ability to do work
Work is defined as applying a force in order to move an object in a given direction When work is done on an object by another object there is a transfer of energy between objects
Since energy is equal to work the unit for both is the same the Joule (J)
1 Joule = 1 Newtonshymeter
8
Work can only be done to a system by an external force a force from something that is not a part of the system
Work
So lets say our system is a plane The gate assistance vehicle is not part of the system When the vehicle comes along and pushes back the plane it increases the energy of the plane
The assistance truck is an outside force doing work on the plane
9
The amount of work done is the change in the amount of energy that the system will experience This is given by the equation
W = E final shy Einitial
Work
Fill in the blanks with positive or negative HINT Think about how these statements relate to acceleration
bull When a force is applied to an object that causes it to speed up and move a distance the work is _______________ bull When a resistive force is applied to an object that causes it to slow down over a distance or not move at all the work would be ____________
10
If an object moves in the same direction as the direction of the force applied to it the energy of the system is increased
The work is positive W gt 0
Positive Work
They can push the truck to get it to move
11
If an object moves in the direction opposite to the direction of the
force applied to it then the work is negative W lt 0
The energy of the system is reduced
Negative Work
The parachute moves downwards while air resistance acts upwards
on the parachute
12
If an object does not move even when there is a force applied to it then no work is done on the object
W=0 J
Zero Work
The people exert a force onto the wall but the wall does not move
13
NonshyMechanical Energy The energy of an object that is not due to its motion or position Nonshymechanical energy usually describes an object at its atomic level
Exampleselectrical energychemical energythermal energysound energy
Mechanical Energy shy The energy of an object due to its motion and position Mechanical energy is usually used to describe a large object
It is the sum of kinetic and potential energy
Mechanical vs NonshyMechanical EnergyEnergy exists in many forms but can be broken down into two major forms
14
1 Which of the following is the unit for energy
A Meter
B Newton
C Second
D Joule Answer
15
2 A wagon is rolling down a hill A man tries to stop the wagon by trying to push it back up the hill but he is unsuccessful Is the man doing positive or negative work
A positive
B negative
Answer
16
3 A boy kicks a soccer ball into a net Did the boy do positive or negative work on the ball
A positive
B negative
Answer
17
4 A woman walks across an icy sidewalk that has been covered in salt to help make it less slippery Is the salt doing positive or negative work on the womans shoes
A positive
B negative Answer
18
5 Jill is waiting for the bus and she forgot her mittens She rubs her hands together to keep them warm In this situation there is ______________ energy due to the movement of her hands There is also _______________ energy due to the heat she generates by rubbing her hands together
A mechanical nonshymechanical
B nonshymechanical mechanical
Answer
19
Mechanical Energy
Return to Tableof Contents
20
__________ Energy
__________ Energy __________ Energy
Forms of Mechanical EnergyMechanical Energy can be broken down into two different types of Energy energy of motion which is called Kinetic Energy and stored energy which is called Potential Energy Potential Energy has two forms Gravitational and Elastic depending upon how the energy is stored
Write the underlined words into the correct
place in the diagram
21
6 Which of the following is a form of mechanical energy
A Kinetic
B Thermal
C Chemical
D Solar
Answer
A shy Kinetic
22
Energy of Motion
Return to Tableof Contents
23
7 Which of the following is a type of energy which is used to describe the motion of an object
A Electrical Energy
B Nuclear Energy
C Kinetic Energy
D All of the above
Answer
C shy Kinetic
24
Energy of Motion
In order for an object to move one of two scenarios has to occur
1 The object uses some of the potential energy that it had stored
2 Energy is transferred to the object from an outside source
In either case now that the object is in motion the object is experiencing kinetic energy
25
An objects state of motion can be described by looking at the amount of kinetic energy that the object has at that moment in time
Kinetic Energy
Since the state of motion of an object can change with time the kinetic energy of an object can also change with time
26
velocitymass
The amount of kinetic energy that an object possesses is dependent on two factors
Kinetic Energy
Both of these factors are directly proportional to the kinetic energy We talked about this mathematical relationship in the
last chapter What did directly proportional mean
and
27
Kinetic Energy Mass Velocity
Since kinetic energy is the energy of motion
the object has to have a velocity to have kinetic energy The larger the
velocity the __________________ the kinetic energy
The larger the mass the more energy is needed to move the object
therefore the _______________ the kinetic energy
28
How Does Kinetic Energy Depend on MassIf two identical objects are moving at the same velocity they will have the same kinetic energy
v = 5 ms
v = 5 ms
A tennis ball and a bowling ball are both shown above The bowling ball is heavier than the tennis ball Which ball would have more kinetic energy
However if one object has more mass than the other the heavier object will have more kinetic energy
29
Velocity vs Speed
Remember that velocity is another way to measure motion V elocity is the speed of an object with direction Speed does not have a direction so we call speed a scalar quantity
Since velocity has both magnitude and direction it is a vector quantity
Runners speed 10 kmhr
Runners velocity 10 kmhr to the East
30
How Does Kinetic Energy Depend on Velocity
In this picture the hare is moving faster than the tortoise at this point
If we assumed that they had the same mass who would have more kinetic energy Why Discuss this with a partner
31
v = 5 ms
v = 10 ms
How Does Kinetic Energy Depend upon Velocity
If two identical objects are moving at the same velocity then they will have the same kinetic energy However if one of the objects is moving faster the faster one will have more kinetic energy
In the diagram above two identical tennis balls are moving Which tennis ball has more kinetic energy and why
32
8 Three different emergency vehicles are noticed driving on the highway at a speed of 25 ms Which of the following cars have the most kinetic energy at that moment
A a police car
B an ambulance
C a firetruck
D they all have the same kinetic energy
Answer
C
33
9 Three different baseball pitchers had the speed of their fastball measured by a radar gun Which of the following pitchers fastball had the smallest amount of kinetic energy
A a little league pitcher (22 ms)
B a high school pitcher (33 ms)
C a major league pitcher (41ms)
D they all had the same kinetic energy
Answer
34
10 Which of the following situations has the least kinetic energy Be ready to explain your answer
A a man sitting still on a park bench
B a child riding a bike
C a woman driving a car
D it is impossible to tell
Answer
35
Calculating Kinetic Energy
Kinetic energy can be solved for by using the equation
12KE = mv2
Lets fill in the table below
variable unitsName
Kinetic Energy
mms
36
Example shy Calculating Kinetic Energy
A car which has a mass of 1000 kg is moving with a velocity of 5 ms How much kinetic energy does the car possess Calculate the cars kinetic energy
KE = mv2KE = (05)(1000 kg)(5 ms)2
KE = (05)(1000 kg)(25 m2s2)KE = 125000 J
12
Click on the box to see the solution
Teacher N
otes
37
11 A 10 kg snowball is rolling down a hill Just before reaching the bottom its velocity is measured to be 10 ms What is the kinetic energy of the ball at this position
Answer
38
12 A 100 kg running back in football is running with a velocity of 2 ms What is his kinetic energy
Answer
KE= 12 mv2KE= 12 (100 kg) (2 ms)2KE= 12 (100 kg) (4m2s2)KE= 200 J
39
13 A 2000 kg car with a velocity of 20 ms slows down and stops at a red light What is the change in kinetic energy
Answer
40
14 A 50 kg girl rode her 12 kg bicycle in a race She started from rest and peddled with a velocity of 10 ms What is the change in kinetic energy of the girl and her bicycle
Answer
41
Thinking Mathematically
KE = mv212
We have already said that mass is directly proportional to kinetic energy
This means that if the mass of the object doubles the
kinetic energy ___________ If the mass of the object increases by a
factor of 5 then the kinetic energy___________ by ______________
If the mass of the object decreases by half then the kinetic
energy will ____________ by ___________
doubles
increases a factor of 5
decrease half
42
15 If the mass of a wagon is doubled its kinetic energy
A increases
B decreases
Answer
43
16 If the mass of a wagon is doubled by what factor does the kinetic energy increase
Answer
44
Thinking Mathematically
Kinetic energy can be solved by using the equation
KE = mv212
From the equation we can see that the kinetic energy is also directly proportional to the square of the velocity
This means that if the velocity doubles the kinetic energy increases by a factor of 4
22=4
If the velocity is quadrupled then the kinetic energy increases by a factor of 16
42= 16
45
17 If the velocity of a wagon is tripled its kinetic energy
Answer
A increases
B decreases
46
18 If the velocity of a wagon is tripled by what factor does the kinetic energy increase
Answer
47
19 Two balls are moving with the same velocity ball A has a mass of 10 kg and ball B has a mass of 40 kg How much more kinetic energy does ball B have
Answer
48
20 A cart halves its mass and at the same time doubles its speed Does the kinetic energy increase or decrease By what factor does the kinetic energy change
A increase 2
B increase 4
C decrease 2
D decrease 4
Answer
bull half the mass gives 12 the KEbull double the speed gives 4 x KEbull therefore (12)(4)= 2
A
49
Stored Energy
Return to Tableof Contents
50
Where does Kinetic Energy Come From
Imagine a roller coaster car that is at the top of the first hill and is stopped
Does the car stay stopped at the top of the hill for the entire ride
What happens
51
Where does Kinetic Energy Come From
Once the car leans over the edge gravity pulls it down The ride is taking advantage of the gravitational attraction between the car and Earth to give the car kinetic energy and make it go faster as it falls
The kinetic energy the car is receiving is coming from another type of energy called potential energy
52
Where does Kinetic Energy Come From
Potential energy is energy stored in an object due to the objects position The roller coaster car on the previous slide had stored energy due to its height above the ground
There are two forms of potential energy that we will be looking at in this unit
Gravitational Potential Energy
and
Elastic Potential Energy
53
Gravitational Potential Energy
The potential energy due to elevated positions is called gravitational potential energy
Gravitational potential energy is stored energy and it can be used at a later time to cause an object to moveOnce the person steps off the diving board the gravitational potential energy is converted into kinetic energy and the person falls (moves)
54
Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
55
Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
56
h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
6
What is Energy
Energy is a measurement of an objects ability to do work
How would you define work
How would you know if any work was being done
7
What is Energy
Energy is a measurement of an objects ability to do work
Work is defined as applying a force in order to move an object in a given direction When work is done on an object by another object there is a transfer of energy between objects
Since energy is equal to work the unit for both is the same the Joule (J)
1 Joule = 1 Newtonshymeter
8
Work can only be done to a system by an external force a force from something that is not a part of the system
Work
So lets say our system is a plane The gate assistance vehicle is not part of the system When the vehicle comes along and pushes back the plane it increases the energy of the plane
The assistance truck is an outside force doing work on the plane
9
The amount of work done is the change in the amount of energy that the system will experience This is given by the equation
W = E final shy Einitial
Work
Fill in the blanks with positive or negative HINT Think about how these statements relate to acceleration
bull When a force is applied to an object that causes it to speed up and move a distance the work is _______________ bull When a resistive force is applied to an object that causes it to slow down over a distance or not move at all the work would be ____________
10
If an object moves in the same direction as the direction of the force applied to it the energy of the system is increased
The work is positive W gt 0
Positive Work
They can push the truck to get it to move
11
If an object moves in the direction opposite to the direction of the
force applied to it then the work is negative W lt 0
The energy of the system is reduced
Negative Work
The parachute moves downwards while air resistance acts upwards
on the parachute
12
If an object does not move even when there is a force applied to it then no work is done on the object
W=0 J
Zero Work
The people exert a force onto the wall but the wall does not move
13
NonshyMechanical Energy The energy of an object that is not due to its motion or position Nonshymechanical energy usually describes an object at its atomic level
Exampleselectrical energychemical energythermal energysound energy
Mechanical Energy shy The energy of an object due to its motion and position Mechanical energy is usually used to describe a large object
It is the sum of kinetic and potential energy
Mechanical vs NonshyMechanical EnergyEnergy exists in many forms but can be broken down into two major forms
14
1 Which of the following is the unit for energy
A Meter
B Newton
C Second
D Joule Answer
15
2 A wagon is rolling down a hill A man tries to stop the wagon by trying to push it back up the hill but he is unsuccessful Is the man doing positive or negative work
A positive
B negative
Answer
16
3 A boy kicks a soccer ball into a net Did the boy do positive or negative work on the ball
A positive
B negative
Answer
17
4 A woman walks across an icy sidewalk that has been covered in salt to help make it less slippery Is the salt doing positive or negative work on the womans shoes
A positive
B negative Answer
18
5 Jill is waiting for the bus and she forgot her mittens She rubs her hands together to keep them warm In this situation there is ______________ energy due to the movement of her hands There is also _______________ energy due to the heat she generates by rubbing her hands together
A mechanical nonshymechanical
B nonshymechanical mechanical
Answer
19
Mechanical Energy
Return to Tableof Contents
20
__________ Energy
__________ Energy __________ Energy
Forms of Mechanical EnergyMechanical Energy can be broken down into two different types of Energy energy of motion which is called Kinetic Energy and stored energy which is called Potential Energy Potential Energy has two forms Gravitational and Elastic depending upon how the energy is stored
Write the underlined words into the correct
place in the diagram
21
6 Which of the following is a form of mechanical energy
A Kinetic
B Thermal
C Chemical
D Solar
Answer
A shy Kinetic
22
Energy of Motion
Return to Tableof Contents
23
7 Which of the following is a type of energy which is used to describe the motion of an object
A Electrical Energy
B Nuclear Energy
C Kinetic Energy
D All of the above
Answer
C shy Kinetic
24
Energy of Motion
In order for an object to move one of two scenarios has to occur
1 The object uses some of the potential energy that it had stored
2 Energy is transferred to the object from an outside source
In either case now that the object is in motion the object is experiencing kinetic energy
25
An objects state of motion can be described by looking at the amount of kinetic energy that the object has at that moment in time
Kinetic Energy
Since the state of motion of an object can change with time the kinetic energy of an object can also change with time
26
velocitymass
The amount of kinetic energy that an object possesses is dependent on two factors
Kinetic Energy
Both of these factors are directly proportional to the kinetic energy We talked about this mathematical relationship in the
last chapter What did directly proportional mean
and
27
Kinetic Energy Mass Velocity
Since kinetic energy is the energy of motion
the object has to have a velocity to have kinetic energy The larger the
velocity the __________________ the kinetic energy
The larger the mass the more energy is needed to move the object
therefore the _______________ the kinetic energy
28
How Does Kinetic Energy Depend on MassIf two identical objects are moving at the same velocity they will have the same kinetic energy
v = 5 ms
v = 5 ms
A tennis ball and a bowling ball are both shown above The bowling ball is heavier than the tennis ball Which ball would have more kinetic energy
However if one object has more mass than the other the heavier object will have more kinetic energy
29
Velocity vs Speed
Remember that velocity is another way to measure motion V elocity is the speed of an object with direction Speed does not have a direction so we call speed a scalar quantity
Since velocity has both magnitude and direction it is a vector quantity
Runners speed 10 kmhr
Runners velocity 10 kmhr to the East
30
How Does Kinetic Energy Depend on Velocity
In this picture the hare is moving faster than the tortoise at this point
If we assumed that they had the same mass who would have more kinetic energy Why Discuss this with a partner
31
v = 5 ms
v = 10 ms
How Does Kinetic Energy Depend upon Velocity
If two identical objects are moving at the same velocity then they will have the same kinetic energy However if one of the objects is moving faster the faster one will have more kinetic energy
In the diagram above two identical tennis balls are moving Which tennis ball has more kinetic energy and why
32
8 Three different emergency vehicles are noticed driving on the highway at a speed of 25 ms Which of the following cars have the most kinetic energy at that moment
A a police car
B an ambulance
C a firetruck
D they all have the same kinetic energy
Answer
C
33
9 Three different baseball pitchers had the speed of their fastball measured by a radar gun Which of the following pitchers fastball had the smallest amount of kinetic energy
A a little league pitcher (22 ms)
B a high school pitcher (33 ms)
C a major league pitcher (41ms)
D they all had the same kinetic energy
Answer
34
10 Which of the following situations has the least kinetic energy Be ready to explain your answer
A a man sitting still on a park bench
B a child riding a bike
C a woman driving a car
D it is impossible to tell
Answer
35
Calculating Kinetic Energy
Kinetic energy can be solved for by using the equation
12KE = mv2
Lets fill in the table below
variable unitsName
Kinetic Energy
mms
36
Example shy Calculating Kinetic Energy
A car which has a mass of 1000 kg is moving with a velocity of 5 ms How much kinetic energy does the car possess Calculate the cars kinetic energy
KE = mv2KE = (05)(1000 kg)(5 ms)2
KE = (05)(1000 kg)(25 m2s2)KE = 125000 J
12
Click on the box to see the solution
Teacher N
otes
37
11 A 10 kg snowball is rolling down a hill Just before reaching the bottom its velocity is measured to be 10 ms What is the kinetic energy of the ball at this position
Answer
38
12 A 100 kg running back in football is running with a velocity of 2 ms What is his kinetic energy
Answer
KE= 12 mv2KE= 12 (100 kg) (2 ms)2KE= 12 (100 kg) (4m2s2)KE= 200 J
39
13 A 2000 kg car with a velocity of 20 ms slows down and stops at a red light What is the change in kinetic energy
Answer
40
14 A 50 kg girl rode her 12 kg bicycle in a race She started from rest and peddled with a velocity of 10 ms What is the change in kinetic energy of the girl and her bicycle
Answer
41
Thinking Mathematically
KE = mv212
We have already said that mass is directly proportional to kinetic energy
This means that if the mass of the object doubles the
kinetic energy ___________ If the mass of the object increases by a
factor of 5 then the kinetic energy___________ by ______________
If the mass of the object decreases by half then the kinetic
energy will ____________ by ___________
doubles
increases a factor of 5
decrease half
42
15 If the mass of a wagon is doubled its kinetic energy
A increases
B decreases
Answer
43
16 If the mass of a wagon is doubled by what factor does the kinetic energy increase
Answer
44
Thinking Mathematically
Kinetic energy can be solved by using the equation
KE = mv212
From the equation we can see that the kinetic energy is also directly proportional to the square of the velocity
This means that if the velocity doubles the kinetic energy increases by a factor of 4
22=4
If the velocity is quadrupled then the kinetic energy increases by a factor of 16
42= 16
45
17 If the velocity of a wagon is tripled its kinetic energy
Answer
A increases
B decreases
46
18 If the velocity of a wagon is tripled by what factor does the kinetic energy increase
Answer
47
19 Two balls are moving with the same velocity ball A has a mass of 10 kg and ball B has a mass of 40 kg How much more kinetic energy does ball B have
Answer
48
20 A cart halves its mass and at the same time doubles its speed Does the kinetic energy increase or decrease By what factor does the kinetic energy change
A increase 2
B increase 4
C decrease 2
D decrease 4
Answer
bull half the mass gives 12 the KEbull double the speed gives 4 x KEbull therefore (12)(4)= 2
A
49
Stored Energy
Return to Tableof Contents
50
Where does Kinetic Energy Come From
Imagine a roller coaster car that is at the top of the first hill and is stopped
Does the car stay stopped at the top of the hill for the entire ride
What happens
51
Where does Kinetic Energy Come From
Once the car leans over the edge gravity pulls it down The ride is taking advantage of the gravitational attraction between the car and Earth to give the car kinetic energy and make it go faster as it falls
The kinetic energy the car is receiving is coming from another type of energy called potential energy
52
Where does Kinetic Energy Come From
Potential energy is energy stored in an object due to the objects position The roller coaster car on the previous slide had stored energy due to its height above the ground
There are two forms of potential energy that we will be looking at in this unit
Gravitational Potential Energy
and
Elastic Potential Energy
53
Gravitational Potential Energy
The potential energy due to elevated positions is called gravitational potential energy
Gravitational potential energy is stored energy and it can be used at a later time to cause an object to moveOnce the person steps off the diving board the gravitational potential energy is converted into kinetic energy and the person falls (moves)
54
Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
55
Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
56
h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
7
What is Energy
Energy is a measurement of an objects ability to do work
Work is defined as applying a force in order to move an object in a given direction When work is done on an object by another object there is a transfer of energy between objects
Since energy is equal to work the unit for both is the same the Joule (J)
1 Joule = 1 Newtonshymeter
8
Work can only be done to a system by an external force a force from something that is not a part of the system
Work
So lets say our system is a plane The gate assistance vehicle is not part of the system When the vehicle comes along and pushes back the plane it increases the energy of the plane
The assistance truck is an outside force doing work on the plane
9
The amount of work done is the change in the amount of energy that the system will experience This is given by the equation
W = E final shy Einitial
Work
Fill in the blanks with positive or negative HINT Think about how these statements relate to acceleration
bull When a force is applied to an object that causes it to speed up and move a distance the work is _______________ bull When a resistive force is applied to an object that causes it to slow down over a distance or not move at all the work would be ____________
10
If an object moves in the same direction as the direction of the force applied to it the energy of the system is increased
The work is positive W gt 0
Positive Work
They can push the truck to get it to move
11
If an object moves in the direction opposite to the direction of the
force applied to it then the work is negative W lt 0
The energy of the system is reduced
Negative Work
The parachute moves downwards while air resistance acts upwards
on the parachute
12
If an object does not move even when there is a force applied to it then no work is done on the object
W=0 J
Zero Work
The people exert a force onto the wall but the wall does not move
13
NonshyMechanical Energy The energy of an object that is not due to its motion or position Nonshymechanical energy usually describes an object at its atomic level
Exampleselectrical energychemical energythermal energysound energy
Mechanical Energy shy The energy of an object due to its motion and position Mechanical energy is usually used to describe a large object
It is the sum of kinetic and potential energy
Mechanical vs NonshyMechanical EnergyEnergy exists in many forms but can be broken down into two major forms
14
1 Which of the following is the unit for energy
A Meter
B Newton
C Second
D Joule Answer
15
2 A wagon is rolling down a hill A man tries to stop the wagon by trying to push it back up the hill but he is unsuccessful Is the man doing positive or negative work
A positive
B negative
Answer
16
3 A boy kicks a soccer ball into a net Did the boy do positive or negative work on the ball
A positive
B negative
Answer
17
4 A woman walks across an icy sidewalk that has been covered in salt to help make it less slippery Is the salt doing positive or negative work on the womans shoes
A positive
B negative Answer
18
5 Jill is waiting for the bus and she forgot her mittens She rubs her hands together to keep them warm In this situation there is ______________ energy due to the movement of her hands There is also _______________ energy due to the heat she generates by rubbing her hands together
A mechanical nonshymechanical
B nonshymechanical mechanical
Answer
19
Mechanical Energy
Return to Tableof Contents
20
__________ Energy
__________ Energy __________ Energy
Forms of Mechanical EnergyMechanical Energy can be broken down into two different types of Energy energy of motion which is called Kinetic Energy and stored energy which is called Potential Energy Potential Energy has two forms Gravitational and Elastic depending upon how the energy is stored
Write the underlined words into the correct
place in the diagram
21
6 Which of the following is a form of mechanical energy
A Kinetic
B Thermal
C Chemical
D Solar
Answer
A shy Kinetic
22
Energy of Motion
Return to Tableof Contents
23
7 Which of the following is a type of energy which is used to describe the motion of an object
A Electrical Energy
B Nuclear Energy
C Kinetic Energy
D All of the above
Answer
C shy Kinetic
24
Energy of Motion
In order for an object to move one of two scenarios has to occur
1 The object uses some of the potential energy that it had stored
2 Energy is transferred to the object from an outside source
In either case now that the object is in motion the object is experiencing kinetic energy
25
An objects state of motion can be described by looking at the amount of kinetic energy that the object has at that moment in time
Kinetic Energy
Since the state of motion of an object can change with time the kinetic energy of an object can also change with time
26
velocitymass
The amount of kinetic energy that an object possesses is dependent on two factors
Kinetic Energy
Both of these factors are directly proportional to the kinetic energy We talked about this mathematical relationship in the
last chapter What did directly proportional mean
and
27
Kinetic Energy Mass Velocity
Since kinetic energy is the energy of motion
the object has to have a velocity to have kinetic energy The larger the
velocity the __________________ the kinetic energy
The larger the mass the more energy is needed to move the object
therefore the _______________ the kinetic energy
28
How Does Kinetic Energy Depend on MassIf two identical objects are moving at the same velocity they will have the same kinetic energy
v = 5 ms
v = 5 ms
A tennis ball and a bowling ball are both shown above The bowling ball is heavier than the tennis ball Which ball would have more kinetic energy
However if one object has more mass than the other the heavier object will have more kinetic energy
29
Velocity vs Speed
Remember that velocity is another way to measure motion V elocity is the speed of an object with direction Speed does not have a direction so we call speed a scalar quantity
Since velocity has both magnitude and direction it is a vector quantity
Runners speed 10 kmhr
Runners velocity 10 kmhr to the East
30
How Does Kinetic Energy Depend on Velocity
In this picture the hare is moving faster than the tortoise at this point
If we assumed that they had the same mass who would have more kinetic energy Why Discuss this with a partner
31
v = 5 ms
v = 10 ms
How Does Kinetic Energy Depend upon Velocity
If two identical objects are moving at the same velocity then they will have the same kinetic energy However if one of the objects is moving faster the faster one will have more kinetic energy
In the diagram above two identical tennis balls are moving Which tennis ball has more kinetic energy and why
32
8 Three different emergency vehicles are noticed driving on the highway at a speed of 25 ms Which of the following cars have the most kinetic energy at that moment
A a police car
B an ambulance
C a firetruck
D they all have the same kinetic energy
Answer
C
33
9 Three different baseball pitchers had the speed of their fastball measured by a radar gun Which of the following pitchers fastball had the smallest amount of kinetic energy
A a little league pitcher (22 ms)
B a high school pitcher (33 ms)
C a major league pitcher (41ms)
D they all had the same kinetic energy
Answer
34
10 Which of the following situations has the least kinetic energy Be ready to explain your answer
A a man sitting still on a park bench
B a child riding a bike
C a woman driving a car
D it is impossible to tell
Answer
35
Calculating Kinetic Energy
Kinetic energy can be solved for by using the equation
12KE = mv2
Lets fill in the table below
variable unitsName
Kinetic Energy
mms
36
Example shy Calculating Kinetic Energy
A car which has a mass of 1000 kg is moving with a velocity of 5 ms How much kinetic energy does the car possess Calculate the cars kinetic energy
KE = mv2KE = (05)(1000 kg)(5 ms)2
KE = (05)(1000 kg)(25 m2s2)KE = 125000 J
12
Click on the box to see the solution
Teacher N
otes
37
11 A 10 kg snowball is rolling down a hill Just before reaching the bottom its velocity is measured to be 10 ms What is the kinetic energy of the ball at this position
Answer
38
12 A 100 kg running back in football is running with a velocity of 2 ms What is his kinetic energy
Answer
KE= 12 mv2KE= 12 (100 kg) (2 ms)2KE= 12 (100 kg) (4m2s2)KE= 200 J
39
13 A 2000 kg car with a velocity of 20 ms slows down and stops at a red light What is the change in kinetic energy
Answer
40
14 A 50 kg girl rode her 12 kg bicycle in a race She started from rest and peddled with a velocity of 10 ms What is the change in kinetic energy of the girl and her bicycle
Answer
41
Thinking Mathematically
KE = mv212
We have already said that mass is directly proportional to kinetic energy
This means that if the mass of the object doubles the
kinetic energy ___________ If the mass of the object increases by a
factor of 5 then the kinetic energy___________ by ______________
If the mass of the object decreases by half then the kinetic
energy will ____________ by ___________
doubles
increases a factor of 5
decrease half
42
15 If the mass of a wagon is doubled its kinetic energy
A increases
B decreases
Answer
43
16 If the mass of a wagon is doubled by what factor does the kinetic energy increase
Answer
44
Thinking Mathematically
Kinetic energy can be solved by using the equation
KE = mv212
From the equation we can see that the kinetic energy is also directly proportional to the square of the velocity
This means that if the velocity doubles the kinetic energy increases by a factor of 4
22=4
If the velocity is quadrupled then the kinetic energy increases by a factor of 16
42= 16
45
17 If the velocity of a wagon is tripled its kinetic energy
Answer
A increases
B decreases
46
18 If the velocity of a wagon is tripled by what factor does the kinetic energy increase
Answer
47
19 Two balls are moving with the same velocity ball A has a mass of 10 kg and ball B has a mass of 40 kg How much more kinetic energy does ball B have
Answer
48
20 A cart halves its mass and at the same time doubles its speed Does the kinetic energy increase or decrease By what factor does the kinetic energy change
A increase 2
B increase 4
C decrease 2
D decrease 4
Answer
bull half the mass gives 12 the KEbull double the speed gives 4 x KEbull therefore (12)(4)= 2
A
49
Stored Energy
Return to Tableof Contents
50
Where does Kinetic Energy Come From
Imagine a roller coaster car that is at the top of the first hill and is stopped
Does the car stay stopped at the top of the hill for the entire ride
What happens
51
Where does Kinetic Energy Come From
Once the car leans over the edge gravity pulls it down The ride is taking advantage of the gravitational attraction between the car and Earth to give the car kinetic energy and make it go faster as it falls
The kinetic energy the car is receiving is coming from another type of energy called potential energy
52
Where does Kinetic Energy Come From
Potential energy is energy stored in an object due to the objects position The roller coaster car on the previous slide had stored energy due to its height above the ground
There are two forms of potential energy that we will be looking at in this unit
Gravitational Potential Energy
and
Elastic Potential Energy
53
Gravitational Potential Energy
The potential energy due to elevated positions is called gravitational potential energy
Gravitational potential energy is stored energy and it can be used at a later time to cause an object to moveOnce the person steps off the diving board the gravitational potential energy is converted into kinetic energy and the person falls (moves)
54
Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
55
Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
56
h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
8
Work can only be done to a system by an external force a force from something that is not a part of the system
Work
So lets say our system is a plane The gate assistance vehicle is not part of the system When the vehicle comes along and pushes back the plane it increases the energy of the plane
The assistance truck is an outside force doing work on the plane
9
The amount of work done is the change in the amount of energy that the system will experience This is given by the equation
W = E final shy Einitial
Work
Fill in the blanks with positive or negative HINT Think about how these statements relate to acceleration
bull When a force is applied to an object that causes it to speed up and move a distance the work is _______________ bull When a resistive force is applied to an object that causes it to slow down over a distance or not move at all the work would be ____________
10
If an object moves in the same direction as the direction of the force applied to it the energy of the system is increased
The work is positive W gt 0
Positive Work
They can push the truck to get it to move
11
If an object moves in the direction opposite to the direction of the
force applied to it then the work is negative W lt 0
The energy of the system is reduced
Negative Work
The parachute moves downwards while air resistance acts upwards
on the parachute
12
If an object does not move even when there is a force applied to it then no work is done on the object
W=0 J
Zero Work
The people exert a force onto the wall but the wall does not move
13
NonshyMechanical Energy The energy of an object that is not due to its motion or position Nonshymechanical energy usually describes an object at its atomic level
Exampleselectrical energychemical energythermal energysound energy
Mechanical Energy shy The energy of an object due to its motion and position Mechanical energy is usually used to describe a large object
It is the sum of kinetic and potential energy
Mechanical vs NonshyMechanical EnergyEnergy exists in many forms but can be broken down into two major forms
14
1 Which of the following is the unit for energy
A Meter
B Newton
C Second
D Joule Answer
15
2 A wagon is rolling down a hill A man tries to stop the wagon by trying to push it back up the hill but he is unsuccessful Is the man doing positive or negative work
A positive
B negative
Answer
16
3 A boy kicks a soccer ball into a net Did the boy do positive or negative work on the ball
A positive
B negative
Answer
17
4 A woman walks across an icy sidewalk that has been covered in salt to help make it less slippery Is the salt doing positive or negative work on the womans shoes
A positive
B negative Answer
18
5 Jill is waiting for the bus and she forgot her mittens She rubs her hands together to keep them warm In this situation there is ______________ energy due to the movement of her hands There is also _______________ energy due to the heat she generates by rubbing her hands together
A mechanical nonshymechanical
B nonshymechanical mechanical
Answer
19
Mechanical Energy
Return to Tableof Contents
20
__________ Energy
__________ Energy __________ Energy
Forms of Mechanical EnergyMechanical Energy can be broken down into two different types of Energy energy of motion which is called Kinetic Energy and stored energy which is called Potential Energy Potential Energy has two forms Gravitational and Elastic depending upon how the energy is stored
Write the underlined words into the correct
place in the diagram
21
6 Which of the following is a form of mechanical energy
A Kinetic
B Thermal
C Chemical
D Solar
Answer
A shy Kinetic
22
Energy of Motion
Return to Tableof Contents
23
7 Which of the following is a type of energy which is used to describe the motion of an object
A Electrical Energy
B Nuclear Energy
C Kinetic Energy
D All of the above
Answer
C shy Kinetic
24
Energy of Motion
In order for an object to move one of two scenarios has to occur
1 The object uses some of the potential energy that it had stored
2 Energy is transferred to the object from an outside source
In either case now that the object is in motion the object is experiencing kinetic energy
25
An objects state of motion can be described by looking at the amount of kinetic energy that the object has at that moment in time
Kinetic Energy
Since the state of motion of an object can change with time the kinetic energy of an object can also change with time
26
velocitymass
The amount of kinetic energy that an object possesses is dependent on two factors
Kinetic Energy
Both of these factors are directly proportional to the kinetic energy We talked about this mathematical relationship in the
last chapter What did directly proportional mean
and
27
Kinetic Energy Mass Velocity
Since kinetic energy is the energy of motion
the object has to have a velocity to have kinetic energy The larger the
velocity the __________________ the kinetic energy
The larger the mass the more energy is needed to move the object
therefore the _______________ the kinetic energy
28
How Does Kinetic Energy Depend on MassIf two identical objects are moving at the same velocity they will have the same kinetic energy
v = 5 ms
v = 5 ms
A tennis ball and a bowling ball are both shown above The bowling ball is heavier than the tennis ball Which ball would have more kinetic energy
However if one object has more mass than the other the heavier object will have more kinetic energy
29
Velocity vs Speed
Remember that velocity is another way to measure motion V elocity is the speed of an object with direction Speed does not have a direction so we call speed a scalar quantity
Since velocity has both magnitude and direction it is a vector quantity
Runners speed 10 kmhr
Runners velocity 10 kmhr to the East
30
How Does Kinetic Energy Depend on Velocity
In this picture the hare is moving faster than the tortoise at this point
If we assumed that they had the same mass who would have more kinetic energy Why Discuss this with a partner
31
v = 5 ms
v = 10 ms
How Does Kinetic Energy Depend upon Velocity
If two identical objects are moving at the same velocity then they will have the same kinetic energy However if one of the objects is moving faster the faster one will have more kinetic energy
In the diagram above two identical tennis balls are moving Which tennis ball has more kinetic energy and why
32
8 Three different emergency vehicles are noticed driving on the highway at a speed of 25 ms Which of the following cars have the most kinetic energy at that moment
A a police car
B an ambulance
C a firetruck
D they all have the same kinetic energy
Answer
C
33
9 Three different baseball pitchers had the speed of their fastball measured by a radar gun Which of the following pitchers fastball had the smallest amount of kinetic energy
A a little league pitcher (22 ms)
B a high school pitcher (33 ms)
C a major league pitcher (41ms)
D they all had the same kinetic energy
Answer
34
10 Which of the following situations has the least kinetic energy Be ready to explain your answer
A a man sitting still on a park bench
B a child riding a bike
C a woman driving a car
D it is impossible to tell
Answer
35
Calculating Kinetic Energy
Kinetic energy can be solved for by using the equation
12KE = mv2
Lets fill in the table below
variable unitsName
Kinetic Energy
mms
36
Example shy Calculating Kinetic Energy
A car which has a mass of 1000 kg is moving with a velocity of 5 ms How much kinetic energy does the car possess Calculate the cars kinetic energy
KE = mv2KE = (05)(1000 kg)(5 ms)2
KE = (05)(1000 kg)(25 m2s2)KE = 125000 J
12
Click on the box to see the solution
Teacher N
otes
37
11 A 10 kg snowball is rolling down a hill Just before reaching the bottom its velocity is measured to be 10 ms What is the kinetic energy of the ball at this position
Answer
38
12 A 100 kg running back in football is running with a velocity of 2 ms What is his kinetic energy
Answer
KE= 12 mv2KE= 12 (100 kg) (2 ms)2KE= 12 (100 kg) (4m2s2)KE= 200 J
39
13 A 2000 kg car with a velocity of 20 ms slows down and stops at a red light What is the change in kinetic energy
Answer
40
14 A 50 kg girl rode her 12 kg bicycle in a race She started from rest and peddled with a velocity of 10 ms What is the change in kinetic energy of the girl and her bicycle
Answer
41
Thinking Mathematically
KE = mv212
We have already said that mass is directly proportional to kinetic energy
This means that if the mass of the object doubles the
kinetic energy ___________ If the mass of the object increases by a
factor of 5 then the kinetic energy___________ by ______________
If the mass of the object decreases by half then the kinetic
energy will ____________ by ___________
doubles
increases a factor of 5
decrease half
42
15 If the mass of a wagon is doubled its kinetic energy
A increases
B decreases
Answer
43
16 If the mass of a wagon is doubled by what factor does the kinetic energy increase
Answer
44
Thinking Mathematically
Kinetic energy can be solved by using the equation
KE = mv212
From the equation we can see that the kinetic energy is also directly proportional to the square of the velocity
This means that if the velocity doubles the kinetic energy increases by a factor of 4
22=4
If the velocity is quadrupled then the kinetic energy increases by a factor of 16
42= 16
45
17 If the velocity of a wagon is tripled its kinetic energy
Answer
A increases
B decreases
46
18 If the velocity of a wagon is tripled by what factor does the kinetic energy increase
Answer
47
19 Two balls are moving with the same velocity ball A has a mass of 10 kg and ball B has a mass of 40 kg How much more kinetic energy does ball B have
Answer
48
20 A cart halves its mass and at the same time doubles its speed Does the kinetic energy increase or decrease By what factor does the kinetic energy change
A increase 2
B increase 4
C decrease 2
D decrease 4
Answer
bull half the mass gives 12 the KEbull double the speed gives 4 x KEbull therefore (12)(4)= 2
A
49
Stored Energy
Return to Tableof Contents
50
Where does Kinetic Energy Come From
Imagine a roller coaster car that is at the top of the first hill and is stopped
Does the car stay stopped at the top of the hill for the entire ride
What happens
51
Where does Kinetic Energy Come From
Once the car leans over the edge gravity pulls it down The ride is taking advantage of the gravitational attraction between the car and Earth to give the car kinetic energy and make it go faster as it falls
The kinetic energy the car is receiving is coming from another type of energy called potential energy
52
Where does Kinetic Energy Come From
Potential energy is energy stored in an object due to the objects position The roller coaster car on the previous slide had stored energy due to its height above the ground
There are two forms of potential energy that we will be looking at in this unit
Gravitational Potential Energy
and
Elastic Potential Energy
53
Gravitational Potential Energy
The potential energy due to elevated positions is called gravitational potential energy
Gravitational potential energy is stored energy and it can be used at a later time to cause an object to moveOnce the person steps off the diving board the gravitational potential energy is converted into kinetic energy and the person falls (moves)
54
Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
55
Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
56
h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
9
The amount of work done is the change in the amount of energy that the system will experience This is given by the equation
W = E final shy Einitial
Work
Fill in the blanks with positive or negative HINT Think about how these statements relate to acceleration
bull When a force is applied to an object that causes it to speed up and move a distance the work is _______________ bull When a resistive force is applied to an object that causes it to slow down over a distance or not move at all the work would be ____________
10
If an object moves in the same direction as the direction of the force applied to it the energy of the system is increased
The work is positive W gt 0
Positive Work
They can push the truck to get it to move
11
If an object moves in the direction opposite to the direction of the
force applied to it then the work is negative W lt 0
The energy of the system is reduced
Negative Work
The parachute moves downwards while air resistance acts upwards
on the parachute
12
If an object does not move even when there is a force applied to it then no work is done on the object
W=0 J
Zero Work
The people exert a force onto the wall but the wall does not move
13
NonshyMechanical Energy The energy of an object that is not due to its motion or position Nonshymechanical energy usually describes an object at its atomic level
Exampleselectrical energychemical energythermal energysound energy
Mechanical Energy shy The energy of an object due to its motion and position Mechanical energy is usually used to describe a large object
It is the sum of kinetic and potential energy
Mechanical vs NonshyMechanical EnergyEnergy exists in many forms but can be broken down into two major forms
14
1 Which of the following is the unit for energy
A Meter
B Newton
C Second
D Joule Answer
15
2 A wagon is rolling down a hill A man tries to stop the wagon by trying to push it back up the hill but he is unsuccessful Is the man doing positive or negative work
A positive
B negative
Answer
16
3 A boy kicks a soccer ball into a net Did the boy do positive or negative work on the ball
A positive
B negative
Answer
17
4 A woman walks across an icy sidewalk that has been covered in salt to help make it less slippery Is the salt doing positive or negative work on the womans shoes
A positive
B negative Answer
18
5 Jill is waiting for the bus and she forgot her mittens She rubs her hands together to keep them warm In this situation there is ______________ energy due to the movement of her hands There is also _______________ energy due to the heat she generates by rubbing her hands together
A mechanical nonshymechanical
B nonshymechanical mechanical
Answer
19
Mechanical Energy
Return to Tableof Contents
20
__________ Energy
__________ Energy __________ Energy
Forms of Mechanical EnergyMechanical Energy can be broken down into two different types of Energy energy of motion which is called Kinetic Energy and stored energy which is called Potential Energy Potential Energy has two forms Gravitational and Elastic depending upon how the energy is stored
Write the underlined words into the correct
place in the diagram
21
6 Which of the following is a form of mechanical energy
A Kinetic
B Thermal
C Chemical
D Solar
Answer
A shy Kinetic
22
Energy of Motion
Return to Tableof Contents
23
7 Which of the following is a type of energy which is used to describe the motion of an object
A Electrical Energy
B Nuclear Energy
C Kinetic Energy
D All of the above
Answer
C shy Kinetic
24
Energy of Motion
In order for an object to move one of two scenarios has to occur
1 The object uses some of the potential energy that it had stored
2 Energy is transferred to the object from an outside source
In either case now that the object is in motion the object is experiencing kinetic energy
25
An objects state of motion can be described by looking at the amount of kinetic energy that the object has at that moment in time
Kinetic Energy
Since the state of motion of an object can change with time the kinetic energy of an object can also change with time
26
velocitymass
The amount of kinetic energy that an object possesses is dependent on two factors
Kinetic Energy
Both of these factors are directly proportional to the kinetic energy We talked about this mathematical relationship in the
last chapter What did directly proportional mean
and
27
Kinetic Energy Mass Velocity
Since kinetic energy is the energy of motion
the object has to have a velocity to have kinetic energy The larger the
velocity the __________________ the kinetic energy
The larger the mass the more energy is needed to move the object
therefore the _______________ the kinetic energy
28
How Does Kinetic Energy Depend on MassIf two identical objects are moving at the same velocity they will have the same kinetic energy
v = 5 ms
v = 5 ms
A tennis ball and a bowling ball are both shown above The bowling ball is heavier than the tennis ball Which ball would have more kinetic energy
However if one object has more mass than the other the heavier object will have more kinetic energy
29
Velocity vs Speed
Remember that velocity is another way to measure motion V elocity is the speed of an object with direction Speed does not have a direction so we call speed a scalar quantity
Since velocity has both magnitude and direction it is a vector quantity
Runners speed 10 kmhr
Runners velocity 10 kmhr to the East
30
How Does Kinetic Energy Depend on Velocity
In this picture the hare is moving faster than the tortoise at this point
If we assumed that they had the same mass who would have more kinetic energy Why Discuss this with a partner
31
v = 5 ms
v = 10 ms
How Does Kinetic Energy Depend upon Velocity
If two identical objects are moving at the same velocity then they will have the same kinetic energy However if one of the objects is moving faster the faster one will have more kinetic energy
In the diagram above two identical tennis balls are moving Which tennis ball has more kinetic energy and why
32
8 Three different emergency vehicles are noticed driving on the highway at a speed of 25 ms Which of the following cars have the most kinetic energy at that moment
A a police car
B an ambulance
C a firetruck
D they all have the same kinetic energy
Answer
C
33
9 Three different baseball pitchers had the speed of their fastball measured by a radar gun Which of the following pitchers fastball had the smallest amount of kinetic energy
A a little league pitcher (22 ms)
B a high school pitcher (33 ms)
C a major league pitcher (41ms)
D they all had the same kinetic energy
Answer
34
10 Which of the following situations has the least kinetic energy Be ready to explain your answer
A a man sitting still on a park bench
B a child riding a bike
C a woman driving a car
D it is impossible to tell
Answer
35
Calculating Kinetic Energy
Kinetic energy can be solved for by using the equation
12KE = mv2
Lets fill in the table below
variable unitsName
Kinetic Energy
mms
36
Example shy Calculating Kinetic Energy
A car which has a mass of 1000 kg is moving with a velocity of 5 ms How much kinetic energy does the car possess Calculate the cars kinetic energy
KE = mv2KE = (05)(1000 kg)(5 ms)2
KE = (05)(1000 kg)(25 m2s2)KE = 125000 J
12
Click on the box to see the solution
Teacher N
otes
37
11 A 10 kg snowball is rolling down a hill Just before reaching the bottom its velocity is measured to be 10 ms What is the kinetic energy of the ball at this position
Answer
38
12 A 100 kg running back in football is running with a velocity of 2 ms What is his kinetic energy
Answer
KE= 12 mv2KE= 12 (100 kg) (2 ms)2KE= 12 (100 kg) (4m2s2)KE= 200 J
39
13 A 2000 kg car with a velocity of 20 ms slows down and stops at a red light What is the change in kinetic energy
Answer
40
14 A 50 kg girl rode her 12 kg bicycle in a race She started from rest and peddled with a velocity of 10 ms What is the change in kinetic energy of the girl and her bicycle
Answer
41
Thinking Mathematically
KE = mv212
We have already said that mass is directly proportional to kinetic energy
This means that if the mass of the object doubles the
kinetic energy ___________ If the mass of the object increases by a
factor of 5 then the kinetic energy___________ by ______________
If the mass of the object decreases by half then the kinetic
energy will ____________ by ___________
doubles
increases a factor of 5
decrease half
42
15 If the mass of a wagon is doubled its kinetic energy
A increases
B decreases
Answer
43
16 If the mass of a wagon is doubled by what factor does the kinetic energy increase
Answer
44
Thinking Mathematically
Kinetic energy can be solved by using the equation
KE = mv212
From the equation we can see that the kinetic energy is also directly proportional to the square of the velocity
This means that if the velocity doubles the kinetic energy increases by a factor of 4
22=4
If the velocity is quadrupled then the kinetic energy increases by a factor of 16
42= 16
45
17 If the velocity of a wagon is tripled its kinetic energy
Answer
A increases
B decreases
46
18 If the velocity of a wagon is tripled by what factor does the kinetic energy increase
Answer
47
19 Two balls are moving with the same velocity ball A has a mass of 10 kg and ball B has a mass of 40 kg How much more kinetic energy does ball B have
Answer
48
20 A cart halves its mass and at the same time doubles its speed Does the kinetic energy increase or decrease By what factor does the kinetic energy change
A increase 2
B increase 4
C decrease 2
D decrease 4
Answer
bull half the mass gives 12 the KEbull double the speed gives 4 x KEbull therefore (12)(4)= 2
A
49
Stored Energy
Return to Tableof Contents
50
Where does Kinetic Energy Come From
Imagine a roller coaster car that is at the top of the first hill and is stopped
Does the car stay stopped at the top of the hill for the entire ride
What happens
51
Where does Kinetic Energy Come From
Once the car leans over the edge gravity pulls it down The ride is taking advantage of the gravitational attraction between the car and Earth to give the car kinetic energy and make it go faster as it falls
The kinetic energy the car is receiving is coming from another type of energy called potential energy
52
Where does Kinetic Energy Come From
Potential energy is energy stored in an object due to the objects position The roller coaster car on the previous slide had stored energy due to its height above the ground
There are two forms of potential energy that we will be looking at in this unit
Gravitational Potential Energy
and
Elastic Potential Energy
53
Gravitational Potential Energy
The potential energy due to elevated positions is called gravitational potential energy
Gravitational potential energy is stored energy and it can be used at a later time to cause an object to moveOnce the person steps off the diving board the gravitational potential energy is converted into kinetic energy and the person falls (moves)
54
Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
55
Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
56
h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
10
If an object moves in the same direction as the direction of the force applied to it the energy of the system is increased
The work is positive W gt 0
Positive Work
They can push the truck to get it to move
11
If an object moves in the direction opposite to the direction of the
force applied to it then the work is negative W lt 0
The energy of the system is reduced
Negative Work
The parachute moves downwards while air resistance acts upwards
on the parachute
12
If an object does not move even when there is a force applied to it then no work is done on the object
W=0 J
Zero Work
The people exert a force onto the wall but the wall does not move
13
NonshyMechanical Energy The energy of an object that is not due to its motion or position Nonshymechanical energy usually describes an object at its atomic level
Exampleselectrical energychemical energythermal energysound energy
Mechanical Energy shy The energy of an object due to its motion and position Mechanical energy is usually used to describe a large object
It is the sum of kinetic and potential energy
Mechanical vs NonshyMechanical EnergyEnergy exists in many forms but can be broken down into two major forms
14
1 Which of the following is the unit for energy
A Meter
B Newton
C Second
D Joule Answer
15
2 A wagon is rolling down a hill A man tries to stop the wagon by trying to push it back up the hill but he is unsuccessful Is the man doing positive or negative work
A positive
B negative
Answer
16
3 A boy kicks a soccer ball into a net Did the boy do positive or negative work on the ball
A positive
B negative
Answer
17
4 A woman walks across an icy sidewalk that has been covered in salt to help make it less slippery Is the salt doing positive or negative work on the womans shoes
A positive
B negative Answer
18
5 Jill is waiting for the bus and she forgot her mittens She rubs her hands together to keep them warm In this situation there is ______________ energy due to the movement of her hands There is also _______________ energy due to the heat she generates by rubbing her hands together
A mechanical nonshymechanical
B nonshymechanical mechanical
Answer
19
Mechanical Energy
Return to Tableof Contents
20
__________ Energy
__________ Energy __________ Energy
Forms of Mechanical EnergyMechanical Energy can be broken down into two different types of Energy energy of motion which is called Kinetic Energy and stored energy which is called Potential Energy Potential Energy has two forms Gravitational and Elastic depending upon how the energy is stored
Write the underlined words into the correct
place in the diagram
21
6 Which of the following is a form of mechanical energy
A Kinetic
B Thermal
C Chemical
D Solar
Answer
A shy Kinetic
22
Energy of Motion
Return to Tableof Contents
23
7 Which of the following is a type of energy which is used to describe the motion of an object
A Electrical Energy
B Nuclear Energy
C Kinetic Energy
D All of the above
Answer
C shy Kinetic
24
Energy of Motion
In order for an object to move one of two scenarios has to occur
1 The object uses some of the potential energy that it had stored
2 Energy is transferred to the object from an outside source
In either case now that the object is in motion the object is experiencing kinetic energy
25
An objects state of motion can be described by looking at the amount of kinetic energy that the object has at that moment in time
Kinetic Energy
Since the state of motion of an object can change with time the kinetic energy of an object can also change with time
26
velocitymass
The amount of kinetic energy that an object possesses is dependent on two factors
Kinetic Energy
Both of these factors are directly proportional to the kinetic energy We talked about this mathematical relationship in the
last chapter What did directly proportional mean
and
27
Kinetic Energy Mass Velocity
Since kinetic energy is the energy of motion
the object has to have a velocity to have kinetic energy The larger the
velocity the __________________ the kinetic energy
The larger the mass the more energy is needed to move the object
therefore the _______________ the kinetic energy
28
How Does Kinetic Energy Depend on MassIf two identical objects are moving at the same velocity they will have the same kinetic energy
v = 5 ms
v = 5 ms
A tennis ball and a bowling ball are both shown above The bowling ball is heavier than the tennis ball Which ball would have more kinetic energy
However if one object has more mass than the other the heavier object will have more kinetic energy
29
Velocity vs Speed
Remember that velocity is another way to measure motion V elocity is the speed of an object with direction Speed does not have a direction so we call speed a scalar quantity
Since velocity has both magnitude and direction it is a vector quantity
Runners speed 10 kmhr
Runners velocity 10 kmhr to the East
30
How Does Kinetic Energy Depend on Velocity
In this picture the hare is moving faster than the tortoise at this point
If we assumed that they had the same mass who would have more kinetic energy Why Discuss this with a partner
31
v = 5 ms
v = 10 ms
How Does Kinetic Energy Depend upon Velocity
If two identical objects are moving at the same velocity then they will have the same kinetic energy However if one of the objects is moving faster the faster one will have more kinetic energy
In the diagram above two identical tennis balls are moving Which tennis ball has more kinetic energy and why
32
8 Three different emergency vehicles are noticed driving on the highway at a speed of 25 ms Which of the following cars have the most kinetic energy at that moment
A a police car
B an ambulance
C a firetruck
D they all have the same kinetic energy
Answer
C
33
9 Three different baseball pitchers had the speed of their fastball measured by a radar gun Which of the following pitchers fastball had the smallest amount of kinetic energy
A a little league pitcher (22 ms)
B a high school pitcher (33 ms)
C a major league pitcher (41ms)
D they all had the same kinetic energy
Answer
34
10 Which of the following situations has the least kinetic energy Be ready to explain your answer
A a man sitting still on a park bench
B a child riding a bike
C a woman driving a car
D it is impossible to tell
Answer
35
Calculating Kinetic Energy
Kinetic energy can be solved for by using the equation
12KE = mv2
Lets fill in the table below
variable unitsName
Kinetic Energy
mms
36
Example shy Calculating Kinetic Energy
A car which has a mass of 1000 kg is moving with a velocity of 5 ms How much kinetic energy does the car possess Calculate the cars kinetic energy
KE = mv2KE = (05)(1000 kg)(5 ms)2
KE = (05)(1000 kg)(25 m2s2)KE = 125000 J
12
Click on the box to see the solution
Teacher N
otes
37
11 A 10 kg snowball is rolling down a hill Just before reaching the bottom its velocity is measured to be 10 ms What is the kinetic energy of the ball at this position
Answer
38
12 A 100 kg running back in football is running with a velocity of 2 ms What is his kinetic energy
Answer
KE= 12 mv2KE= 12 (100 kg) (2 ms)2KE= 12 (100 kg) (4m2s2)KE= 200 J
39
13 A 2000 kg car with a velocity of 20 ms slows down and stops at a red light What is the change in kinetic energy
Answer
40
14 A 50 kg girl rode her 12 kg bicycle in a race She started from rest and peddled with a velocity of 10 ms What is the change in kinetic energy of the girl and her bicycle
Answer
41
Thinking Mathematically
KE = mv212
We have already said that mass is directly proportional to kinetic energy
This means that if the mass of the object doubles the
kinetic energy ___________ If the mass of the object increases by a
factor of 5 then the kinetic energy___________ by ______________
If the mass of the object decreases by half then the kinetic
energy will ____________ by ___________
doubles
increases a factor of 5
decrease half
42
15 If the mass of a wagon is doubled its kinetic energy
A increases
B decreases
Answer
43
16 If the mass of a wagon is doubled by what factor does the kinetic energy increase
Answer
44
Thinking Mathematically
Kinetic energy can be solved by using the equation
KE = mv212
From the equation we can see that the kinetic energy is also directly proportional to the square of the velocity
This means that if the velocity doubles the kinetic energy increases by a factor of 4
22=4
If the velocity is quadrupled then the kinetic energy increases by a factor of 16
42= 16
45
17 If the velocity of a wagon is tripled its kinetic energy
Answer
A increases
B decreases
46
18 If the velocity of a wagon is tripled by what factor does the kinetic energy increase
Answer
47
19 Two balls are moving with the same velocity ball A has a mass of 10 kg and ball B has a mass of 40 kg How much more kinetic energy does ball B have
Answer
48
20 A cart halves its mass and at the same time doubles its speed Does the kinetic energy increase or decrease By what factor does the kinetic energy change
A increase 2
B increase 4
C decrease 2
D decrease 4
Answer
bull half the mass gives 12 the KEbull double the speed gives 4 x KEbull therefore (12)(4)= 2
A
49
Stored Energy
Return to Tableof Contents
50
Where does Kinetic Energy Come From
Imagine a roller coaster car that is at the top of the first hill and is stopped
Does the car stay stopped at the top of the hill for the entire ride
What happens
51
Where does Kinetic Energy Come From
Once the car leans over the edge gravity pulls it down The ride is taking advantage of the gravitational attraction between the car and Earth to give the car kinetic energy and make it go faster as it falls
The kinetic energy the car is receiving is coming from another type of energy called potential energy
52
Where does Kinetic Energy Come From
Potential energy is energy stored in an object due to the objects position The roller coaster car on the previous slide had stored energy due to its height above the ground
There are two forms of potential energy that we will be looking at in this unit
Gravitational Potential Energy
and
Elastic Potential Energy
53
Gravitational Potential Energy
The potential energy due to elevated positions is called gravitational potential energy
Gravitational potential energy is stored energy and it can be used at a later time to cause an object to moveOnce the person steps off the diving board the gravitational potential energy is converted into kinetic energy and the person falls (moves)
54
Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
55
Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
56
h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
11
If an object moves in the direction opposite to the direction of the
force applied to it then the work is negative W lt 0
The energy of the system is reduced
Negative Work
The parachute moves downwards while air resistance acts upwards
on the parachute
12
If an object does not move even when there is a force applied to it then no work is done on the object
W=0 J
Zero Work
The people exert a force onto the wall but the wall does not move
13
NonshyMechanical Energy The energy of an object that is not due to its motion or position Nonshymechanical energy usually describes an object at its atomic level
Exampleselectrical energychemical energythermal energysound energy
Mechanical Energy shy The energy of an object due to its motion and position Mechanical energy is usually used to describe a large object
It is the sum of kinetic and potential energy
Mechanical vs NonshyMechanical EnergyEnergy exists in many forms but can be broken down into two major forms
14
1 Which of the following is the unit for energy
A Meter
B Newton
C Second
D Joule Answer
15
2 A wagon is rolling down a hill A man tries to stop the wagon by trying to push it back up the hill but he is unsuccessful Is the man doing positive or negative work
A positive
B negative
Answer
16
3 A boy kicks a soccer ball into a net Did the boy do positive or negative work on the ball
A positive
B negative
Answer
17
4 A woman walks across an icy sidewalk that has been covered in salt to help make it less slippery Is the salt doing positive or negative work on the womans shoes
A positive
B negative Answer
18
5 Jill is waiting for the bus and she forgot her mittens She rubs her hands together to keep them warm In this situation there is ______________ energy due to the movement of her hands There is also _______________ energy due to the heat she generates by rubbing her hands together
A mechanical nonshymechanical
B nonshymechanical mechanical
Answer
19
Mechanical Energy
Return to Tableof Contents
20
__________ Energy
__________ Energy __________ Energy
Forms of Mechanical EnergyMechanical Energy can be broken down into two different types of Energy energy of motion which is called Kinetic Energy and stored energy which is called Potential Energy Potential Energy has two forms Gravitational and Elastic depending upon how the energy is stored
Write the underlined words into the correct
place in the diagram
21
6 Which of the following is a form of mechanical energy
A Kinetic
B Thermal
C Chemical
D Solar
Answer
A shy Kinetic
22
Energy of Motion
Return to Tableof Contents
23
7 Which of the following is a type of energy which is used to describe the motion of an object
A Electrical Energy
B Nuclear Energy
C Kinetic Energy
D All of the above
Answer
C shy Kinetic
24
Energy of Motion
In order for an object to move one of two scenarios has to occur
1 The object uses some of the potential energy that it had stored
2 Energy is transferred to the object from an outside source
In either case now that the object is in motion the object is experiencing kinetic energy
25
An objects state of motion can be described by looking at the amount of kinetic energy that the object has at that moment in time
Kinetic Energy
Since the state of motion of an object can change with time the kinetic energy of an object can also change with time
26
velocitymass
The amount of kinetic energy that an object possesses is dependent on two factors
Kinetic Energy
Both of these factors are directly proportional to the kinetic energy We talked about this mathematical relationship in the
last chapter What did directly proportional mean
and
27
Kinetic Energy Mass Velocity
Since kinetic energy is the energy of motion
the object has to have a velocity to have kinetic energy The larger the
velocity the __________________ the kinetic energy
The larger the mass the more energy is needed to move the object
therefore the _______________ the kinetic energy
28
How Does Kinetic Energy Depend on MassIf two identical objects are moving at the same velocity they will have the same kinetic energy
v = 5 ms
v = 5 ms
A tennis ball and a bowling ball are both shown above The bowling ball is heavier than the tennis ball Which ball would have more kinetic energy
However if one object has more mass than the other the heavier object will have more kinetic energy
29
Velocity vs Speed
Remember that velocity is another way to measure motion V elocity is the speed of an object with direction Speed does not have a direction so we call speed a scalar quantity
Since velocity has both magnitude and direction it is a vector quantity
Runners speed 10 kmhr
Runners velocity 10 kmhr to the East
30
How Does Kinetic Energy Depend on Velocity
In this picture the hare is moving faster than the tortoise at this point
If we assumed that they had the same mass who would have more kinetic energy Why Discuss this with a partner
31
v = 5 ms
v = 10 ms
How Does Kinetic Energy Depend upon Velocity
If two identical objects are moving at the same velocity then they will have the same kinetic energy However if one of the objects is moving faster the faster one will have more kinetic energy
In the diagram above two identical tennis balls are moving Which tennis ball has more kinetic energy and why
32
8 Three different emergency vehicles are noticed driving on the highway at a speed of 25 ms Which of the following cars have the most kinetic energy at that moment
A a police car
B an ambulance
C a firetruck
D they all have the same kinetic energy
Answer
C
33
9 Three different baseball pitchers had the speed of their fastball measured by a radar gun Which of the following pitchers fastball had the smallest amount of kinetic energy
A a little league pitcher (22 ms)
B a high school pitcher (33 ms)
C a major league pitcher (41ms)
D they all had the same kinetic energy
Answer
34
10 Which of the following situations has the least kinetic energy Be ready to explain your answer
A a man sitting still on a park bench
B a child riding a bike
C a woman driving a car
D it is impossible to tell
Answer
35
Calculating Kinetic Energy
Kinetic energy can be solved for by using the equation
12KE = mv2
Lets fill in the table below
variable unitsName
Kinetic Energy
mms
36
Example shy Calculating Kinetic Energy
A car which has a mass of 1000 kg is moving with a velocity of 5 ms How much kinetic energy does the car possess Calculate the cars kinetic energy
KE = mv2KE = (05)(1000 kg)(5 ms)2
KE = (05)(1000 kg)(25 m2s2)KE = 125000 J
12
Click on the box to see the solution
Teacher N
otes
37
11 A 10 kg snowball is rolling down a hill Just before reaching the bottom its velocity is measured to be 10 ms What is the kinetic energy of the ball at this position
Answer
38
12 A 100 kg running back in football is running with a velocity of 2 ms What is his kinetic energy
Answer
KE= 12 mv2KE= 12 (100 kg) (2 ms)2KE= 12 (100 kg) (4m2s2)KE= 200 J
39
13 A 2000 kg car with a velocity of 20 ms slows down and stops at a red light What is the change in kinetic energy
Answer
40
14 A 50 kg girl rode her 12 kg bicycle in a race She started from rest and peddled with a velocity of 10 ms What is the change in kinetic energy of the girl and her bicycle
Answer
41
Thinking Mathematically
KE = mv212
We have already said that mass is directly proportional to kinetic energy
This means that if the mass of the object doubles the
kinetic energy ___________ If the mass of the object increases by a
factor of 5 then the kinetic energy___________ by ______________
If the mass of the object decreases by half then the kinetic
energy will ____________ by ___________
doubles
increases a factor of 5
decrease half
42
15 If the mass of a wagon is doubled its kinetic energy
A increases
B decreases
Answer
43
16 If the mass of a wagon is doubled by what factor does the kinetic energy increase
Answer
44
Thinking Mathematically
Kinetic energy can be solved by using the equation
KE = mv212
From the equation we can see that the kinetic energy is also directly proportional to the square of the velocity
This means that if the velocity doubles the kinetic energy increases by a factor of 4
22=4
If the velocity is quadrupled then the kinetic energy increases by a factor of 16
42= 16
45
17 If the velocity of a wagon is tripled its kinetic energy
Answer
A increases
B decreases
46
18 If the velocity of a wagon is tripled by what factor does the kinetic energy increase
Answer
47
19 Two balls are moving with the same velocity ball A has a mass of 10 kg and ball B has a mass of 40 kg How much more kinetic energy does ball B have
Answer
48
20 A cart halves its mass and at the same time doubles its speed Does the kinetic energy increase or decrease By what factor does the kinetic energy change
A increase 2
B increase 4
C decrease 2
D decrease 4
Answer
bull half the mass gives 12 the KEbull double the speed gives 4 x KEbull therefore (12)(4)= 2
A
49
Stored Energy
Return to Tableof Contents
50
Where does Kinetic Energy Come From
Imagine a roller coaster car that is at the top of the first hill and is stopped
Does the car stay stopped at the top of the hill for the entire ride
What happens
51
Where does Kinetic Energy Come From
Once the car leans over the edge gravity pulls it down The ride is taking advantage of the gravitational attraction between the car and Earth to give the car kinetic energy and make it go faster as it falls
The kinetic energy the car is receiving is coming from another type of energy called potential energy
52
Where does Kinetic Energy Come From
Potential energy is energy stored in an object due to the objects position The roller coaster car on the previous slide had stored energy due to its height above the ground
There are two forms of potential energy that we will be looking at in this unit
Gravitational Potential Energy
and
Elastic Potential Energy
53
Gravitational Potential Energy
The potential energy due to elevated positions is called gravitational potential energy
Gravitational potential energy is stored energy and it can be used at a later time to cause an object to moveOnce the person steps off the diving board the gravitational potential energy is converted into kinetic energy and the person falls (moves)
54
Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
55
Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
56
h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
12
If an object does not move even when there is a force applied to it then no work is done on the object
W=0 J
Zero Work
The people exert a force onto the wall but the wall does not move
13
NonshyMechanical Energy The energy of an object that is not due to its motion or position Nonshymechanical energy usually describes an object at its atomic level
Exampleselectrical energychemical energythermal energysound energy
Mechanical Energy shy The energy of an object due to its motion and position Mechanical energy is usually used to describe a large object
It is the sum of kinetic and potential energy
Mechanical vs NonshyMechanical EnergyEnergy exists in many forms but can be broken down into two major forms
14
1 Which of the following is the unit for energy
A Meter
B Newton
C Second
D Joule Answer
15
2 A wagon is rolling down a hill A man tries to stop the wagon by trying to push it back up the hill but he is unsuccessful Is the man doing positive or negative work
A positive
B negative
Answer
16
3 A boy kicks a soccer ball into a net Did the boy do positive or negative work on the ball
A positive
B negative
Answer
17
4 A woman walks across an icy sidewalk that has been covered in salt to help make it less slippery Is the salt doing positive or negative work on the womans shoes
A positive
B negative Answer
18
5 Jill is waiting for the bus and she forgot her mittens She rubs her hands together to keep them warm In this situation there is ______________ energy due to the movement of her hands There is also _______________ energy due to the heat she generates by rubbing her hands together
A mechanical nonshymechanical
B nonshymechanical mechanical
Answer
19
Mechanical Energy
Return to Tableof Contents
20
__________ Energy
__________ Energy __________ Energy
Forms of Mechanical EnergyMechanical Energy can be broken down into two different types of Energy energy of motion which is called Kinetic Energy and stored energy which is called Potential Energy Potential Energy has two forms Gravitational and Elastic depending upon how the energy is stored
Write the underlined words into the correct
place in the diagram
21
6 Which of the following is a form of mechanical energy
A Kinetic
B Thermal
C Chemical
D Solar
Answer
A shy Kinetic
22
Energy of Motion
Return to Tableof Contents
23
7 Which of the following is a type of energy which is used to describe the motion of an object
A Electrical Energy
B Nuclear Energy
C Kinetic Energy
D All of the above
Answer
C shy Kinetic
24
Energy of Motion
In order for an object to move one of two scenarios has to occur
1 The object uses some of the potential energy that it had stored
2 Energy is transferred to the object from an outside source
In either case now that the object is in motion the object is experiencing kinetic energy
25
An objects state of motion can be described by looking at the amount of kinetic energy that the object has at that moment in time
Kinetic Energy
Since the state of motion of an object can change with time the kinetic energy of an object can also change with time
26
velocitymass
The amount of kinetic energy that an object possesses is dependent on two factors
Kinetic Energy
Both of these factors are directly proportional to the kinetic energy We talked about this mathematical relationship in the
last chapter What did directly proportional mean
and
27
Kinetic Energy Mass Velocity
Since kinetic energy is the energy of motion
the object has to have a velocity to have kinetic energy The larger the
velocity the __________________ the kinetic energy
The larger the mass the more energy is needed to move the object
therefore the _______________ the kinetic energy
28
How Does Kinetic Energy Depend on MassIf two identical objects are moving at the same velocity they will have the same kinetic energy
v = 5 ms
v = 5 ms
A tennis ball and a bowling ball are both shown above The bowling ball is heavier than the tennis ball Which ball would have more kinetic energy
However if one object has more mass than the other the heavier object will have more kinetic energy
29
Velocity vs Speed
Remember that velocity is another way to measure motion V elocity is the speed of an object with direction Speed does not have a direction so we call speed a scalar quantity
Since velocity has both magnitude and direction it is a vector quantity
Runners speed 10 kmhr
Runners velocity 10 kmhr to the East
30
How Does Kinetic Energy Depend on Velocity
In this picture the hare is moving faster than the tortoise at this point
If we assumed that they had the same mass who would have more kinetic energy Why Discuss this with a partner
31
v = 5 ms
v = 10 ms
How Does Kinetic Energy Depend upon Velocity
If two identical objects are moving at the same velocity then they will have the same kinetic energy However if one of the objects is moving faster the faster one will have more kinetic energy
In the diagram above two identical tennis balls are moving Which tennis ball has more kinetic energy and why
32
8 Three different emergency vehicles are noticed driving on the highway at a speed of 25 ms Which of the following cars have the most kinetic energy at that moment
A a police car
B an ambulance
C a firetruck
D they all have the same kinetic energy
Answer
C
33
9 Three different baseball pitchers had the speed of their fastball measured by a radar gun Which of the following pitchers fastball had the smallest amount of kinetic energy
A a little league pitcher (22 ms)
B a high school pitcher (33 ms)
C a major league pitcher (41ms)
D they all had the same kinetic energy
Answer
34
10 Which of the following situations has the least kinetic energy Be ready to explain your answer
A a man sitting still on a park bench
B a child riding a bike
C a woman driving a car
D it is impossible to tell
Answer
35
Calculating Kinetic Energy
Kinetic energy can be solved for by using the equation
12KE = mv2
Lets fill in the table below
variable unitsName
Kinetic Energy
mms
36
Example shy Calculating Kinetic Energy
A car which has a mass of 1000 kg is moving with a velocity of 5 ms How much kinetic energy does the car possess Calculate the cars kinetic energy
KE = mv2KE = (05)(1000 kg)(5 ms)2
KE = (05)(1000 kg)(25 m2s2)KE = 125000 J
12
Click on the box to see the solution
Teacher N
otes
37
11 A 10 kg snowball is rolling down a hill Just before reaching the bottom its velocity is measured to be 10 ms What is the kinetic energy of the ball at this position
Answer
38
12 A 100 kg running back in football is running with a velocity of 2 ms What is his kinetic energy
Answer
KE= 12 mv2KE= 12 (100 kg) (2 ms)2KE= 12 (100 kg) (4m2s2)KE= 200 J
39
13 A 2000 kg car with a velocity of 20 ms slows down and stops at a red light What is the change in kinetic energy
Answer
40
14 A 50 kg girl rode her 12 kg bicycle in a race She started from rest and peddled with a velocity of 10 ms What is the change in kinetic energy of the girl and her bicycle
Answer
41
Thinking Mathematically
KE = mv212
We have already said that mass is directly proportional to kinetic energy
This means that if the mass of the object doubles the
kinetic energy ___________ If the mass of the object increases by a
factor of 5 then the kinetic energy___________ by ______________
If the mass of the object decreases by half then the kinetic
energy will ____________ by ___________
doubles
increases a factor of 5
decrease half
42
15 If the mass of a wagon is doubled its kinetic energy
A increases
B decreases
Answer
43
16 If the mass of a wagon is doubled by what factor does the kinetic energy increase
Answer
44
Thinking Mathematically
Kinetic energy can be solved by using the equation
KE = mv212
From the equation we can see that the kinetic energy is also directly proportional to the square of the velocity
This means that if the velocity doubles the kinetic energy increases by a factor of 4
22=4
If the velocity is quadrupled then the kinetic energy increases by a factor of 16
42= 16
45
17 If the velocity of a wagon is tripled its kinetic energy
Answer
A increases
B decreases
46
18 If the velocity of a wagon is tripled by what factor does the kinetic energy increase
Answer
47
19 Two balls are moving with the same velocity ball A has a mass of 10 kg and ball B has a mass of 40 kg How much more kinetic energy does ball B have
Answer
48
20 A cart halves its mass and at the same time doubles its speed Does the kinetic energy increase or decrease By what factor does the kinetic energy change
A increase 2
B increase 4
C decrease 2
D decrease 4
Answer
bull half the mass gives 12 the KEbull double the speed gives 4 x KEbull therefore (12)(4)= 2
A
49
Stored Energy
Return to Tableof Contents
50
Where does Kinetic Energy Come From
Imagine a roller coaster car that is at the top of the first hill and is stopped
Does the car stay stopped at the top of the hill for the entire ride
What happens
51
Where does Kinetic Energy Come From
Once the car leans over the edge gravity pulls it down The ride is taking advantage of the gravitational attraction between the car and Earth to give the car kinetic energy and make it go faster as it falls
The kinetic energy the car is receiving is coming from another type of energy called potential energy
52
Where does Kinetic Energy Come From
Potential energy is energy stored in an object due to the objects position The roller coaster car on the previous slide had stored energy due to its height above the ground
There are two forms of potential energy that we will be looking at in this unit
Gravitational Potential Energy
and
Elastic Potential Energy
53
Gravitational Potential Energy
The potential energy due to elevated positions is called gravitational potential energy
Gravitational potential energy is stored energy and it can be used at a later time to cause an object to moveOnce the person steps off the diving board the gravitational potential energy is converted into kinetic energy and the person falls (moves)
54
Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
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Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
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h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
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Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
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GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
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What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
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How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
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Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
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91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
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This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
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When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
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Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
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At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
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At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
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At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
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Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
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Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
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39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
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113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
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Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
13
NonshyMechanical Energy The energy of an object that is not due to its motion or position Nonshymechanical energy usually describes an object at its atomic level
Exampleselectrical energychemical energythermal energysound energy
Mechanical Energy shy The energy of an object due to its motion and position Mechanical energy is usually used to describe a large object
It is the sum of kinetic and potential energy
Mechanical vs NonshyMechanical EnergyEnergy exists in many forms but can be broken down into two major forms
14
1 Which of the following is the unit for energy
A Meter
B Newton
C Second
D Joule Answer
15
2 A wagon is rolling down a hill A man tries to stop the wagon by trying to push it back up the hill but he is unsuccessful Is the man doing positive or negative work
A positive
B negative
Answer
16
3 A boy kicks a soccer ball into a net Did the boy do positive or negative work on the ball
A positive
B negative
Answer
17
4 A woman walks across an icy sidewalk that has been covered in salt to help make it less slippery Is the salt doing positive or negative work on the womans shoes
A positive
B negative Answer
18
5 Jill is waiting for the bus and she forgot her mittens She rubs her hands together to keep them warm In this situation there is ______________ energy due to the movement of her hands There is also _______________ energy due to the heat she generates by rubbing her hands together
A mechanical nonshymechanical
B nonshymechanical mechanical
Answer
19
Mechanical Energy
Return to Tableof Contents
20
__________ Energy
__________ Energy __________ Energy
Forms of Mechanical EnergyMechanical Energy can be broken down into two different types of Energy energy of motion which is called Kinetic Energy and stored energy which is called Potential Energy Potential Energy has two forms Gravitational and Elastic depending upon how the energy is stored
Write the underlined words into the correct
place in the diagram
21
6 Which of the following is a form of mechanical energy
A Kinetic
B Thermal
C Chemical
D Solar
Answer
A shy Kinetic
22
Energy of Motion
Return to Tableof Contents
23
7 Which of the following is a type of energy which is used to describe the motion of an object
A Electrical Energy
B Nuclear Energy
C Kinetic Energy
D All of the above
Answer
C shy Kinetic
24
Energy of Motion
In order for an object to move one of two scenarios has to occur
1 The object uses some of the potential energy that it had stored
2 Energy is transferred to the object from an outside source
In either case now that the object is in motion the object is experiencing kinetic energy
25
An objects state of motion can be described by looking at the amount of kinetic energy that the object has at that moment in time
Kinetic Energy
Since the state of motion of an object can change with time the kinetic energy of an object can also change with time
26
velocitymass
The amount of kinetic energy that an object possesses is dependent on two factors
Kinetic Energy
Both of these factors are directly proportional to the kinetic energy We talked about this mathematical relationship in the
last chapter What did directly proportional mean
and
27
Kinetic Energy Mass Velocity
Since kinetic energy is the energy of motion
the object has to have a velocity to have kinetic energy The larger the
velocity the __________________ the kinetic energy
The larger the mass the more energy is needed to move the object
therefore the _______________ the kinetic energy
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How Does Kinetic Energy Depend on MassIf two identical objects are moving at the same velocity they will have the same kinetic energy
v = 5 ms
v = 5 ms
A tennis ball and a bowling ball are both shown above The bowling ball is heavier than the tennis ball Which ball would have more kinetic energy
However if one object has more mass than the other the heavier object will have more kinetic energy
29
Velocity vs Speed
Remember that velocity is another way to measure motion V elocity is the speed of an object with direction Speed does not have a direction so we call speed a scalar quantity
Since velocity has both magnitude and direction it is a vector quantity
Runners speed 10 kmhr
Runners velocity 10 kmhr to the East
30
How Does Kinetic Energy Depend on Velocity
In this picture the hare is moving faster than the tortoise at this point
If we assumed that they had the same mass who would have more kinetic energy Why Discuss this with a partner
31
v = 5 ms
v = 10 ms
How Does Kinetic Energy Depend upon Velocity
If two identical objects are moving at the same velocity then they will have the same kinetic energy However if one of the objects is moving faster the faster one will have more kinetic energy
In the diagram above two identical tennis balls are moving Which tennis ball has more kinetic energy and why
32
8 Three different emergency vehicles are noticed driving on the highway at a speed of 25 ms Which of the following cars have the most kinetic energy at that moment
A a police car
B an ambulance
C a firetruck
D they all have the same kinetic energy
Answer
C
33
9 Three different baseball pitchers had the speed of their fastball measured by a radar gun Which of the following pitchers fastball had the smallest amount of kinetic energy
A a little league pitcher (22 ms)
B a high school pitcher (33 ms)
C a major league pitcher (41ms)
D they all had the same kinetic energy
Answer
34
10 Which of the following situations has the least kinetic energy Be ready to explain your answer
A a man sitting still on a park bench
B a child riding a bike
C a woman driving a car
D it is impossible to tell
Answer
35
Calculating Kinetic Energy
Kinetic energy can be solved for by using the equation
12KE = mv2
Lets fill in the table below
variable unitsName
Kinetic Energy
mms
36
Example shy Calculating Kinetic Energy
A car which has a mass of 1000 kg is moving with a velocity of 5 ms How much kinetic energy does the car possess Calculate the cars kinetic energy
KE = mv2KE = (05)(1000 kg)(5 ms)2
KE = (05)(1000 kg)(25 m2s2)KE = 125000 J
12
Click on the box to see the solution
Teacher N
otes
37
11 A 10 kg snowball is rolling down a hill Just before reaching the bottom its velocity is measured to be 10 ms What is the kinetic energy of the ball at this position
Answer
38
12 A 100 kg running back in football is running with a velocity of 2 ms What is his kinetic energy
Answer
KE= 12 mv2KE= 12 (100 kg) (2 ms)2KE= 12 (100 kg) (4m2s2)KE= 200 J
39
13 A 2000 kg car with a velocity of 20 ms slows down and stops at a red light What is the change in kinetic energy
Answer
40
14 A 50 kg girl rode her 12 kg bicycle in a race She started from rest and peddled with a velocity of 10 ms What is the change in kinetic energy of the girl and her bicycle
Answer
41
Thinking Mathematically
KE = mv212
We have already said that mass is directly proportional to kinetic energy
This means that if the mass of the object doubles the
kinetic energy ___________ If the mass of the object increases by a
factor of 5 then the kinetic energy___________ by ______________
If the mass of the object decreases by half then the kinetic
energy will ____________ by ___________
doubles
increases a factor of 5
decrease half
42
15 If the mass of a wagon is doubled its kinetic energy
A increases
B decreases
Answer
43
16 If the mass of a wagon is doubled by what factor does the kinetic energy increase
Answer
44
Thinking Mathematically
Kinetic energy can be solved by using the equation
KE = mv212
From the equation we can see that the kinetic energy is also directly proportional to the square of the velocity
This means that if the velocity doubles the kinetic energy increases by a factor of 4
22=4
If the velocity is quadrupled then the kinetic energy increases by a factor of 16
42= 16
45
17 If the velocity of a wagon is tripled its kinetic energy
Answer
A increases
B decreases
46
18 If the velocity of a wagon is tripled by what factor does the kinetic energy increase
Answer
47
19 Two balls are moving with the same velocity ball A has a mass of 10 kg and ball B has a mass of 40 kg How much more kinetic energy does ball B have
Answer
48
20 A cart halves its mass and at the same time doubles its speed Does the kinetic energy increase or decrease By what factor does the kinetic energy change
A increase 2
B increase 4
C decrease 2
D decrease 4
Answer
bull half the mass gives 12 the KEbull double the speed gives 4 x KEbull therefore (12)(4)= 2
A
49
Stored Energy
Return to Tableof Contents
50
Where does Kinetic Energy Come From
Imagine a roller coaster car that is at the top of the first hill and is stopped
Does the car stay stopped at the top of the hill for the entire ride
What happens
51
Where does Kinetic Energy Come From
Once the car leans over the edge gravity pulls it down The ride is taking advantage of the gravitational attraction between the car and Earth to give the car kinetic energy and make it go faster as it falls
The kinetic energy the car is receiving is coming from another type of energy called potential energy
52
Where does Kinetic Energy Come From
Potential energy is energy stored in an object due to the objects position The roller coaster car on the previous slide had stored energy due to its height above the ground
There are two forms of potential energy that we will be looking at in this unit
Gravitational Potential Energy
and
Elastic Potential Energy
53
Gravitational Potential Energy
The potential energy due to elevated positions is called gravitational potential energy
Gravitational potential energy is stored energy and it can be used at a later time to cause an object to moveOnce the person steps off the diving board the gravitational potential energy is converted into kinetic energy and the person falls (moves)
54
Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
55
Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
56
h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
14
1 Which of the following is the unit for energy
A Meter
B Newton
C Second
D Joule Answer
15
2 A wagon is rolling down a hill A man tries to stop the wagon by trying to push it back up the hill but he is unsuccessful Is the man doing positive or negative work
A positive
B negative
Answer
16
3 A boy kicks a soccer ball into a net Did the boy do positive or negative work on the ball
A positive
B negative
Answer
17
4 A woman walks across an icy sidewalk that has been covered in salt to help make it less slippery Is the salt doing positive or negative work on the womans shoes
A positive
B negative Answer
18
5 Jill is waiting for the bus and she forgot her mittens She rubs her hands together to keep them warm In this situation there is ______________ energy due to the movement of her hands There is also _______________ energy due to the heat she generates by rubbing her hands together
A mechanical nonshymechanical
B nonshymechanical mechanical
Answer
19
Mechanical Energy
Return to Tableof Contents
20
__________ Energy
__________ Energy __________ Energy
Forms of Mechanical EnergyMechanical Energy can be broken down into two different types of Energy energy of motion which is called Kinetic Energy and stored energy which is called Potential Energy Potential Energy has two forms Gravitational and Elastic depending upon how the energy is stored
Write the underlined words into the correct
place in the diagram
21
6 Which of the following is a form of mechanical energy
A Kinetic
B Thermal
C Chemical
D Solar
Answer
A shy Kinetic
22
Energy of Motion
Return to Tableof Contents
23
7 Which of the following is a type of energy which is used to describe the motion of an object
A Electrical Energy
B Nuclear Energy
C Kinetic Energy
D All of the above
Answer
C shy Kinetic
24
Energy of Motion
In order for an object to move one of two scenarios has to occur
1 The object uses some of the potential energy that it had stored
2 Energy is transferred to the object from an outside source
In either case now that the object is in motion the object is experiencing kinetic energy
25
An objects state of motion can be described by looking at the amount of kinetic energy that the object has at that moment in time
Kinetic Energy
Since the state of motion of an object can change with time the kinetic energy of an object can also change with time
26
velocitymass
The amount of kinetic energy that an object possesses is dependent on two factors
Kinetic Energy
Both of these factors are directly proportional to the kinetic energy We talked about this mathematical relationship in the
last chapter What did directly proportional mean
and
27
Kinetic Energy Mass Velocity
Since kinetic energy is the energy of motion
the object has to have a velocity to have kinetic energy The larger the
velocity the __________________ the kinetic energy
The larger the mass the more energy is needed to move the object
therefore the _______________ the kinetic energy
28
How Does Kinetic Energy Depend on MassIf two identical objects are moving at the same velocity they will have the same kinetic energy
v = 5 ms
v = 5 ms
A tennis ball and a bowling ball are both shown above The bowling ball is heavier than the tennis ball Which ball would have more kinetic energy
However if one object has more mass than the other the heavier object will have more kinetic energy
29
Velocity vs Speed
Remember that velocity is another way to measure motion V elocity is the speed of an object with direction Speed does not have a direction so we call speed a scalar quantity
Since velocity has both magnitude and direction it is a vector quantity
Runners speed 10 kmhr
Runners velocity 10 kmhr to the East
30
How Does Kinetic Energy Depend on Velocity
In this picture the hare is moving faster than the tortoise at this point
If we assumed that they had the same mass who would have more kinetic energy Why Discuss this with a partner
31
v = 5 ms
v = 10 ms
How Does Kinetic Energy Depend upon Velocity
If two identical objects are moving at the same velocity then they will have the same kinetic energy However if one of the objects is moving faster the faster one will have more kinetic energy
In the diagram above two identical tennis balls are moving Which tennis ball has more kinetic energy and why
32
8 Three different emergency vehicles are noticed driving on the highway at a speed of 25 ms Which of the following cars have the most kinetic energy at that moment
A a police car
B an ambulance
C a firetruck
D they all have the same kinetic energy
Answer
C
33
9 Three different baseball pitchers had the speed of their fastball measured by a radar gun Which of the following pitchers fastball had the smallest amount of kinetic energy
A a little league pitcher (22 ms)
B a high school pitcher (33 ms)
C a major league pitcher (41ms)
D they all had the same kinetic energy
Answer
34
10 Which of the following situations has the least kinetic energy Be ready to explain your answer
A a man sitting still on a park bench
B a child riding a bike
C a woman driving a car
D it is impossible to tell
Answer
35
Calculating Kinetic Energy
Kinetic energy can be solved for by using the equation
12KE = mv2
Lets fill in the table below
variable unitsName
Kinetic Energy
mms
36
Example shy Calculating Kinetic Energy
A car which has a mass of 1000 kg is moving with a velocity of 5 ms How much kinetic energy does the car possess Calculate the cars kinetic energy
KE = mv2KE = (05)(1000 kg)(5 ms)2
KE = (05)(1000 kg)(25 m2s2)KE = 125000 J
12
Click on the box to see the solution
Teacher N
otes
37
11 A 10 kg snowball is rolling down a hill Just before reaching the bottom its velocity is measured to be 10 ms What is the kinetic energy of the ball at this position
Answer
38
12 A 100 kg running back in football is running with a velocity of 2 ms What is his kinetic energy
Answer
KE= 12 mv2KE= 12 (100 kg) (2 ms)2KE= 12 (100 kg) (4m2s2)KE= 200 J
39
13 A 2000 kg car with a velocity of 20 ms slows down and stops at a red light What is the change in kinetic energy
Answer
40
14 A 50 kg girl rode her 12 kg bicycle in a race She started from rest and peddled with a velocity of 10 ms What is the change in kinetic energy of the girl and her bicycle
Answer
41
Thinking Mathematically
KE = mv212
We have already said that mass is directly proportional to kinetic energy
This means that if the mass of the object doubles the
kinetic energy ___________ If the mass of the object increases by a
factor of 5 then the kinetic energy___________ by ______________
If the mass of the object decreases by half then the kinetic
energy will ____________ by ___________
doubles
increases a factor of 5
decrease half
42
15 If the mass of a wagon is doubled its kinetic energy
A increases
B decreases
Answer
43
16 If the mass of a wagon is doubled by what factor does the kinetic energy increase
Answer
44
Thinking Mathematically
Kinetic energy can be solved by using the equation
KE = mv212
From the equation we can see that the kinetic energy is also directly proportional to the square of the velocity
This means that if the velocity doubles the kinetic energy increases by a factor of 4
22=4
If the velocity is quadrupled then the kinetic energy increases by a factor of 16
42= 16
45
17 If the velocity of a wagon is tripled its kinetic energy
Answer
A increases
B decreases
46
18 If the velocity of a wagon is tripled by what factor does the kinetic energy increase
Answer
47
19 Two balls are moving with the same velocity ball A has a mass of 10 kg and ball B has a mass of 40 kg How much more kinetic energy does ball B have
Answer
48
20 A cart halves its mass and at the same time doubles its speed Does the kinetic energy increase or decrease By what factor does the kinetic energy change
A increase 2
B increase 4
C decrease 2
D decrease 4
Answer
bull half the mass gives 12 the KEbull double the speed gives 4 x KEbull therefore (12)(4)= 2
A
49
Stored Energy
Return to Tableof Contents
50
Where does Kinetic Energy Come From
Imagine a roller coaster car that is at the top of the first hill and is stopped
Does the car stay stopped at the top of the hill for the entire ride
What happens
51
Where does Kinetic Energy Come From
Once the car leans over the edge gravity pulls it down The ride is taking advantage of the gravitational attraction between the car and Earth to give the car kinetic energy and make it go faster as it falls
The kinetic energy the car is receiving is coming from another type of energy called potential energy
52
Where does Kinetic Energy Come From
Potential energy is energy stored in an object due to the objects position The roller coaster car on the previous slide had stored energy due to its height above the ground
There are two forms of potential energy that we will be looking at in this unit
Gravitational Potential Energy
and
Elastic Potential Energy
53
Gravitational Potential Energy
The potential energy due to elevated positions is called gravitational potential energy
Gravitational potential energy is stored energy and it can be used at a later time to cause an object to moveOnce the person steps off the diving board the gravitational potential energy is converted into kinetic energy and the person falls (moves)
54
Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
55
Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
56
h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
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91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
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113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
15
2 A wagon is rolling down a hill A man tries to stop the wagon by trying to push it back up the hill but he is unsuccessful Is the man doing positive or negative work
A positive
B negative
Answer
16
3 A boy kicks a soccer ball into a net Did the boy do positive or negative work on the ball
A positive
B negative
Answer
17
4 A woman walks across an icy sidewalk that has been covered in salt to help make it less slippery Is the salt doing positive or negative work on the womans shoes
A positive
B negative Answer
18
5 Jill is waiting for the bus and she forgot her mittens She rubs her hands together to keep them warm In this situation there is ______________ energy due to the movement of her hands There is also _______________ energy due to the heat she generates by rubbing her hands together
A mechanical nonshymechanical
B nonshymechanical mechanical
Answer
19
Mechanical Energy
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20
__________ Energy
__________ Energy __________ Energy
Forms of Mechanical EnergyMechanical Energy can be broken down into two different types of Energy energy of motion which is called Kinetic Energy and stored energy which is called Potential Energy Potential Energy has two forms Gravitational and Elastic depending upon how the energy is stored
Write the underlined words into the correct
place in the diagram
21
6 Which of the following is a form of mechanical energy
A Kinetic
B Thermal
C Chemical
D Solar
Answer
A shy Kinetic
22
Energy of Motion
Return to Tableof Contents
23
7 Which of the following is a type of energy which is used to describe the motion of an object
A Electrical Energy
B Nuclear Energy
C Kinetic Energy
D All of the above
Answer
C shy Kinetic
24
Energy of Motion
In order for an object to move one of two scenarios has to occur
1 The object uses some of the potential energy that it had stored
2 Energy is transferred to the object from an outside source
In either case now that the object is in motion the object is experiencing kinetic energy
25
An objects state of motion can be described by looking at the amount of kinetic energy that the object has at that moment in time
Kinetic Energy
Since the state of motion of an object can change with time the kinetic energy of an object can also change with time
26
velocitymass
The amount of kinetic energy that an object possesses is dependent on two factors
Kinetic Energy
Both of these factors are directly proportional to the kinetic energy We talked about this mathematical relationship in the
last chapter What did directly proportional mean
and
27
Kinetic Energy Mass Velocity
Since kinetic energy is the energy of motion
the object has to have a velocity to have kinetic energy The larger the
velocity the __________________ the kinetic energy
The larger the mass the more energy is needed to move the object
therefore the _______________ the kinetic energy
28
How Does Kinetic Energy Depend on MassIf two identical objects are moving at the same velocity they will have the same kinetic energy
v = 5 ms
v = 5 ms
A tennis ball and a bowling ball are both shown above The bowling ball is heavier than the tennis ball Which ball would have more kinetic energy
However if one object has more mass than the other the heavier object will have more kinetic energy
29
Velocity vs Speed
Remember that velocity is another way to measure motion V elocity is the speed of an object with direction Speed does not have a direction so we call speed a scalar quantity
Since velocity has both magnitude and direction it is a vector quantity
Runners speed 10 kmhr
Runners velocity 10 kmhr to the East
30
How Does Kinetic Energy Depend on Velocity
In this picture the hare is moving faster than the tortoise at this point
If we assumed that they had the same mass who would have more kinetic energy Why Discuss this with a partner
31
v = 5 ms
v = 10 ms
How Does Kinetic Energy Depend upon Velocity
If two identical objects are moving at the same velocity then they will have the same kinetic energy However if one of the objects is moving faster the faster one will have more kinetic energy
In the diagram above two identical tennis balls are moving Which tennis ball has more kinetic energy and why
32
8 Three different emergency vehicles are noticed driving on the highway at a speed of 25 ms Which of the following cars have the most kinetic energy at that moment
A a police car
B an ambulance
C a firetruck
D they all have the same kinetic energy
Answer
C
33
9 Three different baseball pitchers had the speed of their fastball measured by a radar gun Which of the following pitchers fastball had the smallest amount of kinetic energy
A a little league pitcher (22 ms)
B a high school pitcher (33 ms)
C a major league pitcher (41ms)
D they all had the same kinetic energy
Answer
34
10 Which of the following situations has the least kinetic energy Be ready to explain your answer
A a man sitting still on a park bench
B a child riding a bike
C a woman driving a car
D it is impossible to tell
Answer
35
Calculating Kinetic Energy
Kinetic energy can be solved for by using the equation
12KE = mv2
Lets fill in the table below
variable unitsName
Kinetic Energy
mms
36
Example shy Calculating Kinetic Energy
A car which has a mass of 1000 kg is moving with a velocity of 5 ms How much kinetic energy does the car possess Calculate the cars kinetic energy
KE = mv2KE = (05)(1000 kg)(5 ms)2
KE = (05)(1000 kg)(25 m2s2)KE = 125000 J
12
Click on the box to see the solution
Teacher N
otes
37
11 A 10 kg snowball is rolling down a hill Just before reaching the bottom its velocity is measured to be 10 ms What is the kinetic energy of the ball at this position
Answer
38
12 A 100 kg running back in football is running with a velocity of 2 ms What is his kinetic energy
Answer
KE= 12 mv2KE= 12 (100 kg) (2 ms)2KE= 12 (100 kg) (4m2s2)KE= 200 J
39
13 A 2000 kg car with a velocity of 20 ms slows down and stops at a red light What is the change in kinetic energy
Answer
40
14 A 50 kg girl rode her 12 kg bicycle in a race She started from rest and peddled with a velocity of 10 ms What is the change in kinetic energy of the girl and her bicycle
Answer
41
Thinking Mathematically
KE = mv212
We have already said that mass is directly proportional to kinetic energy
This means that if the mass of the object doubles the
kinetic energy ___________ If the mass of the object increases by a
factor of 5 then the kinetic energy___________ by ______________
If the mass of the object decreases by half then the kinetic
energy will ____________ by ___________
doubles
increases a factor of 5
decrease half
42
15 If the mass of a wagon is doubled its kinetic energy
A increases
B decreases
Answer
43
16 If the mass of a wagon is doubled by what factor does the kinetic energy increase
Answer
44
Thinking Mathematically
Kinetic energy can be solved by using the equation
KE = mv212
From the equation we can see that the kinetic energy is also directly proportional to the square of the velocity
This means that if the velocity doubles the kinetic energy increases by a factor of 4
22=4
If the velocity is quadrupled then the kinetic energy increases by a factor of 16
42= 16
45
17 If the velocity of a wagon is tripled its kinetic energy
Answer
A increases
B decreases
46
18 If the velocity of a wagon is tripled by what factor does the kinetic energy increase
Answer
47
19 Two balls are moving with the same velocity ball A has a mass of 10 kg and ball B has a mass of 40 kg How much more kinetic energy does ball B have
Answer
48
20 A cart halves its mass and at the same time doubles its speed Does the kinetic energy increase or decrease By what factor does the kinetic energy change
A increase 2
B increase 4
C decrease 2
D decrease 4
Answer
bull half the mass gives 12 the KEbull double the speed gives 4 x KEbull therefore (12)(4)= 2
A
49
Stored Energy
Return to Tableof Contents
50
Where does Kinetic Energy Come From
Imagine a roller coaster car that is at the top of the first hill and is stopped
Does the car stay stopped at the top of the hill for the entire ride
What happens
51
Where does Kinetic Energy Come From
Once the car leans over the edge gravity pulls it down The ride is taking advantage of the gravitational attraction between the car and Earth to give the car kinetic energy and make it go faster as it falls
The kinetic energy the car is receiving is coming from another type of energy called potential energy
52
Where does Kinetic Energy Come From
Potential energy is energy stored in an object due to the objects position The roller coaster car on the previous slide had stored energy due to its height above the ground
There are two forms of potential energy that we will be looking at in this unit
Gravitational Potential Energy
and
Elastic Potential Energy
53
Gravitational Potential Energy
The potential energy due to elevated positions is called gravitational potential energy
Gravitational potential energy is stored energy and it can be used at a later time to cause an object to moveOnce the person steps off the diving board the gravitational potential energy is converted into kinetic energy and the person falls (moves)
54
Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
55
Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
56
h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
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91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
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113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
16
3 A boy kicks a soccer ball into a net Did the boy do positive or negative work on the ball
A positive
B negative
Answer
17
4 A woman walks across an icy sidewalk that has been covered in salt to help make it less slippery Is the salt doing positive or negative work on the womans shoes
A positive
B negative Answer
18
5 Jill is waiting for the bus and she forgot her mittens She rubs her hands together to keep them warm In this situation there is ______________ energy due to the movement of her hands There is also _______________ energy due to the heat she generates by rubbing her hands together
A mechanical nonshymechanical
B nonshymechanical mechanical
Answer
19
Mechanical Energy
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20
__________ Energy
__________ Energy __________ Energy
Forms of Mechanical EnergyMechanical Energy can be broken down into two different types of Energy energy of motion which is called Kinetic Energy and stored energy which is called Potential Energy Potential Energy has two forms Gravitational and Elastic depending upon how the energy is stored
Write the underlined words into the correct
place in the diagram
21
6 Which of the following is a form of mechanical energy
A Kinetic
B Thermal
C Chemical
D Solar
Answer
A shy Kinetic
22
Energy of Motion
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23
7 Which of the following is a type of energy which is used to describe the motion of an object
A Electrical Energy
B Nuclear Energy
C Kinetic Energy
D All of the above
Answer
C shy Kinetic
24
Energy of Motion
In order for an object to move one of two scenarios has to occur
1 The object uses some of the potential energy that it had stored
2 Energy is transferred to the object from an outside source
In either case now that the object is in motion the object is experiencing kinetic energy
25
An objects state of motion can be described by looking at the amount of kinetic energy that the object has at that moment in time
Kinetic Energy
Since the state of motion of an object can change with time the kinetic energy of an object can also change with time
26
velocitymass
The amount of kinetic energy that an object possesses is dependent on two factors
Kinetic Energy
Both of these factors are directly proportional to the kinetic energy We talked about this mathematical relationship in the
last chapter What did directly proportional mean
and
27
Kinetic Energy Mass Velocity
Since kinetic energy is the energy of motion
the object has to have a velocity to have kinetic energy The larger the
velocity the __________________ the kinetic energy
The larger the mass the more energy is needed to move the object
therefore the _______________ the kinetic energy
28
How Does Kinetic Energy Depend on MassIf two identical objects are moving at the same velocity they will have the same kinetic energy
v = 5 ms
v = 5 ms
A tennis ball and a bowling ball are both shown above The bowling ball is heavier than the tennis ball Which ball would have more kinetic energy
However if one object has more mass than the other the heavier object will have more kinetic energy
29
Velocity vs Speed
Remember that velocity is another way to measure motion V elocity is the speed of an object with direction Speed does not have a direction so we call speed a scalar quantity
Since velocity has both magnitude and direction it is a vector quantity
Runners speed 10 kmhr
Runners velocity 10 kmhr to the East
30
How Does Kinetic Energy Depend on Velocity
In this picture the hare is moving faster than the tortoise at this point
If we assumed that they had the same mass who would have more kinetic energy Why Discuss this with a partner
31
v = 5 ms
v = 10 ms
How Does Kinetic Energy Depend upon Velocity
If two identical objects are moving at the same velocity then they will have the same kinetic energy However if one of the objects is moving faster the faster one will have more kinetic energy
In the diagram above two identical tennis balls are moving Which tennis ball has more kinetic energy and why
32
8 Three different emergency vehicles are noticed driving on the highway at a speed of 25 ms Which of the following cars have the most kinetic energy at that moment
A a police car
B an ambulance
C a firetruck
D they all have the same kinetic energy
Answer
C
33
9 Three different baseball pitchers had the speed of their fastball measured by a radar gun Which of the following pitchers fastball had the smallest amount of kinetic energy
A a little league pitcher (22 ms)
B a high school pitcher (33 ms)
C a major league pitcher (41ms)
D they all had the same kinetic energy
Answer
34
10 Which of the following situations has the least kinetic energy Be ready to explain your answer
A a man sitting still on a park bench
B a child riding a bike
C a woman driving a car
D it is impossible to tell
Answer
35
Calculating Kinetic Energy
Kinetic energy can be solved for by using the equation
12KE = mv2
Lets fill in the table below
variable unitsName
Kinetic Energy
mms
36
Example shy Calculating Kinetic Energy
A car which has a mass of 1000 kg is moving with a velocity of 5 ms How much kinetic energy does the car possess Calculate the cars kinetic energy
KE = mv2KE = (05)(1000 kg)(5 ms)2
KE = (05)(1000 kg)(25 m2s2)KE = 125000 J
12
Click on the box to see the solution
Teacher N
otes
37
11 A 10 kg snowball is rolling down a hill Just before reaching the bottom its velocity is measured to be 10 ms What is the kinetic energy of the ball at this position
Answer
38
12 A 100 kg running back in football is running with a velocity of 2 ms What is his kinetic energy
Answer
KE= 12 mv2KE= 12 (100 kg) (2 ms)2KE= 12 (100 kg) (4m2s2)KE= 200 J
39
13 A 2000 kg car with a velocity of 20 ms slows down and stops at a red light What is the change in kinetic energy
Answer
40
14 A 50 kg girl rode her 12 kg bicycle in a race She started from rest and peddled with a velocity of 10 ms What is the change in kinetic energy of the girl and her bicycle
Answer
41
Thinking Mathematically
KE = mv212
We have already said that mass is directly proportional to kinetic energy
This means that if the mass of the object doubles the
kinetic energy ___________ If the mass of the object increases by a
factor of 5 then the kinetic energy___________ by ______________
If the mass of the object decreases by half then the kinetic
energy will ____________ by ___________
doubles
increases a factor of 5
decrease half
42
15 If the mass of a wagon is doubled its kinetic energy
A increases
B decreases
Answer
43
16 If the mass of a wagon is doubled by what factor does the kinetic energy increase
Answer
44
Thinking Mathematically
Kinetic energy can be solved by using the equation
KE = mv212
From the equation we can see that the kinetic energy is also directly proportional to the square of the velocity
This means that if the velocity doubles the kinetic energy increases by a factor of 4
22=4
If the velocity is quadrupled then the kinetic energy increases by a factor of 16
42= 16
45
17 If the velocity of a wagon is tripled its kinetic energy
Answer
A increases
B decreases
46
18 If the velocity of a wagon is tripled by what factor does the kinetic energy increase
Answer
47
19 Two balls are moving with the same velocity ball A has a mass of 10 kg and ball B has a mass of 40 kg How much more kinetic energy does ball B have
Answer
48
20 A cart halves its mass and at the same time doubles its speed Does the kinetic energy increase or decrease By what factor does the kinetic energy change
A increase 2
B increase 4
C decrease 2
D decrease 4
Answer
bull half the mass gives 12 the KEbull double the speed gives 4 x KEbull therefore (12)(4)= 2
A
49
Stored Energy
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50
Where does Kinetic Energy Come From
Imagine a roller coaster car that is at the top of the first hill and is stopped
Does the car stay stopped at the top of the hill for the entire ride
What happens
51
Where does Kinetic Energy Come From
Once the car leans over the edge gravity pulls it down The ride is taking advantage of the gravitational attraction between the car and Earth to give the car kinetic energy and make it go faster as it falls
The kinetic energy the car is receiving is coming from another type of energy called potential energy
52
Where does Kinetic Energy Come From
Potential energy is energy stored in an object due to the objects position The roller coaster car on the previous slide had stored energy due to its height above the ground
There are two forms of potential energy that we will be looking at in this unit
Gravitational Potential Energy
and
Elastic Potential Energy
53
Gravitational Potential Energy
The potential energy due to elevated positions is called gravitational potential energy
Gravitational potential energy is stored energy and it can be used at a later time to cause an object to moveOnce the person steps off the diving board the gravitational potential energy is converted into kinetic energy and the person falls (moves)
54
Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
55
Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
56
h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
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91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
17
4 A woman walks across an icy sidewalk that has been covered in salt to help make it less slippery Is the salt doing positive or negative work on the womans shoes
A positive
B negative Answer
18
5 Jill is waiting for the bus and she forgot her mittens She rubs her hands together to keep them warm In this situation there is ______________ energy due to the movement of her hands There is also _______________ energy due to the heat she generates by rubbing her hands together
A mechanical nonshymechanical
B nonshymechanical mechanical
Answer
19
Mechanical Energy
Return to Tableof Contents
20
__________ Energy
__________ Energy __________ Energy
Forms of Mechanical EnergyMechanical Energy can be broken down into two different types of Energy energy of motion which is called Kinetic Energy and stored energy which is called Potential Energy Potential Energy has two forms Gravitational and Elastic depending upon how the energy is stored
Write the underlined words into the correct
place in the diagram
21
6 Which of the following is a form of mechanical energy
A Kinetic
B Thermal
C Chemical
D Solar
Answer
A shy Kinetic
22
Energy of Motion
Return to Tableof Contents
23
7 Which of the following is a type of energy which is used to describe the motion of an object
A Electrical Energy
B Nuclear Energy
C Kinetic Energy
D All of the above
Answer
C shy Kinetic
24
Energy of Motion
In order for an object to move one of two scenarios has to occur
1 The object uses some of the potential energy that it had stored
2 Energy is transferred to the object from an outside source
In either case now that the object is in motion the object is experiencing kinetic energy
25
An objects state of motion can be described by looking at the amount of kinetic energy that the object has at that moment in time
Kinetic Energy
Since the state of motion of an object can change with time the kinetic energy of an object can also change with time
26
velocitymass
The amount of kinetic energy that an object possesses is dependent on two factors
Kinetic Energy
Both of these factors are directly proportional to the kinetic energy We talked about this mathematical relationship in the
last chapter What did directly proportional mean
and
27
Kinetic Energy Mass Velocity
Since kinetic energy is the energy of motion
the object has to have a velocity to have kinetic energy The larger the
velocity the __________________ the kinetic energy
The larger the mass the more energy is needed to move the object
therefore the _______________ the kinetic energy
28
How Does Kinetic Energy Depend on MassIf two identical objects are moving at the same velocity they will have the same kinetic energy
v = 5 ms
v = 5 ms
A tennis ball and a bowling ball are both shown above The bowling ball is heavier than the tennis ball Which ball would have more kinetic energy
However if one object has more mass than the other the heavier object will have more kinetic energy
29
Velocity vs Speed
Remember that velocity is another way to measure motion V elocity is the speed of an object with direction Speed does not have a direction so we call speed a scalar quantity
Since velocity has both magnitude and direction it is a vector quantity
Runners speed 10 kmhr
Runners velocity 10 kmhr to the East
30
How Does Kinetic Energy Depend on Velocity
In this picture the hare is moving faster than the tortoise at this point
If we assumed that they had the same mass who would have more kinetic energy Why Discuss this with a partner
31
v = 5 ms
v = 10 ms
How Does Kinetic Energy Depend upon Velocity
If two identical objects are moving at the same velocity then they will have the same kinetic energy However if one of the objects is moving faster the faster one will have more kinetic energy
In the diagram above two identical tennis balls are moving Which tennis ball has more kinetic energy and why
32
8 Three different emergency vehicles are noticed driving on the highway at a speed of 25 ms Which of the following cars have the most kinetic energy at that moment
A a police car
B an ambulance
C a firetruck
D they all have the same kinetic energy
Answer
C
33
9 Three different baseball pitchers had the speed of their fastball measured by a radar gun Which of the following pitchers fastball had the smallest amount of kinetic energy
A a little league pitcher (22 ms)
B a high school pitcher (33 ms)
C a major league pitcher (41ms)
D they all had the same kinetic energy
Answer
34
10 Which of the following situations has the least kinetic energy Be ready to explain your answer
A a man sitting still on a park bench
B a child riding a bike
C a woman driving a car
D it is impossible to tell
Answer
35
Calculating Kinetic Energy
Kinetic energy can be solved for by using the equation
12KE = mv2
Lets fill in the table below
variable unitsName
Kinetic Energy
mms
36
Example shy Calculating Kinetic Energy
A car which has a mass of 1000 kg is moving with a velocity of 5 ms How much kinetic energy does the car possess Calculate the cars kinetic energy
KE = mv2KE = (05)(1000 kg)(5 ms)2
KE = (05)(1000 kg)(25 m2s2)KE = 125000 J
12
Click on the box to see the solution
Teacher N
otes
37
11 A 10 kg snowball is rolling down a hill Just before reaching the bottom its velocity is measured to be 10 ms What is the kinetic energy of the ball at this position
Answer
38
12 A 100 kg running back in football is running with a velocity of 2 ms What is his kinetic energy
Answer
KE= 12 mv2KE= 12 (100 kg) (2 ms)2KE= 12 (100 kg) (4m2s2)KE= 200 J
39
13 A 2000 kg car with a velocity of 20 ms slows down and stops at a red light What is the change in kinetic energy
Answer
40
14 A 50 kg girl rode her 12 kg bicycle in a race She started from rest and peddled with a velocity of 10 ms What is the change in kinetic energy of the girl and her bicycle
Answer
41
Thinking Mathematically
KE = mv212
We have already said that mass is directly proportional to kinetic energy
This means that if the mass of the object doubles the
kinetic energy ___________ If the mass of the object increases by a
factor of 5 then the kinetic energy___________ by ______________
If the mass of the object decreases by half then the kinetic
energy will ____________ by ___________
doubles
increases a factor of 5
decrease half
42
15 If the mass of a wagon is doubled its kinetic energy
A increases
B decreases
Answer
43
16 If the mass of a wagon is doubled by what factor does the kinetic energy increase
Answer
44
Thinking Mathematically
Kinetic energy can be solved by using the equation
KE = mv212
From the equation we can see that the kinetic energy is also directly proportional to the square of the velocity
This means that if the velocity doubles the kinetic energy increases by a factor of 4
22=4
If the velocity is quadrupled then the kinetic energy increases by a factor of 16
42= 16
45
17 If the velocity of a wagon is tripled its kinetic energy
Answer
A increases
B decreases
46
18 If the velocity of a wagon is tripled by what factor does the kinetic energy increase
Answer
47
19 Two balls are moving with the same velocity ball A has a mass of 10 kg and ball B has a mass of 40 kg How much more kinetic energy does ball B have
Answer
48
20 A cart halves its mass and at the same time doubles its speed Does the kinetic energy increase or decrease By what factor does the kinetic energy change
A increase 2
B increase 4
C decrease 2
D decrease 4
Answer
bull half the mass gives 12 the KEbull double the speed gives 4 x KEbull therefore (12)(4)= 2
A
49
Stored Energy
Return to Tableof Contents
50
Where does Kinetic Energy Come From
Imagine a roller coaster car that is at the top of the first hill and is stopped
Does the car stay stopped at the top of the hill for the entire ride
What happens
51
Where does Kinetic Energy Come From
Once the car leans over the edge gravity pulls it down The ride is taking advantage of the gravitational attraction between the car and Earth to give the car kinetic energy and make it go faster as it falls
The kinetic energy the car is receiving is coming from another type of energy called potential energy
52
Where does Kinetic Energy Come From
Potential energy is energy stored in an object due to the objects position The roller coaster car on the previous slide had stored energy due to its height above the ground
There are two forms of potential energy that we will be looking at in this unit
Gravitational Potential Energy
and
Elastic Potential Energy
53
Gravitational Potential Energy
The potential energy due to elevated positions is called gravitational potential energy
Gravitational potential energy is stored energy and it can be used at a later time to cause an object to moveOnce the person steps off the diving board the gravitational potential energy is converted into kinetic energy and the person falls (moves)
54
Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
55
Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
56
h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
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18
5 Jill is waiting for the bus and she forgot her mittens She rubs her hands together to keep them warm In this situation there is ______________ energy due to the movement of her hands There is also _______________ energy due to the heat she generates by rubbing her hands together
A mechanical nonshymechanical
B nonshymechanical mechanical
Answer
19
Mechanical Energy
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20
__________ Energy
__________ Energy __________ Energy
Forms of Mechanical EnergyMechanical Energy can be broken down into two different types of Energy energy of motion which is called Kinetic Energy and stored energy which is called Potential Energy Potential Energy has two forms Gravitational and Elastic depending upon how the energy is stored
Write the underlined words into the correct
place in the diagram
21
6 Which of the following is a form of mechanical energy
A Kinetic
B Thermal
C Chemical
D Solar
Answer
A shy Kinetic
22
Energy of Motion
Return to Tableof Contents
23
7 Which of the following is a type of energy which is used to describe the motion of an object
A Electrical Energy
B Nuclear Energy
C Kinetic Energy
D All of the above
Answer
C shy Kinetic
24
Energy of Motion
In order for an object to move one of two scenarios has to occur
1 The object uses some of the potential energy that it had stored
2 Energy is transferred to the object from an outside source
In either case now that the object is in motion the object is experiencing kinetic energy
25
An objects state of motion can be described by looking at the amount of kinetic energy that the object has at that moment in time
Kinetic Energy
Since the state of motion of an object can change with time the kinetic energy of an object can also change with time
26
velocitymass
The amount of kinetic energy that an object possesses is dependent on two factors
Kinetic Energy
Both of these factors are directly proportional to the kinetic energy We talked about this mathematical relationship in the
last chapter What did directly proportional mean
and
27
Kinetic Energy Mass Velocity
Since kinetic energy is the energy of motion
the object has to have a velocity to have kinetic energy The larger the
velocity the __________________ the kinetic energy
The larger the mass the more energy is needed to move the object
therefore the _______________ the kinetic energy
28
How Does Kinetic Energy Depend on MassIf two identical objects are moving at the same velocity they will have the same kinetic energy
v = 5 ms
v = 5 ms
A tennis ball and a bowling ball are both shown above The bowling ball is heavier than the tennis ball Which ball would have more kinetic energy
However if one object has more mass than the other the heavier object will have more kinetic energy
29
Velocity vs Speed
Remember that velocity is another way to measure motion V elocity is the speed of an object with direction Speed does not have a direction so we call speed a scalar quantity
Since velocity has both magnitude and direction it is a vector quantity
Runners speed 10 kmhr
Runners velocity 10 kmhr to the East
30
How Does Kinetic Energy Depend on Velocity
In this picture the hare is moving faster than the tortoise at this point
If we assumed that they had the same mass who would have more kinetic energy Why Discuss this with a partner
31
v = 5 ms
v = 10 ms
How Does Kinetic Energy Depend upon Velocity
If two identical objects are moving at the same velocity then they will have the same kinetic energy However if one of the objects is moving faster the faster one will have more kinetic energy
In the diagram above two identical tennis balls are moving Which tennis ball has more kinetic energy and why
32
8 Three different emergency vehicles are noticed driving on the highway at a speed of 25 ms Which of the following cars have the most kinetic energy at that moment
A a police car
B an ambulance
C a firetruck
D they all have the same kinetic energy
Answer
C
33
9 Three different baseball pitchers had the speed of their fastball measured by a radar gun Which of the following pitchers fastball had the smallest amount of kinetic energy
A a little league pitcher (22 ms)
B a high school pitcher (33 ms)
C a major league pitcher (41ms)
D they all had the same kinetic energy
Answer
34
10 Which of the following situations has the least kinetic energy Be ready to explain your answer
A a man sitting still on a park bench
B a child riding a bike
C a woman driving a car
D it is impossible to tell
Answer
35
Calculating Kinetic Energy
Kinetic energy can be solved for by using the equation
12KE = mv2
Lets fill in the table below
variable unitsName
Kinetic Energy
mms
36
Example shy Calculating Kinetic Energy
A car which has a mass of 1000 kg is moving with a velocity of 5 ms How much kinetic energy does the car possess Calculate the cars kinetic energy
KE = mv2KE = (05)(1000 kg)(5 ms)2
KE = (05)(1000 kg)(25 m2s2)KE = 125000 J
12
Click on the box to see the solution
Teacher N
otes
37
11 A 10 kg snowball is rolling down a hill Just before reaching the bottom its velocity is measured to be 10 ms What is the kinetic energy of the ball at this position
Answer
38
12 A 100 kg running back in football is running with a velocity of 2 ms What is his kinetic energy
Answer
KE= 12 mv2KE= 12 (100 kg) (2 ms)2KE= 12 (100 kg) (4m2s2)KE= 200 J
39
13 A 2000 kg car with a velocity of 20 ms slows down and stops at a red light What is the change in kinetic energy
Answer
40
14 A 50 kg girl rode her 12 kg bicycle in a race She started from rest and peddled with a velocity of 10 ms What is the change in kinetic energy of the girl and her bicycle
Answer
41
Thinking Mathematically
KE = mv212
We have already said that mass is directly proportional to kinetic energy
This means that if the mass of the object doubles the
kinetic energy ___________ If the mass of the object increases by a
factor of 5 then the kinetic energy___________ by ______________
If the mass of the object decreases by half then the kinetic
energy will ____________ by ___________
doubles
increases a factor of 5
decrease half
42
15 If the mass of a wagon is doubled its kinetic energy
A increases
B decreases
Answer
43
16 If the mass of a wagon is doubled by what factor does the kinetic energy increase
Answer
44
Thinking Mathematically
Kinetic energy can be solved by using the equation
KE = mv212
From the equation we can see that the kinetic energy is also directly proportional to the square of the velocity
This means that if the velocity doubles the kinetic energy increases by a factor of 4
22=4
If the velocity is quadrupled then the kinetic energy increases by a factor of 16
42= 16
45
17 If the velocity of a wagon is tripled its kinetic energy
Answer
A increases
B decreases
46
18 If the velocity of a wagon is tripled by what factor does the kinetic energy increase
Answer
47
19 Two balls are moving with the same velocity ball A has a mass of 10 kg and ball B has a mass of 40 kg How much more kinetic energy does ball B have
Answer
48
20 A cart halves its mass and at the same time doubles its speed Does the kinetic energy increase or decrease By what factor does the kinetic energy change
A increase 2
B increase 4
C decrease 2
D decrease 4
Answer
bull half the mass gives 12 the KEbull double the speed gives 4 x KEbull therefore (12)(4)= 2
A
49
Stored Energy
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50
Where does Kinetic Energy Come From
Imagine a roller coaster car that is at the top of the first hill and is stopped
Does the car stay stopped at the top of the hill for the entire ride
What happens
51
Where does Kinetic Energy Come From
Once the car leans over the edge gravity pulls it down The ride is taking advantage of the gravitational attraction between the car and Earth to give the car kinetic energy and make it go faster as it falls
The kinetic energy the car is receiving is coming from another type of energy called potential energy
52
Where does Kinetic Energy Come From
Potential energy is energy stored in an object due to the objects position The roller coaster car on the previous slide had stored energy due to its height above the ground
There are two forms of potential energy that we will be looking at in this unit
Gravitational Potential Energy
and
Elastic Potential Energy
53
Gravitational Potential Energy
The potential energy due to elevated positions is called gravitational potential energy
Gravitational potential energy is stored energy and it can be used at a later time to cause an object to moveOnce the person steps off the diving board the gravitational potential energy is converted into kinetic energy and the person falls (moves)
54
Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
55
Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
56
h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
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91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
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113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
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19
Mechanical Energy
Return to Tableof Contents
20
__________ Energy
__________ Energy __________ Energy
Forms of Mechanical EnergyMechanical Energy can be broken down into two different types of Energy energy of motion which is called Kinetic Energy and stored energy which is called Potential Energy Potential Energy has two forms Gravitational and Elastic depending upon how the energy is stored
Write the underlined words into the correct
place in the diagram
21
6 Which of the following is a form of mechanical energy
A Kinetic
B Thermal
C Chemical
D Solar
Answer
A shy Kinetic
22
Energy of Motion
Return to Tableof Contents
23
7 Which of the following is a type of energy which is used to describe the motion of an object
A Electrical Energy
B Nuclear Energy
C Kinetic Energy
D All of the above
Answer
C shy Kinetic
24
Energy of Motion
In order for an object to move one of two scenarios has to occur
1 The object uses some of the potential energy that it had stored
2 Energy is transferred to the object from an outside source
In either case now that the object is in motion the object is experiencing kinetic energy
25
An objects state of motion can be described by looking at the amount of kinetic energy that the object has at that moment in time
Kinetic Energy
Since the state of motion of an object can change with time the kinetic energy of an object can also change with time
26
velocitymass
The amount of kinetic energy that an object possesses is dependent on two factors
Kinetic Energy
Both of these factors are directly proportional to the kinetic energy We talked about this mathematical relationship in the
last chapter What did directly proportional mean
and
27
Kinetic Energy Mass Velocity
Since kinetic energy is the energy of motion
the object has to have a velocity to have kinetic energy The larger the
velocity the __________________ the kinetic energy
The larger the mass the more energy is needed to move the object
therefore the _______________ the kinetic energy
28
How Does Kinetic Energy Depend on MassIf two identical objects are moving at the same velocity they will have the same kinetic energy
v = 5 ms
v = 5 ms
A tennis ball and a bowling ball are both shown above The bowling ball is heavier than the tennis ball Which ball would have more kinetic energy
However if one object has more mass than the other the heavier object will have more kinetic energy
29
Velocity vs Speed
Remember that velocity is another way to measure motion V elocity is the speed of an object with direction Speed does not have a direction so we call speed a scalar quantity
Since velocity has both magnitude and direction it is a vector quantity
Runners speed 10 kmhr
Runners velocity 10 kmhr to the East
30
How Does Kinetic Energy Depend on Velocity
In this picture the hare is moving faster than the tortoise at this point
If we assumed that they had the same mass who would have more kinetic energy Why Discuss this with a partner
31
v = 5 ms
v = 10 ms
How Does Kinetic Energy Depend upon Velocity
If two identical objects are moving at the same velocity then they will have the same kinetic energy However if one of the objects is moving faster the faster one will have more kinetic energy
In the diagram above two identical tennis balls are moving Which tennis ball has more kinetic energy and why
32
8 Three different emergency vehicles are noticed driving on the highway at a speed of 25 ms Which of the following cars have the most kinetic energy at that moment
A a police car
B an ambulance
C a firetruck
D they all have the same kinetic energy
Answer
C
33
9 Three different baseball pitchers had the speed of their fastball measured by a radar gun Which of the following pitchers fastball had the smallest amount of kinetic energy
A a little league pitcher (22 ms)
B a high school pitcher (33 ms)
C a major league pitcher (41ms)
D they all had the same kinetic energy
Answer
34
10 Which of the following situations has the least kinetic energy Be ready to explain your answer
A a man sitting still on a park bench
B a child riding a bike
C a woman driving a car
D it is impossible to tell
Answer
35
Calculating Kinetic Energy
Kinetic energy can be solved for by using the equation
12KE = mv2
Lets fill in the table below
variable unitsName
Kinetic Energy
mms
36
Example shy Calculating Kinetic Energy
A car which has a mass of 1000 kg is moving with a velocity of 5 ms How much kinetic energy does the car possess Calculate the cars kinetic energy
KE = mv2KE = (05)(1000 kg)(5 ms)2
KE = (05)(1000 kg)(25 m2s2)KE = 125000 J
12
Click on the box to see the solution
Teacher N
otes
37
11 A 10 kg snowball is rolling down a hill Just before reaching the bottom its velocity is measured to be 10 ms What is the kinetic energy of the ball at this position
Answer
38
12 A 100 kg running back in football is running with a velocity of 2 ms What is his kinetic energy
Answer
KE= 12 mv2KE= 12 (100 kg) (2 ms)2KE= 12 (100 kg) (4m2s2)KE= 200 J
39
13 A 2000 kg car with a velocity of 20 ms slows down and stops at a red light What is the change in kinetic energy
Answer
40
14 A 50 kg girl rode her 12 kg bicycle in a race She started from rest and peddled with a velocity of 10 ms What is the change in kinetic energy of the girl and her bicycle
Answer
41
Thinking Mathematically
KE = mv212
We have already said that mass is directly proportional to kinetic energy
This means that if the mass of the object doubles the
kinetic energy ___________ If the mass of the object increases by a
factor of 5 then the kinetic energy___________ by ______________
If the mass of the object decreases by half then the kinetic
energy will ____________ by ___________
doubles
increases a factor of 5
decrease half
42
15 If the mass of a wagon is doubled its kinetic energy
A increases
B decreases
Answer
43
16 If the mass of a wagon is doubled by what factor does the kinetic energy increase
Answer
44
Thinking Mathematically
Kinetic energy can be solved by using the equation
KE = mv212
From the equation we can see that the kinetic energy is also directly proportional to the square of the velocity
This means that if the velocity doubles the kinetic energy increases by a factor of 4
22=4
If the velocity is quadrupled then the kinetic energy increases by a factor of 16
42= 16
45
17 If the velocity of a wagon is tripled its kinetic energy
Answer
A increases
B decreases
46
18 If the velocity of a wagon is tripled by what factor does the kinetic energy increase
Answer
47
19 Two balls are moving with the same velocity ball A has a mass of 10 kg and ball B has a mass of 40 kg How much more kinetic energy does ball B have
Answer
48
20 A cart halves its mass and at the same time doubles its speed Does the kinetic energy increase or decrease By what factor does the kinetic energy change
A increase 2
B increase 4
C decrease 2
D decrease 4
Answer
bull half the mass gives 12 the KEbull double the speed gives 4 x KEbull therefore (12)(4)= 2
A
49
Stored Energy
Return to Tableof Contents
50
Where does Kinetic Energy Come From
Imagine a roller coaster car that is at the top of the first hill and is stopped
Does the car stay stopped at the top of the hill for the entire ride
What happens
51
Where does Kinetic Energy Come From
Once the car leans over the edge gravity pulls it down The ride is taking advantage of the gravitational attraction between the car and Earth to give the car kinetic energy and make it go faster as it falls
The kinetic energy the car is receiving is coming from another type of energy called potential energy
52
Where does Kinetic Energy Come From
Potential energy is energy stored in an object due to the objects position The roller coaster car on the previous slide had stored energy due to its height above the ground
There are two forms of potential energy that we will be looking at in this unit
Gravitational Potential Energy
and
Elastic Potential Energy
53
Gravitational Potential Energy
The potential energy due to elevated positions is called gravitational potential energy
Gravitational potential energy is stored energy and it can be used at a later time to cause an object to moveOnce the person steps off the diving board the gravitational potential energy is converted into kinetic energy and the person falls (moves)
54
Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
55
Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
56
h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
20
__________ Energy
__________ Energy __________ Energy
Forms of Mechanical EnergyMechanical Energy can be broken down into two different types of Energy energy of motion which is called Kinetic Energy and stored energy which is called Potential Energy Potential Energy has two forms Gravitational and Elastic depending upon how the energy is stored
Write the underlined words into the correct
place in the diagram
21
6 Which of the following is a form of mechanical energy
A Kinetic
B Thermal
C Chemical
D Solar
Answer
A shy Kinetic
22
Energy of Motion
Return to Tableof Contents
23
7 Which of the following is a type of energy which is used to describe the motion of an object
A Electrical Energy
B Nuclear Energy
C Kinetic Energy
D All of the above
Answer
C shy Kinetic
24
Energy of Motion
In order for an object to move one of two scenarios has to occur
1 The object uses some of the potential energy that it had stored
2 Energy is transferred to the object from an outside source
In either case now that the object is in motion the object is experiencing kinetic energy
25
An objects state of motion can be described by looking at the amount of kinetic energy that the object has at that moment in time
Kinetic Energy
Since the state of motion of an object can change with time the kinetic energy of an object can also change with time
26
velocitymass
The amount of kinetic energy that an object possesses is dependent on two factors
Kinetic Energy
Both of these factors are directly proportional to the kinetic energy We talked about this mathematical relationship in the
last chapter What did directly proportional mean
and
27
Kinetic Energy Mass Velocity
Since kinetic energy is the energy of motion
the object has to have a velocity to have kinetic energy The larger the
velocity the __________________ the kinetic energy
The larger the mass the more energy is needed to move the object
therefore the _______________ the kinetic energy
28
How Does Kinetic Energy Depend on MassIf two identical objects are moving at the same velocity they will have the same kinetic energy
v = 5 ms
v = 5 ms
A tennis ball and a bowling ball are both shown above The bowling ball is heavier than the tennis ball Which ball would have more kinetic energy
However if one object has more mass than the other the heavier object will have more kinetic energy
29
Velocity vs Speed
Remember that velocity is another way to measure motion V elocity is the speed of an object with direction Speed does not have a direction so we call speed a scalar quantity
Since velocity has both magnitude and direction it is a vector quantity
Runners speed 10 kmhr
Runners velocity 10 kmhr to the East
30
How Does Kinetic Energy Depend on Velocity
In this picture the hare is moving faster than the tortoise at this point
If we assumed that they had the same mass who would have more kinetic energy Why Discuss this with a partner
31
v = 5 ms
v = 10 ms
How Does Kinetic Energy Depend upon Velocity
If two identical objects are moving at the same velocity then they will have the same kinetic energy However if one of the objects is moving faster the faster one will have more kinetic energy
In the diagram above two identical tennis balls are moving Which tennis ball has more kinetic energy and why
32
8 Three different emergency vehicles are noticed driving on the highway at a speed of 25 ms Which of the following cars have the most kinetic energy at that moment
A a police car
B an ambulance
C a firetruck
D they all have the same kinetic energy
Answer
C
33
9 Three different baseball pitchers had the speed of their fastball measured by a radar gun Which of the following pitchers fastball had the smallest amount of kinetic energy
A a little league pitcher (22 ms)
B a high school pitcher (33 ms)
C a major league pitcher (41ms)
D they all had the same kinetic energy
Answer
34
10 Which of the following situations has the least kinetic energy Be ready to explain your answer
A a man sitting still on a park bench
B a child riding a bike
C a woman driving a car
D it is impossible to tell
Answer
35
Calculating Kinetic Energy
Kinetic energy can be solved for by using the equation
12KE = mv2
Lets fill in the table below
variable unitsName
Kinetic Energy
mms
36
Example shy Calculating Kinetic Energy
A car which has a mass of 1000 kg is moving with a velocity of 5 ms How much kinetic energy does the car possess Calculate the cars kinetic energy
KE = mv2KE = (05)(1000 kg)(5 ms)2
KE = (05)(1000 kg)(25 m2s2)KE = 125000 J
12
Click on the box to see the solution
Teacher N
otes
37
11 A 10 kg snowball is rolling down a hill Just before reaching the bottom its velocity is measured to be 10 ms What is the kinetic energy of the ball at this position
Answer
38
12 A 100 kg running back in football is running with a velocity of 2 ms What is his kinetic energy
Answer
KE= 12 mv2KE= 12 (100 kg) (2 ms)2KE= 12 (100 kg) (4m2s2)KE= 200 J
39
13 A 2000 kg car with a velocity of 20 ms slows down and stops at a red light What is the change in kinetic energy
Answer
40
14 A 50 kg girl rode her 12 kg bicycle in a race She started from rest and peddled with a velocity of 10 ms What is the change in kinetic energy of the girl and her bicycle
Answer
41
Thinking Mathematically
KE = mv212
We have already said that mass is directly proportional to kinetic energy
This means that if the mass of the object doubles the
kinetic energy ___________ If the mass of the object increases by a
factor of 5 then the kinetic energy___________ by ______________
If the mass of the object decreases by half then the kinetic
energy will ____________ by ___________
doubles
increases a factor of 5
decrease half
42
15 If the mass of a wagon is doubled its kinetic energy
A increases
B decreases
Answer
43
16 If the mass of a wagon is doubled by what factor does the kinetic energy increase
Answer
44
Thinking Mathematically
Kinetic energy can be solved by using the equation
KE = mv212
From the equation we can see that the kinetic energy is also directly proportional to the square of the velocity
This means that if the velocity doubles the kinetic energy increases by a factor of 4
22=4
If the velocity is quadrupled then the kinetic energy increases by a factor of 16
42= 16
45
17 If the velocity of a wagon is tripled its kinetic energy
Answer
A increases
B decreases
46
18 If the velocity of a wagon is tripled by what factor does the kinetic energy increase
Answer
47
19 Two balls are moving with the same velocity ball A has a mass of 10 kg and ball B has a mass of 40 kg How much more kinetic energy does ball B have
Answer
48
20 A cart halves its mass and at the same time doubles its speed Does the kinetic energy increase or decrease By what factor does the kinetic energy change
A increase 2
B increase 4
C decrease 2
D decrease 4
Answer
bull half the mass gives 12 the KEbull double the speed gives 4 x KEbull therefore (12)(4)= 2
A
49
Stored Energy
Return to Tableof Contents
50
Where does Kinetic Energy Come From
Imagine a roller coaster car that is at the top of the first hill and is stopped
Does the car stay stopped at the top of the hill for the entire ride
What happens
51
Where does Kinetic Energy Come From
Once the car leans over the edge gravity pulls it down The ride is taking advantage of the gravitational attraction between the car and Earth to give the car kinetic energy and make it go faster as it falls
The kinetic energy the car is receiving is coming from another type of energy called potential energy
52
Where does Kinetic Energy Come From
Potential energy is energy stored in an object due to the objects position The roller coaster car on the previous slide had stored energy due to its height above the ground
There are two forms of potential energy that we will be looking at in this unit
Gravitational Potential Energy
and
Elastic Potential Energy
53
Gravitational Potential Energy
The potential energy due to elevated positions is called gravitational potential energy
Gravitational potential energy is stored energy and it can be used at a later time to cause an object to moveOnce the person steps off the diving board the gravitational potential energy is converted into kinetic energy and the person falls (moves)
54
Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
55
Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
56
h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
21
6 Which of the following is a form of mechanical energy
A Kinetic
B Thermal
C Chemical
D Solar
Answer
A shy Kinetic
22
Energy of Motion
Return to Tableof Contents
23
7 Which of the following is a type of energy which is used to describe the motion of an object
A Electrical Energy
B Nuclear Energy
C Kinetic Energy
D All of the above
Answer
C shy Kinetic
24
Energy of Motion
In order for an object to move one of two scenarios has to occur
1 The object uses some of the potential energy that it had stored
2 Energy is transferred to the object from an outside source
In either case now that the object is in motion the object is experiencing kinetic energy
25
An objects state of motion can be described by looking at the amount of kinetic energy that the object has at that moment in time
Kinetic Energy
Since the state of motion of an object can change with time the kinetic energy of an object can also change with time
26
velocitymass
The amount of kinetic energy that an object possesses is dependent on two factors
Kinetic Energy
Both of these factors are directly proportional to the kinetic energy We talked about this mathematical relationship in the
last chapter What did directly proportional mean
and
27
Kinetic Energy Mass Velocity
Since kinetic energy is the energy of motion
the object has to have a velocity to have kinetic energy The larger the
velocity the __________________ the kinetic energy
The larger the mass the more energy is needed to move the object
therefore the _______________ the kinetic energy
28
How Does Kinetic Energy Depend on MassIf two identical objects are moving at the same velocity they will have the same kinetic energy
v = 5 ms
v = 5 ms
A tennis ball and a bowling ball are both shown above The bowling ball is heavier than the tennis ball Which ball would have more kinetic energy
However if one object has more mass than the other the heavier object will have more kinetic energy
29
Velocity vs Speed
Remember that velocity is another way to measure motion V elocity is the speed of an object with direction Speed does not have a direction so we call speed a scalar quantity
Since velocity has both magnitude and direction it is a vector quantity
Runners speed 10 kmhr
Runners velocity 10 kmhr to the East
30
How Does Kinetic Energy Depend on Velocity
In this picture the hare is moving faster than the tortoise at this point
If we assumed that they had the same mass who would have more kinetic energy Why Discuss this with a partner
31
v = 5 ms
v = 10 ms
How Does Kinetic Energy Depend upon Velocity
If two identical objects are moving at the same velocity then they will have the same kinetic energy However if one of the objects is moving faster the faster one will have more kinetic energy
In the diagram above two identical tennis balls are moving Which tennis ball has more kinetic energy and why
32
8 Three different emergency vehicles are noticed driving on the highway at a speed of 25 ms Which of the following cars have the most kinetic energy at that moment
A a police car
B an ambulance
C a firetruck
D they all have the same kinetic energy
Answer
C
33
9 Three different baseball pitchers had the speed of their fastball measured by a radar gun Which of the following pitchers fastball had the smallest amount of kinetic energy
A a little league pitcher (22 ms)
B a high school pitcher (33 ms)
C a major league pitcher (41ms)
D they all had the same kinetic energy
Answer
34
10 Which of the following situations has the least kinetic energy Be ready to explain your answer
A a man sitting still on a park bench
B a child riding a bike
C a woman driving a car
D it is impossible to tell
Answer
35
Calculating Kinetic Energy
Kinetic energy can be solved for by using the equation
12KE = mv2
Lets fill in the table below
variable unitsName
Kinetic Energy
mms
36
Example shy Calculating Kinetic Energy
A car which has a mass of 1000 kg is moving with a velocity of 5 ms How much kinetic energy does the car possess Calculate the cars kinetic energy
KE = mv2KE = (05)(1000 kg)(5 ms)2
KE = (05)(1000 kg)(25 m2s2)KE = 125000 J
12
Click on the box to see the solution
Teacher N
otes
37
11 A 10 kg snowball is rolling down a hill Just before reaching the bottom its velocity is measured to be 10 ms What is the kinetic energy of the ball at this position
Answer
38
12 A 100 kg running back in football is running with a velocity of 2 ms What is his kinetic energy
Answer
KE= 12 mv2KE= 12 (100 kg) (2 ms)2KE= 12 (100 kg) (4m2s2)KE= 200 J
39
13 A 2000 kg car with a velocity of 20 ms slows down and stops at a red light What is the change in kinetic energy
Answer
40
14 A 50 kg girl rode her 12 kg bicycle in a race She started from rest and peddled with a velocity of 10 ms What is the change in kinetic energy of the girl and her bicycle
Answer
41
Thinking Mathematically
KE = mv212
We have already said that mass is directly proportional to kinetic energy
This means that if the mass of the object doubles the
kinetic energy ___________ If the mass of the object increases by a
factor of 5 then the kinetic energy___________ by ______________
If the mass of the object decreases by half then the kinetic
energy will ____________ by ___________
doubles
increases a factor of 5
decrease half
42
15 If the mass of a wagon is doubled its kinetic energy
A increases
B decreases
Answer
43
16 If the mass of a wagon is doubled by what factor does the kinetic energy increase
Answer
44
Thinking Mathematically
Kinetic energy can be solved by using the equation
KE = mv212
From the equation we can see that the kinetic energy is also directly proportional to the square of the velocity
This means that if the velocity doubles the kinetic energy increases by a factor of 4
22=4
If the velocity is quadrupled then the kinetic energy increases by a factor of 16
42= 16
45
17 If the velocity of a wagon is tripled its kinetic energy
Answer
A increases
B decreases
46
18 If the velocity of a wagon is tripled by what factor does the kinetic energy increase
Answer
47
19 Two balls are moving with the same velocity ball A has a mass of 10 kg and ball B has a mass of 40 kg How much more kinetic energy does ball B have
Answer
48
20 A cart halves its mass and at the same time doubles its speed Does the kinetic energy increase or decrease By what factor does the kinetic energy change
A increase 2
B increase 4
C decrease 2
D decrease 4
Answer
bull half the mass gives 12 the KEbull double the speed gives 4 x KEbull therefore (12)(4)= 2
A
49
Stored Energy
Return to Tableof Contents
50
Where does Kinetic Energy Come From
Imagine a roller coaster car that is at the top of the first hill and is stopped
Does the car stay stopped at the top of the hill for the entire ride
What happens
51
Where does Kinetic Energy Come From
Once the car leans over the edge gravity pulls it down The ride is taking advantage of the gravitational attraction between the car and Earth to give the car kinetic energy and make it go faster as it falls
The kinetic energy the car is receiving is coming from another type of energy called potential energy
52
Where does Kinetic Energy Come From
Potential energy is energy stored in an object due to the objects position The roller coaster car on the previous slide had stored energy due to its height above the ground
There are two forms of potential energy that we will be looking at in this unit
Gravitational Potential Energy
and
Elastic Potential Energy
53
Gravitational Potential Energy
The potential energy due to elevated positions is called gravitational potential energy
Gravitational potential energy is stored energy and it can be used at a later time to cause an object to moveOnce the person steps off the diving board the gravitational potential energy is converted into kinetic energy and the person falls (moves)
54
Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
55
Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
56
h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
22
Energy of Motion
Return to Tableof Contents
23
7 Which of the following is a type of energy which is used to describe the motion of an object
A Electrical Energy
B Nuclear Energy
C Kinetic Energy
D All of the above
Answer
C shy Kinetic
24
Energy of Motion
In order for an object to move one of two scenarios has to occur
1 The object uses some of the potential energy that it had stored
2 Energy is transferred to the object from an outside source
In either case now that the object is in motion the object is experiencing kinetic energy
25
An objects state of motion can be described by looking at the amount of kinetic energy that the object has at that moment in time
Kinetic Energy
Since the state of motion of an object can change with time the kinetic energy of an object can also change with time
26
velocitymass
The amount of kinetic energy that an object possesses is dependent on two factors
Kinetic Energy
Both of these factors are directly proportional to the kinetic energy We talked about this mathematical relationship in the
last chapter What did directly proportional mean
and
27
Kinetic Energy Mass Velocity
Since kinetic energy is the energy of motion
the object has to have a velocity to have kinetic energy The larger the
velocity the __________________ the kinetic energy
The larger the mass the more energy is needed to move the object
therefore the _______________ the kinetic energy
28
How Does Kinetic Energy Depend on MassIf two identical objects are moving at the same velocity they will have the same kinetic energy
v = 5 ms
v = 5 ms
A tennis ball and a bowling ball are both shown above The bowling ball is heavier than the tennis ball Which ball would have more kinetic energy
However if one object has more mass than the other the heavier object will have more kinetic energy
29
Velocity vs Speed
Remember that velocity is another way to measure motion V elocity is the speed of an object with direction Speed does not have a direction so we call speed a scalar quantity
Since velocity has both magnitude and direction it is a vector quantity
Runners speed 10 kmhr
Runners velocity 10 kmhr to the East
30
How Does Kinetic Energy Depend on Velocity
In this picture the hare is moving faster than the tortoise at this point
If we assumed that they had the same mass who would have more kinetic energy Why Discuss this with a partner
31
v = 5 ms
v = 10 ms
How Does Kinetic Energy Depend upon Velocity
If two identical objects are moving at the same velocity then they will have the same kinetic energy However if one of the objects is moving faster the faster one will have more kinetic energy
In the diagram above two identical tennis balls are moving Which tennis ball has more kinetic energy and why
32
8 Three different emergency vehicles are noticed driving on the highway at a speed of 25 ms Which of the following cars have the most kinetic energy at that moment
A a police car
B an ambulance
C a firetruck
D they all have the same kinetic energy
Answer
C
33
9 Three different baseball pitchers had the speed of their fastball measured by a radar gun Which of the following pitchers fastball had the smallest amount of kinetic energy
A a little league pitcher (22 ms)
B a high school pitcher (33 ms)
C a major league pitcher (41ms)
D they all had the same kinetic energy
Answer
34
10 Which of the following situations has the least kinetic energy Be ready to explain your answer
A a man sitting still on a park bench
B a child riding a bike
C a woman driving a car
D it is impossible to tell
Answer
35
Calculating Kinetic Energy
Kinetic energy can be solved for by using the equation
12KE = mv2
Lets fill in the table below
variable unitsName
Kinetic Energy
mms
36
Example shy Calculating Kinetic Energy
A car which has a mass of 1000 kg is moving with a velocity of 5 ms How much kinetic energy does the car possess Calculate the cars kinetic energy
KE = mv2KE = (05)(1000 kg)(5 ms)2
KE = (05)(1000 kg)(25 m2s2)KE = 125000 J
12
Click on the box to see the solution
Teacher N
otes
37
11 A 10 kg snowball is rolling down a hill Just before reaching the bottom its velocity is measured to be 10 ms What is the kinetic energy of the ball at this position
Answer
38
12 A 100 kg running back in football is running with a velocity of 2 ms What is his kinetic energy
Answer
KE= 12 mv2KE= 12 (100 kg) (2 ms)2KE= 12 (100 kg) (4m2s2)KE= 200 J
39
13 A 2000 kg car with a velocity of 20 ms slows down and stops at a red light What is the change in kinetic energy
Answer
40
14 A 50 kg girl rode her 12 kg bicycle in a race She started from rest and peddled with a velocity of 10 ms What is the change in kinetic energy of the girl and her bicycle
Answer
41
Thinking Mathematically
KE = mv212
We have already said that mass is directly proportional to kinetic energy
This means that if the mass of the object doubles the
kinetic energy ___________ If the mass of the object increases by a
factor of 5 then the kinetic energy___________ by ______________
If the mass of the object decreases by half then the kinetic
energy will ____________ by ___________
doubles
increases a factor of 5
decrease half
42
15 If the mass of a wagon is doubled its kinetic energy
A increases
B decreases
Answer
43
16 If the mass of a wagon is doubled by what factor does the kinetic energy increase
Answer
44
Thinking Mathematically
Kinetic energy can be solved by using the equation
KE = mv212
From the equation we can see that the kinetic energy is also directly proportional to the square of the velocity
This means that if the velocity doubles the kinetic energy increases by a factor of 4
22=4
If the velocity is quadrupled then the kinetic energy increases by a factor of 16
42= 16
45
17 If the velocity of a wagon is tripled its kinetic energy
Answer
A increases
B decreases
46
18 If the velocity of a wagon is tripled by what factor does the kinetic energy increase
Answer
47
19 Two balls are moving with the same velocity ball A has a mass of 10 kg and ball B has a mass of 40 kg How much more kinetic energy does ball B have
Answer
48
20 A cart halves its mass and at the same time doubles its speed Does the kinetic energy increase or decrease By what factor does the kinetic energy change
A increase 2
B increase 4
C decrease 2
D decrease 4
Answer
bull half the mass gives 12 the KEbull double the speed gives 4 x KEbull therefore (12)(4)= 2
A
49
Stored Energy
Return to Tableof Contents
50
Where does Kinetic Energy Come From
Imagine a roller coaster car that is at the top of the first hill and is stopped
Does the car stay stopped at the top of the hill for the entire ride
What happens
51
Where does Kinetic Energy Come From
Once the car leans over the edge gravity pulls it down The ride is taking advantage of the gravitational attraction between the car and Earth to give the car kinetic energy and make it go faster as it falls
The kinetic energy the car is receiving is coming from another type of energy called potential energy
52
Where does Kinetic Energy Come From
Potential energy is energy stored in an object due to the objects position The roller coaster car on the previous slide had stored energy due to its height above the ground
There are two forms of potential energy that we will be looking at in this unit
Gravitational Potential Energy
and
Elastic Potential Energy
53
Gravitational Potential Energy
The potential energy due to elevated positions is called gravitational potential energy
Gravitational potential energy is stored energy and it can be used at a later time to cause an object to moveOnce the person steps off the diving board the gravitational potential energy is converted into kinetic energy and the person falls (moves)
54
Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
55
Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
56
h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
23
7 Which of the following is a type of energy which is used to describe the motion of an object
A Electrical Energy
B Nuclear Energy
C Kinetic Energy
D All of the above
Answer
C shy Kinetic
24
Energy of Motion
In order for an object to move one of two scenarios has to occur
1 The object uses some of the potential energy that it had stored
2 Energy is transferred to the object from an outside source
In either case now that the object is in motion the object is experiencing kinetic energy
25
An objects state of motion can be described by looking at the amount of kinetic energy that the object has at that moment in time
Kinetic Energy
Since the state of motion of an object can change with time the kinetic energy of an object can also change with time
26
velocitymass
The amount of kinetic energy that an object possesses is dependent on two factors
Kinetic Energy
Both of these factors are directly proportional to the kinetic energy We talked about this mathematical relationship in the
last chapter What did directly proportional mean
and
27
Kinetic Energy Mass Velocity
Since kinetic energy is the energy of motion
the object has to have a velocity to have kinetic energy The larger the
velocity the __________________ the kinetic energy
The larger the mass the more energy is needed to move the object
therefore the _______________ the kinetic energy
28
How Does Kinetic Energy Depend on MassIf two identical objects are moving at the same velocity they will have the same kinetic energy
v = 5 ms
v = 5 ms
A tennis ball and a bowling ball are both shown above The bowling ball is heavier than the tennis ball Which ball would have more kinetic energy
However if one object has more mass than the other the heavier object will have more kinetic energy
29
Velocity vs Speed
Remember that velocity is another way to measure motion V elocity is the speed of an object with direction Speed does not have a direction so we call speed a scalar quantity
Since velocity has both magnitude and direction it is a vector quantity
Runners speed 10 kmhr
Runners velocity 10 kmhr to the East
30
How Does Kinetic Energy Depend on Velocity
In this picture the hare is moving faster than the tortoise at this point
If we assumed that they had the same mass who would have more kinetic energy Why Discuss this with a partner
31
v = 5 ms
v = 10 ms
How Does Kinetic Energy Depend upon Velocity
If two identical objects are moving at the same velocity then they will have the same kinetic energy However if one of the objects is moving faster the faster one will have more kinetic energy
In the diagram above two identical tennis balls are moving Which tennis ball has more kinetic energy and why
32
8 Three different emergency vehicles are noticed driving on the highway at a speed of 25 ms Which of the following cars have the most kinetic energy at that moment
A a police car
B an ambulance
C a firetruck
D they all have the same kinetic energy
Answer
C
33
9 Three different baseball pitchers had the speed of their fastball measured by a radar gun Which of the following pitchers fastball had the smallest amount of kinetic energy
A a little league pitcher (22 ms)
B a high school pitcher (33 ms)
C a major league pitcher (41ms)
D they all had the same kinetic energy
Answer
34
10 Which of the following situations has the least kinetic energy Be ready to explain your answer
A a man sitting still on a park bench
B a child riding a bike
C a woman driving a car
D it is impossible to tell
Answer
35
Calculating Kinetic Energy
Kinetic energy can be solved for by using the equation
12KE = mv2
Lets fill in the table below
variable unitsName
Kinetic Energy
mms
36
Example shy Calculating Kinetic Energy
A car which has a mass of 1000 kg is moving with a velocity of 5 ms How much kinetic energy does the car possess Calculate the cars kinetic energy
KE = mv2KE = (05)(1000 kg)(5 ms)2
KE = (05)(1000 kg)(25 m2s2)KE = 125000 J
12
Click on the box to see the solution
Teacher N
otes
37
11 A 10 kg snowball is rolling down a hill Just before reaching the bottom its velocity is measured to be 10 ms What is the kinetic energy of the ball at this position
Answer
38
12 A 100 kg running back in football is running with a velocity of 2 ms What is his kinetic energy
Answer
KE= 12 mv2KE= 12 (100 kg) (2 ms)2KE= 12 (100 kg) (4m2s2)KE= 200 J
39
13 A 2000 kg car with a velocity of 20 ms slows down and stops at a red light What is the change in kinetic energy
Answer
40
14 A 50 kg girl rode her 12 kg bicycle in a race She started from rest and peddled with a velocity of 10 ms What is the change in kinetic energy of the girl and her bicycle
Answer
41
Thinking Mathematically
KE = mv212
We have already said that mass is directly proportional to kinetic energy
This means that if the mass of the object doubles the
kinetic energy ___________ If the mass of the object increases by a
factor of 5 then the kinetic energy___________ by ______________
If the mass of the object decreases by half then the kinetic
energy will ____________ by ___________
doubles
increases a factor of 5
decrease half
42
15 If the mass of a wagon is doubled its kinetic energy
A increases
B decreases
Answer
43
16 If the mass of a wagon is doubled by what factor does the kinetic energy increase
Answer
44
Thinking Mathematically
Kinetic energy can be solved by using the equation
KE = mv212
From the equation we can see that the kinetic energy is also directly proportional to the square of the velocity
This means that if the velocity doubles the kinetic energy increases by a factor of 4
22=4
If the velocity is quadrupled then the kinetic energy increases by a factor of 16
42= 16
45
17 If the velocity of a wagon is tripled its kinetic energy
Answer
A increases
B decreases
46
18 If the velocity of a wagon is tripled by what factor does the kinetic energy increase
Answer
47
19 Two balls are moving with the same velocity ball A has a mass of 10 kg and ball B has a mass of 40 kg How much more kinetic energy does ball B have
Answer
48
20 A cart halves its mass and at the same time doubles its speed Does the kinetic energy increase or decrease By what factor does the kinetic energy change
A increase 2
B increase 4
C decrease 2
D decrease 4
Answer
bull half the mass gives 12 the KEbull double the speed gives 4 x KEbull therefore (12)(4)= 2
A
49
Stored Energy
Return to Tableof Contents
50
Where does Kinetic Energy Come From
Imagine a roller coaster car that is at the top of the first hill and is stopped
Does the car stay stopped at the top of the hill for the entire ride
What happens
51
Where does Kinetic Energy Come From
Once the car leans over the edge gravity pulls it down The ride is taking advantage of the gravitational attraction between the car and Earth to give the car kinetic energy and make it go faster as it falls
The kinetic energy the car is receiving is coming from another type of energy called potential energy
52
Where does Kinetic Energy Come From
Potential energy is energy stored in an object due to the objects position The roller coaster car on the previous slide had stored energy due to its height above the ground
There are two forms of potential energy that we will be looking at in this unit
Gravitational Potential Energy
and
Elastic Potential Energy
53
Gravitational Potential Energy
The potential energy due to elevated positions is called gravitational potential energy
Gravitational potential energy is stored energy and it can be used at a later time to cause an object to moveOnce the person steps off the diving board the gravitational potential energy is converted into kinetic energy and the person falls (moves)
54
Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
55
Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
56
h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
24
Energy of Motion
In order for an object to move one of two scenarios has to occur
1 The object uses some of the potential energy that it had stored
2 Energy is transferred to the object from an outside source
In either case now that the object is in motion the object is experiencing kinetic energy
25
An objects state of motion can be described by looking at the amount of kinetic energy that the object has at that moment in time
Kinetic Energy
Since the state of motion of an object can change with time the kinetic energy of an object can also change with time
26
velocitymass
The amount of kinetic energy that an object possesses is dependent on two factors
Kinetic Energy
Both of these factors are directly proportional to the kinetic energy We talked about this mathematical relationship in the
last chapter What did directly proportional mean
and
27
Kinetic Energy Mass Velocity
Since kinetic energy is the energy of motion
the object has to have a velocity to have kinetic energy The larger the
velocity the __________________ the kinetic energy
The larger the mass the more energy is needed to move the object
therefore the _______________ the kinetic energy
28
How Does Kinetic Energy Depend on MassIf two identical objects are moving at the same velocity they will have the same kinetic energy
v = 5 ms
v = 5 ms
A tennis ball and a bowling ball are both shown above The bowling ball is heavier than the tennis ball Which ball would have more kinetic energy
However if one object has more mass than the other the heavier object will have more kinetic energy
29
Velocity vs Speed
Remember that velocity is another way to measure motion V elocity is the speed of an object with direction Speed does not have a direction so we call speed a scalar quantity
Since velocity has both magnitude and direction it is a vector quantity
Runners speed 10 kmhr
Runners velocity 10 kmhr to the East
30
How Does Kinetic Energy Depend on Velocity
In this picture the hare is moving faster than the tortoise at this point
If we assumed that they had the same mass who would have more kinetic energy Why Discuss this with a partner
31
v = 5 ms
v = 10 ms
How Does Kinetic Energy Depend upon Velocity
If two identical objects are moving at the same velocity then they will have the same kinetic energy However if one of the objects is moving faster the faster one will have more kinetic energy
In the diagram above two identical tennis balls are moving Which tennis ball has more kinetic energy and why
32
8 Three different emergency vehicles are noticed driving on the highway at a speed of 25 ms Which of the following cars have the most kinetic energy at that moment
A a police car
B an ambulance
C a firetruck
D they all have the same kinetic energy
Answer
C
33
9 Three different baseball pitchers had the speed of their fastball measured by a radar gun Which of the following pitchers fastball had the smallest amount of kinetic energy
A a little league pitcher (22 ms)
B a high school pitcher (33 ms)
C a major league pitcher (41ms)
D they all had the same kinetic energy
Answer
34
10 Which of the following situations has the least kinetic energy Be ready to explain your answer
A a man sitting still on a park bench
B a child riding a bike
C a woman driving a car
D it is impossible to tell
Answer
35
Calculating Kinetic Energy
Kinetic energy can be solved for by using the equation
12KE = mv2
Lets fill in the table below
variable unitsName
Kinetic Energy
mms
36
Example shy Calculating Kinetic Energy
A car which has a mass of 1000 kg is moving with a velocity of 5 ms How much kinetic energy does the car possess Calculate the cars kinetic energy
KE = mv2KE = (05)(1000 kg)(5 ms)2
KE = (05)(1000 kg)(25 m2s2)KE = 125000 J
12
Click on the box to see the solution
Teacher N
otes
37
11 A 10 kg snowball is rolling down a hill Just before reaching the bottom its velocity is measured to be 10 ms What is the kinetic energy of the ball at this position
Answer
38
12 A 100 kg running back in football is running with a velocity of 2 ms What is his kinetic energy
Answer
KE= 12 mv2KE= 12 (100 kg) (2 ms)2KE= 12 (100 kg) (4m2s2)KE= 200 J
39
13 A 2000 kg car with a velocity of 20 ms slows down and stops at a red light What is the change in kinetic energy
Answer
40
14 A 50 kg girl rode her 12 kg bicycle in a race She started from rest and peddled with a velocity of 10 ms What is the change in kinetic energy of the girl and her bicycle
Answer
41
Thinking Mathematically
KE = mv212
We have already said that mass is directly proportional to kinetic energy
This means that if the mass of the object doubles the
kinetic energy ___________ If the mass of the object increases by a
factor of 5 then the kinetic energy___________ by ______________
If the mass of the object decreases by half then the kinetic
energy will ____________ by ___________
doubles
increases a factor of 5
decrease half
42
15 If the mass of a wagon is doubled its kinetic energy
A increases
B decreases
Answer
43
16 If the mass of a wagon is doubled by what factor does the kinetic energy increase
Answer
44
Thinking Mathematically
Kinetic energy can be solved by using the equation
KE = mv212
From the equation we can see that the kinetic energy is also directly proportional to the square of the velocity
This means that if the velocity doubles the kinetic energy increases by a factor of 4
22=4
If the velocity is quadrupled then the kinetic energy increases by a factor of 16
42= 16
45
17 If the velocity of a wagon is tripled its kinetic energy
Answer
A increases
B decreases
46
18 If the velocity of a wagon is tripled by what factor does the kinetic energy increase
Answer
47
19 Two balls are moving with the same velocity ball A has a mass of 10 kg and ball B has a mass of 40 kg How much more kinetic energy does ball B have
Answer
48
20 A cart halves its mass and at the same time doubles its speed Does the kinetic energy increase or decrease By what factor does the kinetic energy change
A increase 2
B increase 4
C decrease 2
D decrease 4
Answer
bull half the mass gives 12 the KEbull double the speed gives 4 x KEbull therefore (12)(4)= 2
A
49
Stored Energy
Return to Tableof Contents
50
Where does Kinetic Energy Come From
Imagine a roller coaster car that is at the top of the first hill and is stopped
Does the car stay stopped at the top of the hill for the entire ride
What happens
51
Where does Kinetic Energy Come From
Once the car leans over the edge gravity pulls it down The ride is taking advantage of the gravitational attraction between the car and Earth to give the car kinetic energy and make it go faster as it falls
The kinetic energy the car is receiving is coming from another type of energy called potential energy
52
Where does Kinetic Energy Come From
Potential energy is energy stored in an object due to the objects position The roller coaster car on the previous slide had stored energy due to its height above the ground
There are two forms of potential energy that we will be looking at in this unit
Gravitational Potential Energy
and
Elastic Potential Energy
53
Gravitational Potential Energy
The potential energy due to elevated positions is called gravitational potential energy
Gravitational potential energy is stored energy and it can be used at a later time to cause an object to moveOnce the person steps off the diving board the gravitational potential energy is converted into kinetic energy and the person falls (moves)
54
Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
55
Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
56
h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
25
An objects state of motion can be described by looking at the amount of kinetic energy that the object has at that moment in time
Kinetic Energy
Since the state of motion of an object can change with time the kinetic energy of an object can also change with time
26
velocitymass
The amount of kinetic energy that an object possesses is dependent on two factors
Kinetic Energy
Both of these factors are directly proportional to the kinetic energy We talked about this mathematical relationship in the
last chapter What did directly proportional mean
and
27
Kinetic Energy Mass Velocity
Since kinetic energy is the energy of motion
the object has to have a velocity to have kinetic energy The larger the
velocity the __________________ the kinetic energy
The larger the mass the more energy is needed to move the object
therefore the _______________ the kinetic energy
28
How Does Kinetic Energy Depend on MassIf two identical objects are moving at the same velocity they will have the same kinetic energy
v = 5 ms
v = 5 ms
A tennis ball and a bowling ball are both shown above The bowling ball is heavier than the tennis ball Which ball would have more kinetic energy
However if one object has more mass than the other the heavier object will have more kinetic energy
29
Velocity vs Speed
Remember that velocity is another way to measure motion V elocity is the speed of an object with direction Speed does not have a direction so we call speed a scalar quantity
Since velocity has both magnitude and direction it is a vector quantity
Runners speed 10 kmhr
Runners velocity 10 kmhr to the East
30
How Does Kinetic Energy Depend on Velocity
In this picture the hare is moving faster than the tortoise at this point
If we assumed that they had the same mass who would have more kinetic energy Why Discuss this with a partner
31
v = 5 ms
v = 10 ms
How Does Kinetic Energy Depend upon Velocity
If two identical objects are moving at the same velocity then they will have the same kinetic energy However if one of the objects is moving faster the faster one will have more kinetic energy
In the diagram above two identical tennis balls are moving Which tennis ball has more kinetic energy and why
32
8 Three different emergency vehicles are noticed driving on the highway at a speed of 25 ms Which of the following cars have the most kinetic energy at that moment
A a police car
B an ambulance
C a firetruck
D they all have the same kinetic energy
Answer
C
33
9 Three different baseball pitchers had the speed of their fastball measured by a radar gun Which of the following pitchers fastball had the smallest amount of kinetic energy
A a little league pitcher (22 ms)
B a high school pitcher (33 ms)
C a major league pitcher (41ms)
D they all had the same kinetic energy
Answer
34
10 Which of the following situations has the least kinetic energy Be ready to explain your answer
A a man sitting still on a park bench
B a child riding a bike
C a woman driving a car
D it is impossible to tell
Answer
35
Calculating Kinetic Energy
Kinetic energy can be solved for by using the equation
12KE = mv2
Lets fill in the table below
variable unitsName
Kinetic Energy
mms
36
Example shy Calculating Kinetic Energy
A car which has a mass of 1000 kg is moving with a velocity of 5 ms How much kinetic energy does the car possess Calculate the cars kinetic energy
KE = mv2KE = (05)(1000 kg)(5 ms)2
KE = (05)(1000 kg)(25 m2s2)KE = 125000 J
12
Click on the box to see the solution
Teacher N
otes
37
11 A 10 kg snowball is rolling down a hill Just before reaching the bottom its velocity is measured to be 10 ms What is the kinetic energy of the ball at this position
Answer
38
12 A 100 kg running back in football is running with a velocity of 2 ms What is his kinetic energy
Answer
KE= 12 mv2KE= 12 (100 kg) (2 ms)2KE= 12 (100 kg) (4m2s2)KE= 200 J
39
13 A 2000 kg car with a velocity of 20 ms slows down and stops at a red light What is the change in kinetic energy
Answer
40
14 A 50 kg girl rode her 12 kg bicycle in a race She started from rest and peddled with a velocity of 10 ms What is the change in kinetic energy of the girl and her bicycle
Answer
41
Thinking Mathematically
KE = mv212
We have already said that mass is directly proportional to kinetic energy
This means that if the mass of the object doubles the
kinetic energy ___________ If the mass of the object increases by a
factor of 5 then the kinetic energy___________ by ______________
If the mass of the object decreases by half then the kinetic
energy will ____________ by ___________
doubles
increases a factor of 5
decrease half
42
15 If the mass of a wagon is doubled its kinetic energy
A increases
B decreases
Answer
43
16 If the mass of a wagon is doubled by what factor does the kinetic energy increase
Answer
44
Thinking Mathematically
Kinetic energy can be solved by using the equation
KE = mv212
From the equation we can see that the kinetic energy is also directly proportional to the square of the velocity
This means that if the velocity doubles the kinetic energy increases by a factor of 4
22=4
If the velocity is quadrupled then the kinetic energy increases by a factor of 16
42= 16
45
17 If the velocity of a wagon is tripled its kinetic energy
Answer
A increases
B decreases
46
18 If the velocity of a wagon is tripled by what factor does the kinetic energy increase
Answer
47
19 Two balls are moving with the same velocity ball A has a mass of 10 kg and ball B has a mass of 40 kg How much more kinetic energy does ball B have
Answer
48
20 A cart halves its mass and at the same time doubles its speed Does the kinetic energy increase or decrease By what factor does the kinetic energy change
A increase 2
B increase 4
C decrease 2
D decrease 4
Answer
bull half the mass gives 12 the KEbull double the speed gives 4 x KEbull therefore (12)(4)= 2
A
49
Stored Energy
Return to Tableof Contents
50
Where does Kinetic Energy Come From
Imagine a roller coaster car that is at the top of the first hill and is stopped
Does the car stay stopped at the top of the hill for the entire ride
What happens
51
Where does Kinetic Energy Come From
Once the car leans over the edge gravity pulls it down The ride is taking advantage of the gravitational attraction between the car and Earth to give the car kinetic energy and make it go faster as it falls
The kinetic energy the car is receiving is coming from another type of energy called potential energy
52
Where does Kinetic Energy Come From
Potential energy is energy stored in an object due to the objects position The roller coaster car on the previous slide had stored energy due to its height above the ground
There are two forms of potential energy that we will be looking at in this unit
Gravitational Potential Energy
and
Elastic Potential Energy
53
Gravitational Potential Energy
The potential energy due to elevated positions is called gravitational potential energy
Gravitational potential energy is stored energy and it can be used at a later time to cause an object to moveOnce the person steps off the diving board the gravitational potential energy is converted into kinetic energy and the person falls (moves)
54
Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
55
Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
56
h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
26
velocitymass
The amount of kinetic energy that an object possesses is dependent on two factors
Kinetic Energy
Both of these factors are directly proportional to the kinetic energy We talked about this mathematical relationship in the
last chapter What did directly proportional mean
and
27
Kinetic Energy Mass Velocity
Since kinetic energy is the energy of motion
the object has to have a velocity to have kinetic energy The larger the
velocity the __________________ the kinetic energy
The larger the mass the more energy is needed to move the object
therefore the _______________ the kinetic energy
28
How Does Kinetic Energy Depend on MassIf two identical objects are moving at the same velocity they will have the same kinetic energy
v = 5 ms
v = 5 ms
A tennis ball and a bowling ball are both shown above The bowling ball is heavier than the tennis ball Which ball would have more kinetic energy
However if one object has more mass than the other the heavier object will have more kinetic energy
29
Velocity vs Speed
Remember that velocity is another way to measure motion V elocity is the speed of an object with direction Speed does not have a direction so we call speed a scalar quantity
Since velocity has both magnitude and direction it is a vector quantity
Runners speed 10 kmhr
Runners velocity 10 kmhr to the East
30
How Does Kinetic Energy Depend on Velocity
In this picture the hare is moving faster than the tortoise at this point
If we assumed that they had the same mass who would have more kinetic energy Why Discuss this with a partner
31
v = 5 ms
v = 10 ms
How Does Kinetic Energy Depend upon Velocity
If two identical objects are moving at the same velocity then they will have the same kinetic energy However if one of the objects is moving faster the faster one will have more kinetic energy
In the diagram above two identical tennis balls are moving Which tennis ball has more kinetic energy and why
32
8 Three different emergency vehicles are noticed driving on the highway at a speed of 25 ms Which of the following cars have the most kinetic energy at that moment
A a police car
B an ambulance
C a firetruck
D they all have the same kinetic energy
Answer
C
33
9 Three different baseball pitchers had the speed of their fastball measured by a radar gun Which of the following pitchers fastball had the smallest amount of kinetic energy
A a little league pitcher (22 ms)
B a high school pitcher (33 ms)
C a major league pitcher (41ms)
D they all had the same kinetic energy
Answer
34
10 Which of the following situations has the least kinetic energy Be ready to explain your answer
A a man sitting still on a park bench
B a child riding a bike
C a woman driving a car
D it is impossible to tell
Answer
35
Calculating Kinetic Energy
Kinetic energy can be solved for by using the equation
12KE = mv2
Lets fill in the table below
variable unitsName
Kinetic Energy
mms
36
Example shy Calculating Kinetic Energy
A car which has a mass of 1000 kg is moving with a velocity of 5 ms How much kinetic energy does the car possess Calculate the cars kinetic energy
KE = mv2KE = (05)(1000 kg)(5 ms)2
KE = (05)(1000 kg)(25 m2s2)KE = 125000 J
12
Click on the box to see the solution
Teacher N
otes
37
11 A 10 kg snowball is rolling down a hill Just before reaching the bottom its velocity is measured to be 10 ms What is the kinetic energy of the ball at this position
Answer
38
12 A 100 kg running back in football is running with a velocity of 2 ms What is his kinetic energy
Answer
KE= 12 mv2KE= 12 (100 kg) (2 ms)2KE= 12 (100 kg) (4m2s2)KE= 200 J
39
13 A 2000 kg car with a velocity of 20 ms slows down and stops at a red light What is the change in kinetic energy
Answer
40
14 A 50 kg girl rode her 12 kg bicycle in a race She started from rest and peddled with a velocity of 10 ms What is the change in kinetic energy of the girl and her bicycle
Answer
41
Thinking Mathematically
KE = mv212
We have already said that mass is directly proportional to kinetic energy
This means that if the mass of the object doubles the
kinetic energy ___________ If the mass of the object increases by a
factor of 5 then the kinetic energy___________ by ______________
If the mass of the object decreases by half then the kinetic
energy will ____________ by ___________
doubles
increases a factor of 5
decrease half
42
15 If the mass of a wagon is doubled its kinetic energy
A increases
B decreases
Answer
43
16 If the mass of a wagon is doubled by what factor does the kinetic energy increase
Answer
44
Thinking Mathematically
Kinetic energy can be solved by using the equation
KE = mv212
From the equation we can see that the kinetic energy is also directly proportional to the square of the velocity
This means that if the velocity doubles the kinetic energy increases by a factor of 4
22=4
If the velocity is quadrupled then the kinetic energy increases by a factor of 16
42= 16
45
17 If the velocity of a wagon is tripled its kinetic energy
Answer
A increases
B decreases
46
18 If the velocity of a wagon is tripled by what factor does the kinetic energy increase
Answer
47
19 Two balls are moving with the same velocity ball A has a mass of 10 kg and ball B has a mass of 40 kg How much more kinetic energy does ball B have
Answer
48
20 A cart halves its mass and at the same time doubles its speed Does the kinetic energy increase or decrease By what factor does the kinetic energy change
A increase 2
B increase 4
C decrease 2
D decrease 4
Answer
bull half the mass gives 12 the KEbull double the speed gives 4 x KEbull therefore (12)(4)= 2
A
49
Stored Energy
Return to Tableof Contents
50
Where does Kinetic Energy Come From
Imagine a roller coaster car that is at the top of the first hill and is stopped
Does the car stay stopped at the top of the hill for the entire ride
What happens
51
Where does Kinetic Energy Come From
Once the car leans over the edge gravity pulls it down The ride is taking advantage of the gravitational attraction between the car and Earth to give the car kinetic energy and make it go faster as it falls
The kinetic energy the car is receiving is coming from another type of energy called potential energy
52
Where does Kinetic Energy Come From
Potential energy is energy stored in an object due to the objects position The roller coaster car on the previous slide had stored energy due to its height above the ground
There are two forms of potential energy that we will be looking at in this unit
Gravitational Potential Energy
and
Elastic Potential Energy
53
Gravitational Potential Energy
The potential energy due to elevated positions is called gravitational potential energy
Gravitational potential energy is stored energy and it can be used at a later time to cause an object to moveOnce the person steps off the diving board the gravitational potential energy is converted into kinetic energy and the person falls (moves)
54
Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
55
Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
56
h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
27
Kinetic Energy Mass Velocity
Since kinetic energy is the energy of motion
the object has to have a velocity to have kinetic energy The larger the
velocity the __________________ the kinetic energy
The larger the mass the more energy is needed to move the object
therefore the _______________ the kinetic energy
28
How Does Kinetic Energy Depend on MassIf two identical objects are moving at the same velocity they will have the same kinetic energy
v = 5 ms
v = 5 ms
A tennis ball and a bowling ball are both shown above The bowling ball is heavier than the tennis ball Which ball would have more kinetic energy
However if one object has more mass than the other the heavier object will have more kinetic energy
29
Velocity vs Speed
Remember that velocity is another way to measure motion V elocity is the speed of an object with direction Speed does not have a direction so we call speed a scalar quantity
Since velocity has both magnitude and direction it is a vector quantity
Runners speed 10 kmhr
Runners velocity 10 kmhr to the East
30
How Does Kinetic Energy Depend on Velocity
In this picture the hare is moving faster than the tortoise at this point
If we assumed that they had the same mass who would have more kinetic energy Why Discuss this with a partner
31
v = 5 ms
v = 10 ms
How Does Kinetic Energy Depend upon Velocity
If two identical objects are moving at the same velocity then they will have the same kinetic energy However if one of the objects is moving faster the faster one will have more kinetic energy
In the diagram above two identical tennis balls are moving Which tennis ball has more kinetic energy and why
32
8 Three different emergency vehicles are noticed driving on the highway at a speed of 25 ms Which of the following cars have the most kinetic energy at that moment
A a police car
B an ambulance
C a firetruck
D they all have the same kinetic energy
Answer
C
33
9 Three different baseball pitchers had the speed of their fastball measured by a radar gun Which of the following pitchers fastball had the smallest amount of kinetic energy
A a little league pitcher (22 ms)
B a high school pitcher (33 ms)
C a major league pitcher (41ms)
D they all had the same kinetic energy
Answer
34
10 Which of the following situations has the least kinetic energy Be ready to explain your answer
A a man sitting still on a park bench
B a child riding a bike
C a woman driving a car
D it is impossible to tell
Answer
35
Calculating Kinetic Energy
Kinetic energy can be solved for by using the equation
12KE = mv2
Lets fill in the table below
variable unitsName
Kinetic Energy
mms
36
Example shy Calculating Kinetic Energy
A car which has a mass of 1000 kg is moving with a velocity of 5 ms How much kinetic energy does the car possess Calculate the cars kinetic energy
KE = mv2KE = (05)(1000 kg)(5 ms)2
KE = (05)(1000 kg)(25 m2s2)KE = 125000 J
12
Click on the box to see the solution
Teacher N
otes
37
11 A 10 kg snowball is rolling down a hill Just before reaching the bottom its velocity is measured to be 10 ms What is the kinetic energy of the ball at this position
Answer
38
12 A 100 kg running back in football is running with a velocity of 2 ms What is his kinetic energy
Answer
KE= 12 mv2KE= 12 (100 kg) (2 ms)2KE= 12 (100 kg) (4m2s2)KE= 200 J
39
13 A 2000 kg car with a velocity of 20 ms slows down and stops at a red light What is the change in kinetic energy
Answer
40
14 A 50 kg girl rode her 12 kg bicycle in a race She started from rest and peddled with a velocity of 10 ms What is the change in kinetic energy of the girl and her bicycle
Answer
41
Thinking Mathematically
KE = mv212
We have already said that mass is directly proportional to kinetic energy
This means that if the mass of the object doubles the
kinetic energy ___________ If the mass of the object increases by a
factor of 5 then the kinetic energy___________ by ______________
If the mass of the object decreases by half then the kinetic
energy will ____________ by ___________
doubles
increases a factor of 5
decrease half
42
15 If the mass of a wagon is doubled its kinetic energy
A increases
B decreases
Answer
43
16 If the mass of a wagon is doubled by what factor does the kinetic energy increase
Answer
44
Thinking Mathematically
Kinetic energy can be solved by using the equation
KE = mv212
From the equation we can see that the kinetic energy is also directly proportional to the square of the velocity
This means that if the velocity doubles the kinetic energy increases by a factor of 4
22=4
If the velocity is quadrupled then the kinetic energy increases by a factor of 16
42= 16
45
17 If the velocity of a wagon is tripled its kinetic energy
Answer
A increases
B decreases
46
18 If the velocity of a wagon is tripled by what factor does the kinetic energy increase
Answer
47
19 Two balls are moving with the same velocity ball A has a mass of 10 kg and ball B has a mass of 40 kg How much more kinetic energy does ball B have
Answer
48
20 A cart halves its mass and at the same time doubles its speed Does the kinetic energy increase or decrease By what factor does the kinetic energy change
A increase 2
B increase 4
C decrease 2
D decrease 4
Answer
bull half the mass gives 12 the KEbull double the speed gives 4 x KEbull therefore (12)(4)= 2
A
49
Stored Energy
Return to Tableof Contents
50
Where does Kinetic Energy Come From
Imagine a roller coaster car that is at the top of the first hill and is stopped
Does the car stay stopped at the top of the hill for the entire ride
What happens
51
Where does Kinetic Energy Come From
Once the car leans over the edge gravity pulls it down The ride is taking advantage of the gravitational attraction between the car and Earth to give the car kinetic energy and make it go faster as it falls
The kinetic energy the car is receiving is coming from another type of energy called potential energy
52
Where does Kinetic Energy Come From
Potential energy is energy stored in an object due to the objects position The roller coaster car on the previous slide had stored energy due to its height above the ground
There are two forms of potential energy that we will be looking at in this unit
Gravitational Potential Energy
and
Elastic Potential Energy
53
Gravitational Potential Energy
The potential energy due to elevated positions is called gravitational potential energy
Gravitational potential energy is stored energy and it can be used at a later time to cause an object to moveOnce the person steps off the diving board the gravitational potential energy is converted into kinetic energy and the person falls (moves)
54
Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
55
Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
56
h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
28
How Does Kinetic Energy Depend on MassIf two identical objects are moving at the same velocity they will have the same kinetic energy
v = 5 ms
v = 5 ms
A tennis ball and a bowling ball are both shown above The bowling ball is heavier than the tennis ball Which ball would have more kinetic energy
However if one object has more mass than the other the heavier object will have more kinetic energy
29
Velocity vs Speed
Remember that velocity is another way to measure motion V elocity is the speed of an object with direction Speed does not have a direction so we call speed a scalar quantity
Since velocity has both magnitude and direction it is a vector quantity
Runners speed 10 kmhr
Runners velocity 10 kmhr to the East
30
How Does Kinetic Energy Depend on Velocity
In this picture the hare is moving faster than the tortoise at this point
If we assumed that they had the same mass who would have more kinetic energy Why Discuss this with a partner
31
v = 5 ms
v = 10 ms
How Does Kinetic Energy Depend upon Velocity
If two identical objects are moving at the same velocity then they will have the same kinetic energy However if one of the objects is moving faster the faster one will have more kinetic energy
In the diagram above two identical tennis balls are moving Which tennis ball has more kinetic energy and why
32
8 Three different emergency vehicles are noticed driving on the highway at a speed of 25 ms Which of the following cars have the most kinetic energy at that moment
A a police car
B an ambulance
C a firetruck
D they all have the same kinetic energy
Answer
C
33
9 Three different baseball pitchers had the speed of their fastball measured by a radar gun Which of the following pitchers fastball had the smallest amount of kinetic energy
A a little league pitcher (22 ms)
B a high school pitcher (33 ms)
C a major league pitcher (41ms)
D they all had the same kinetic energy
Answer
34
10 Which of the following situations has the least kinetic energy Be ready to explain your answer
A a man sitting still on a park bench
B a child riding a bike
C a woman driving a car
D it is impossible to tell
Answer
35
Calculating Kinetic Energy
Kinetic energy can be solved for by using the equation
12KE = mv2
Lets fill in the table below
variable unitsName
Kinetic Energy
mms
36
Example shy Calculating Kinetic Energy
A car which has a mass of 1000 kg is moving with a velocity of 5 ms How much kinetic energy does the car possess Calculate the cars kinetic energy
KE = mv2KE = (05)(1000 kg)(5 ms)2
KE = (05)(1000 kg)(25 m2s2)KE = 125000 J
12
Click on the box to see the solution
Teacher N
otes
37
11 A 10 kg snowball is rolling down a hill Just before reaching the bottom its velocity is measured to be 10 ms What is the kinetic energy of the ball at this position
Answer
38
12 A 100 kg running back in football is running with a velocity of 2 ms What is his kinetic energy
Answer
KE= 12 mv2KE= 12 (100 kg) (2 ms)2KE= 12 (100 kg) (4m2s2)KE= 200 J
39
13 A 2000 kg car with a velocity of 20 ms slows down and stops at a red light What is the change in kinetic energy
Answer
40
14 A 50 kg girl rode her 12 kg bicycle in a race She started from rest and peddled with a velocity of 10 ms What is the change in kinetic energy of the girl and her bicycle
Answer
41
Thinking Mathematically
KE = mv212
We have already said that mass is directly proportional to kinetic energy
This means that if the mass of the object doubles the
kinetic energy ___________ If the mass of the object increases by a
factor of 5 then the kinetic energy___________ by ______________
If the mass of the object decreases by half then the kinetic
energy will ____________ by ___________
doubles
increases a factor of 5
decrease half
42
15 If the mass of a wagon is doubled its kinetic energy
A increases
B decreases
Answer
43
16 If the mass of a wagon is doubled by what factor does the kinetic energy increase
Answer
44
Thinking Mathematically
Kinetic energy can be solved by using the equation
KE = mv212
From the equation we can see that the kinetic energy is also directly proportional to the square of the velocity
This means that if the velocity doubles the kinetic energy increases by a factor of 4
22=4
If the velocity is quadrupled then the kinetic energy increases by a factor of 16
42= 16
45
17 If the velocity of a wagon is tripled its kinetic energy
Answer
A increases
B decreases
46
18 If the velocity of a wagon is tripled by what factor does the kinetic energy increase
Answer
47
19 Two balls are moving with the same velocity ball A has a mass of 10 kg and ball B has a mass of 40 kg How much more kinetic energy does ball B have
Answer
48
20 A cart halves its mass and at the same time doubles its speed Does the kinetic energy increase or decrease By what factor does the kinetic energy change
A increase 2
B increase 4
C decrease 2
D decrease 4
Answer
bull half the mass gives 12 the KEbull double the speed gives 4 x KEbull therefore (12)(4)= 2
A
49
Stored Energy
Return to Tableof Contents
50
Where does Kinetic Energy Come From
Imagine a roller coaster car that is at the top of the first hill and is stopped
Does the car stay stopped at the top of the hill for the entire ride
What happens
51
Where does Kinetic Energy Come From
Once the car leans over the edge gravity pulls it down The ride is taking advantage of the gravitational attraction between the car and Earth to give the car kinetic energy and make it go faster as it falls
The kinetic energy the car is receiving is coming from another type of energy called potential energy
52
Where does Kinetic Energy Come From
Potential energy is energy stored in an object due to the objects position The roller coaster car on the previous slide had stored energy due to its height above the ground
There are two forms of potential energy that we will be looking at in this unit
Gravitational Potential Energy
and
Elastic Potential Energy
53
Gravitational Potential Energy
The potential energy due to elevated positions is called gravitational potential energy
Gravitational potential energy is stored energy and it can be used at a later time to cause an object to moveOnce the person steps off the diving board the gravitational potential energy is converted into kinetic energy and the person falls (moves)
54
Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
55
Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
56
h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
29
Velocity vs Speed
Remember that velocity is another way to measure motion V elocity is the speed of an object with direction Speed does not have a direction so we call speed a scalar quantity
Since velocity has both magnitude and direction it is a vector quantity
Runners speed 10 kmhr
Runners velocity 10 kmhr to the East
30
How Does Kinetic Energy Depend on Velocity
In this picture the hare is moving faster than the tortoise at this point
If we assumed that they had the same mass who would have more kinetic energy Why Discuss this with a partner
31
v = 5 ms
v = 10 ms
How Does Kinetic Energy Depend upon Velocity
If two identical objects are moving at the same velocity then they will have the same kinetic energy However if one of the objects is moving faster the faster one will have more kinetic energy
In the diagram above two identical tennis balls are moving Which tennis ball has more kinetic energy and why
32
8 Three different emergency vehicles are noticed driving on the highway at a speed of 25 ms Which of the following cars have the most kinetic energy at that moment
A a police car
B an ambulance
C a firetruck
D they all have the same kinetic energy
Answer
C
33
9 Three different baseball pitchers had the speed of their fastball measured by a radar gun Which of the following pitchers fastball had the smallest amount of kinetic energy
A a little league pitcher (22 ms)
B a high school pitcher (33 ms)
C a major league pitcher (41ms)
D they all had the same kinetic energy
Answer
34
10 Which of the following situations has the least kinetic energy Be ready to explain your answer
A a man sitting still on a park bench
B a child riding a bike
C a woman driving a car
D it is impossible to tell
Answer
35
Calculating Kinetic Energy
Kinetic energy can be solved for by using the equation
12KE = mv2
Lets fill in the table below
variable unitsName
Kinetic Energy
mms
36
Example shy Calculating Kinetic Energy
A car which has a mass of 1000 kg is moving with a velocity of 5 ms How much kinetic energy does the car possess Calculate the cars kinetic energy
KE = mv2KE = (05)(1000 kg)(5 ms)2
KE = (05)(1000 kg)(25 m2s2)KE = 125000 J
12
Click on the box to see the solution
Teacher N
otes
37
11 A 10 kg snowball is rolling down a hill Just before reaching the bottom its velocity is measured to be 10 ms What is the kinetic energy of the ball at this position
Answer
38
12 A 100 kg running back in football is running with a velocity of 2 ms What is his kinetic energy
Answer
KE= 12 mv2KE= 12 (100 kg) (2 ms)2KE= 12 (100 kg) (4m2s2)KE= 200 J
39
13 A 2000 kg car with a velocity of 20 ms slows down and stops at a red light What is the change in kinetic energy
Answer
40
14 A 50 kg girl rode her 12 kg bicycle in a race She started from rest and peddled with a velocity of 10 ms What is the change in kinetic energy of the girl and her bicycle
Answer
41
Thinking Mathematically
KE = mv212
We have already said that mass is directly proportional to kinetic energy
This means that if the mass of the object doubles the
kinetic energy ___________ If the mass of the object increases by a
factor of 5 then the kinetic energy___________ by ______________
If the mass of the object decreases by half then the kinetic
energy will ____________ by ___________
doubles
increases a factor of 5
decrease half
42
15 If the mass of a wagon is doubled its kinetic energy
A increases
B decreases
Answer
43
16 If the mass of a wagon is doubled by what factor does the kinetic energy increase
Answer
44
Thinking Mathematically
Kinetic energy can be solved by using the equation
KE = mv212
From the equation we can see that the kinetic energy is also directly proportional to the square of the velocity
This means that if the velocity doubles the kinetic energy increases by a factor of 4
22=4
If the velocity is quadrupled then the kinetic energy increases by a factor of 16
42= 16
45
17 If the velocity of a wagon is tripled its kinetic energy
Answer
A increases
B decreases
46
18 If the velocity of a wagon is tripled by what factor does the kinetic energy increase
Answer
47
19 Two balls are moving with the same velocity ball A has a mass of 10 kg and ball B has a mass of 40 kg How much more kinetic energy does ball B have
Answer
48
20 A cart halves its mass and at the same time doubles its speed Does the kinetic energy increase or decrease By what factor does the kinetic energy change
A increase 2
B increase 4
C decrease 2
D decrease 4
Answer
bull half the mass gives 12 the KEbull double the speed gives 4 x KEbull therefore (12)(4)= 2
A
49
Stored Energy
Return to Tableof Contents
50
Where does Kinetic Energy Come From
Imagine a roller coaster car that is at the top of the first hill and is stopped
Does the car stay stopped at the top of the hill for the entire ride
What happens
51
Where does Kinetic Energy Come From
Once the car leans over the edge gravity pulls it down The ride is taking advantage of the gravitational attraction between the car and Earth to give the car kinetic energy and make it go faster as it falls
The kinetic energy the car is receiving is coming from another type of energy called potential energy
52
Where does Kinetic Energy Come From
Potential energy is energy stored in an object due to the objects position The roller coaster car on the previous slide had stored energy due to its height above the ground
There are two forms of potential energy that we will be looking at in this unit
Gravitational Potential Energy
and
Elastic Potential Energy
53
Gravitational Potential Energy
The potential energy due to elevated positions is called gravitational potential energy
Gravitational potential energy is stored energy and it can be used at a later time to cause an object to moveOnce the person steps off the diving board the gravitational potential energy is converted into kinetic energy and the person falls (moves)
54
Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
55
Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
56
h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
30
How Does Kinetic Energy Depend on Velocity
In this picture the hare is moving faster than the tortoise at this point
If we assumed that they had the same mass who would have more kinetic energy Why Discuss this with a partner
31
v = 5 ms
v = 10 ms
How Does Kinetic Energy Depend upon Velocity
If two identical objects are moving at the same velocity then they will have the same kinetic energy However if one of the objects is moving faster the faster one will have more kinetic energy
In the diagram above two identical tennis balls are moving Which tennis ball has more kinetic energy and why
32
8 Three different emergency vehicles are noticed driving on the highway at a speed of 25 ms Which of the following cars have the most kinetic energy at that moment
A a police car
B an ambulance
C a firetruck
D they all have the same kinetic energy
Answer
C
33
9 Three different baseball pitchers had the speed of their fastball measured by a radar gun Which of the following pitchers fastball had the smallest amount of kinetic energy
A a little league pitcher (22 ms)
B a high school pitcher (33 ms)
C a major league pitcher (41ms)
D they all had the same kinetic energy
Answer
34
10 Which of the following situations has the least kinetic energy Be ready to explain your answer
A a man sitting still on a park bench
B a child riding a bike
C a woman driving a car
D it is impossible to tell
Answer
35
Calculating Kinetic Energy
Kinetic energy can be solved for by using the equation
12KE = mv2
Lets fill in the table below
variable unitsName
Kinetic Energy
mms
36
Example shy Calculating Kinetic Energy
A car which has a mass of 1000 kg is moving with a velocity of 5 ms How much kinetic energy does the car possess Calculate the cars kinetic energy
KE = mv2KE = (05)(1000 kg)(5 ms)2
KE = (05)(1000 kg)(25 m2s2)KE = 125000 J
12
Click on the box to see the solution
Teacher N
otes
37
11 A 10 kg snowball is rolling down a hill Just before reaching the bottom its velocity is measured to be 10 ms What is the kinetic energy of the ball at this position
Answer
38
12 A 100 kg running back in football is running with a velocity of 2 ms What is his kinetic energy
Answer
KE= 12 mv2KE= 12 (100 kg) (2 ms)2KE= 12 (100 kg) (4m2s2)KE= 200 J
39
13 A 2000 kg car with a velocity of 20 ms slows down and stops at a red light What is the change in kinetic energy
Answer
40
14 A 50 kg girl rode her 12 kg bicycle in a race She started from rest and peddled with a velocity of 10 ms What is the change in kinetic energy of the girl and her bicycle
Answer
41
Thinking Mathematically
KE = mv212
We have already said that mass is directly proportional to kinetic energy
This means that if the mass of the object doubles the
kinetic energy ___________ If the mass of the object increases by a
factor of 5 then the kinetic energy___________ by ______________
If the mass of the object decreases by half then the kinetic
energy will ____________ by ___________
doubles
increases a factor of 5
decrease half
42
15 If the mass of a wagon is doubled its kinetic energy
A increases
B decreases
Answer
43
16 If the mass of a wagon is doubled by what factor does the kinetic energy increase
Answer
44
Thinking Mathematically
Kinetic energy can be solved by using the equation
KE = mv212
From the equation we can see that the kinetic energy is also directly proportional to the square of the velocity
This means that if the velocity doubles the kinetic energy increases by a factor of 4
22=4
If the velocity is quadrupled then the kinetic energy increases by a factor of 16
42= 16
45
17 If the velocity of a wagon is tripled its kinetic energy
Answer
A increases
B decreases
46
18 If the velocity of a wagon is tripled by what factor does the kinetic energy increase
Answer
47
19 Two balls are moving with the same velocity ball A has a mass of 10 kg and ball B has a mass of 40 kg How much more kinetic energy does ball B have
Answer
48
20 A cart halves its mass and at the same time doubles its speed Does the kinetic energy increase or decrease By what factor does the kinetic energy change
A increase 2
B increase 4
C decrease 2
D decrease 4
Answer
bull half the mass gives 12 the KEbull double the speed gives 4 x KEbull therefore (12)(4)= 2
A
49
Stored Energy
Return to Tableof Contents
50
Where does Kinetic Energy Come From
Imagine a roller coaster car that is at the top of the first hill and is stopped
Does the car stay stopped at the top of the hill for the entire ride
What happens
51
Where does Kinetic Energy Come From
Once the car leans over the edge gravity pulls it down The ride is taking advantage of the gravitational attraction between the car and Earth to give the car kinetic energy and make it go faster as it falls
The kinetic energy the car is receiving is coming from another type of energy called potential energy
52
Where does Kinetic Energy Come From
Potential energy is energy stored in an object due to the objects position The roller coaster car on the previous slide had stored energy due to its height above the ground
There are two forms of potential energy that we will be looking at in this unit
Gravitational Potential Energy
and
Elastic Potential Energy
53
Gravitational Potential Energy
The potential energy due to elevated positions is called gravitational potential energy
Gravitational potential energy is stored energy and it can be used at a later time to cause an object to moveOnce the person steps off the diving board the gravitational potential energy is converted into kinetic energy and the person falls (moves)
54
Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
55
Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
56
h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
31
v = 5 ms
v = 10 ms
How Does Kinetic Energy Depend upon Velocity
If two identical objects are moving at the same velocity then they will have the same kinetic energy However if one of the objects is moving faster the faster one will have more kinetic energy
In the diagram above two identical tennis balls are moving Which tennis ball has more kinetic energy and why
32
8 Three different emergency vehicles are noticed driving on the highway at a speed of 25 ms Which of the following cars have the most kinetic energy at that moment
A a police car
B an ambulance
C a firetruck
D they all have the same kinetic energy
Answer
C
33
9 Three different baseball pitchers had the speed of their fastball measured by a radar gun Which of the following pitchers fastball had the smallest amount of kinetic energy
A a little league pitcher (22 ms)
B a high school pitcher (33 ms)
C a major league pitcher (41ms)
D they all had the same kinetic energy
Answer
34
10 Which of the following situations has the least kinetic energy Be ready to explain your answer
A a man sitting still on a park bench
B a child riding a bike
C a woman driving a car
D it is impossible to tell
Answer
35
Calculating Kinetic Energy
Kinetic energy can be solved for by using the equation
12KE = mv2
Lets fill in the table below
variable unitsName
Kinetic Energy
mms
36
Example shy Calculating Kinetic Energy
A car which has a mass of 1000 kg is moving with a velocity of 5 ms How much kinetic energy does the car possess Calculate the cars kinetic energy
KE = mv2KE = (05)(1000 kg)(5 ms)2
KE = (05)(1000 kg)(25 m2s2)KE = 125000 J
12
Click on the box to see the solution
Teacher N
otes
37
11 A 10 kg snowball is rolling down a hill Just before reaching the bottom its velocity is measured to be 10 ms What is the kinetic energy of the ball at this position
Answer
38
12 A 100 kg running back in football is running with a velocity of 2 ms What is his kinetic energy
Answer
KE= 12 mv2KE= 12 (100 kg) (2 ms)2KE= 12 (100 kg) (4m2s2)KE= 200 J
39
13 A 2000 kg car with a velocity of 20 ms slows down and stops at a red light What is the change in kinetic energy
Answer
40
14 A 50 kg girl rode her 12 kg bicycle in a race She started from rest and peddled with a velocity of 10 ms What is the change in kinetic energy of the girl and her bicycle
Answer
41
Thinking Mathematically
KE = mv212
We have already said that mass is directly proportional to kinetic energy
This means that if the mass of the object doubles the
kinetic energy ___________ If the mass of the object increases by a
factor of 5 then the kinetic energy___________ by ______________
If the mass of the object decreases by half then the kinetic
energy will ____________ by ___________
doubles
increases a factor of 5
decrease half
42
15 If the mass of a wagon is doubled its kinetic energy
A increases
B decreases
Answer
43
16 If the mass of a wagon is doubled by what factor does the kinetic energy increase
Answer
44
Thinking Mathematically
Kinetic energy can be solved by using the equation
KE = mv212
From the equation we can see that the kinetic energy is also directly proportional to the square of the velocity
This means that if the velocity doubles the kinetic energy increases by a factor of 4
22=4
If the velocity is quadrupled then the kinetic energy increases by a factor of 16
42= 16
45
17 If the velocity of a wagon is tripled its kinetic energy
Answer
A increases
B decreases
46
18 If the velocity of a wagon is tripled by what factor does the kinetic energy increase
Answer
47
19 Two balls are moving with the same velocity ball A has a mass of 10 kg and ball B has a mass of 40 kg How much more kinetic energy does ball B have
Answer
48
20 A cart halves its mass and at the same time doubles its speed Does the kinetic energy increase or decrease By what factor does the kinetic energy change
A increase 2
B increase 4
C decrease 2
D decrease 4
Answer
bull half the mass gives 12 the KEbull double the speed gives 4 x KEbull therefore (12)(4)= 2
A
49
Stored Energy
Return to Tableof Contents
50
Where does Kinetic Energy Come From
Imagine a roller coaster car that is at the top of the first hill and is stopped
Does the car stay stopped at the top of the hill for the entire ride
What happens
51
Where does Kinetic Energy Come From
Once the car leans over the edge gravity pulls it down The ride is taking advantage of the gravitational attraction between the car and Earth to give the car kinetic energy and make it go faster as it falls
The kinetic energy the car is receiving is coming from another type of energy called potential energy
52
Where does Kinetic Energy Come From
Potential energy is energy stored in an object due to the objects position The roller coaster car on the previous slide had stored energy due to its height above the ground
There are two forms of potential energy that we will be looking at in this unit
Gravitational Potential Energy
and
Elastic Potential Energy
53
Gravitational Potential Energy
The potential energy due to elevated positions is called gravitational potential energy
Gravitational potential energy is stored energy and it can be used at a later time to cause an object to moveOnce the person steps off the diving board the gravitational potential energy is converted into kinetic energy and the person falls (moves)
54
Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
55
Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
56
h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
32
8 Three different emergency vehicles are noticed driving on the highway at a speed of 25 ms Which of the following cars have the most kinetic energy at that moment
A a police car
B an ambulance
C a firetruck
D they all have the same kinetic energy
Answer
C
33
9 Three different baseball pitchers had the speed of their fastball measured by a radar gun Which of the following pitchers fastball had the smallest amount of kinetic energy
A a little league pitcher (22 ms)
B a high school pitcher (33 ms)
C a major league pitcher (41ms)
D they all had the same kinetic energy
Answer
34
10 Which of the following situations has the least kinetic energy Be ready to explain your answer
A a man sitting still on a park bench
B a child riding a bike
C a woman driving a car
D it is impossible to tell
Answer
35
Calculating Kinetic Energy
Kinetic energy can be solved for by using the equation
12KE = mv2
Lets fill in the table below
variable unitsName
Kinetic Energy
mms
36
Example shy Calculating Kinetic Energy
A car which has a mass of 1000 kg is moving with a velocity of 5 ms How much kinetic energy does the car possess Calculate the cars kinetic energy
KE = mv2KE = (05)(1000 kg)(5 ms)2
KE = (05)(1000 kg)(25 m2s2)KE = 125000 J
12
Click on the box to see the solution
Teacher N
otes
37
11 A 10 kg snowball is rolling down a hill Just before reaching the bottom its velocity is measured to be 10 ms What is the kinetic energy of the ball at this position
Answer
38
12 A 100 kg running back in football is running with a velocity of 2 ms What is his kinetic energy
Answer
KE= 12 mv2KE= 12 (100 kg) (2 ms)2KE= 12 (100 kg) (4m2s2)KE= 200 J
39
13 A 2000 kg car with a velocity of 20 ms slows down and stops at a red light What is the change in kinetic energy
Answer
40
14 A 50 kg girl rode her 12 kg bicycle in a race She started from rest and peddled with a velocity of 10 ms What is the change in kinetic energy of the girl and her bicycle
Answer
41
Thinking Mathematically
KE = mv212
We have already said that mass is directly proportional to kinetic energy
This means that if the mass of the object doubles the
kinetic energy ___________ If the mass of the object increases by a
factor of 5 then the kinetic energy___________ by ______________
If the mass of the object decreases by half then the kinetic
energy will ____________ by ___________
doubles
increases a factor of 5
decrease half
42
15 If the mass of a wagon is doubled its kinetic energy
A increases
B decreases
Answer
43
16 If the mass of a wagon is doubled by what factor does the kinetic energy increase
Answer
44
Thinking Mathematically
Kinetic energy can be solved by using the equation
KE = mv212
From the equation we can see that the kinetic energy is also directly proportional to the square of the velocity
This means that if the velocity doubles the kinetic energy increases by a factor of 4
22=4
If the velocity is quadrupled then the kinetic energy increases by a factor of 16
42= 16
45
17 If the velocity of a wagon is tripled its kinetic energy
Answer
A increases
B decreases
46
18 If the velocity of a wagon is tripled by what factor does the kinetic energy increase
Answer
47
19 Two balls are moving with the same velocity ball A has a mass of 10 kg and ball B has a mass of 40 kg How much more kinetic energy does ball B have
Answer
48
20 A cart halves its mass and at the same time doubles its speed Does the kinetic energy increase or decrease By what factor does the kinetic energy change
A increase 2
B increase 4
C decrease 2
D decrease 4
Answer
bull half the mass gives 12 the KEbull double the speed gives 4 x KEbull therefore (12)(4)= 2
A
49
Stored Energy
Return to Tableof Contents
50
Where does Kinetic Energy Come From
Imagine a roller coaster car that is at the top of the first hill and is stopped
Does the car stay stopped at the top of the hill for the entire ride
What happens
51
Where does Kinetic Energy Come From
Once the car leans over the edge gravity pulls it down The ride is taking advantage of the gravitational attraction between the car and Earth to give the car kinetic energy and make it go faster as it falls
The kinetic energy the car is receiving is coming from another type of energy called potential energy
52
Where does Kinetic Energy Come From
Potential energy is energy stored in an object due to the objects position The roller coaster car on the previous slide had stored energy due to its height above the ground
There are two forms of potential energy that we will be looking at in this unit
Gravitational Potential Energy
and
Elastic Potential Energy
53
Gravitational Potential Energy
The potential energy due to elevated positions is called gravitational potential energy
Gravitational potential energy is stored energy and it can be used at a later time to cause an object to moveOnce the person steps off the diving board the gravitational potential energy is converted into kinetic energy and the person falls (moves)
54
Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
55
Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
56
h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
33
9 Three different baseball pitchers had the speed of their fastball measured by a radar gun Which of the following pitchers fastball had the smallest amount of kinetic energy
A a little league pitcher (22 ms)
B a high school pitcher (33 ms)
C a major league pitcher (41ms)
D they all had the same kinetic energy
Answer
34
10 Which of the following situations has the least kinetic energy Be ready to explain your answer
A a man sitting still on a park bench
B a child riding a bike
C a woman driving a car
D it is impossible to tell
Answer
35
Calculating Kinetic Energy
Kinetic energy can be solved for by using the equation
12KE = mv2
Lets fill in the table below
variable unitsName
Kinetic Energy
mms
36
Example shy Calculating Kinetic Energy
A car which has a mass of 1000 kg is moving with a velocity of 5 ms How much kinetic energy does the car possess Calculate the cars kinetic energy
KE = mv2KE = (05)(1000 kg)(5 ms)2
KE = (05)(1000 kg)(25 m2s2)KE = 125000 J
12
Click on the box to see the solution
Teacher N
otes
37
11 A 10 kg snowball is rolling down a hill Just before reaching the bottom its velocity is measured to be 10 ms What is the kinetic energy of the ball at this position
Answer
38
12 A 100 kg running back in football is running with a velocity of 2 ms What is his kinetic energy
Answer
KE= 12 mv2KE= 12 (100 kg) (2 ms)2KE= 12 (100 kg) (4m2s2)KE= 200 J
39
13 A 2000 kg car with a velocity of 20 ms slows down and stops at a red light What is the change in kinetic energy
Answer
40
14 A 50 kg girl rode her 12 kg bicycle in a race She started from rest and peddled with a velocity of 10 ms What is the change in kinetic energy of the girl and her bicycle
Answer
41
Thinking Mathematically
KE = mv212
We have already said that mass is directly proportional to kinetic energy
This means that if the mass of the object doubles the
kinetic energy ___________ If the mass of the object increases by a
factor of 5 then the kinetic energy___________ by ______________
If the mass of the object decreases by half then the kinetic
energy will ____________ by ___________
doubles
increases a factor of 5
decrease half
42
15 If the mass of a wagon is doubled its kinetic energy
A increases
B decreases
Answer
43
16 If the mass of a wagon is doubled by what factor does the kinetic energy increase
Answer
44
Thinking Mathematically
Kinetic energy can be solved by using the equation
KE = mv212
From the equation we can see that the kinetic energy is also directly proportional to the square of the velocity
This means that if the velocity doubles the kinetic energy increases by a factor of 4
22=4
If the velocity is quadrupled then the kinetic energy increases by a factor of 16
42= 16
45
17 If the velocity of a wagon is tripled its kinetic energy
Answer
A increases
B decreases
46
18 If the velocity of a wagon is tripled by what factor does the kinetic energy increase
Answer
47
19 Two balls are moving with the same velocity ball A has a mass of 10 kg and ball B has a mass of 40 kg How much more kinetic energy does ball B have
Answer
48
20 A cart halves its mass and at the same time doubles its speed Does the kinetic energy increase or decrease By what factor does the kinetic energy change
A increase 2
B increase 4
C decrease 2
D decrease 4
Answer
bull half the mass gives 12 the KEbull double the speed gives 4 x KEbull therefore (12)(4)= 2
A
49
Stored Energy
Return to Tableof Contents
50
Where does Kinetic Energy Come From
Imagine a roller coaster car that is at the top of the first hill and is stopped
Does the car stay stopped at the top of the hill for the entire ride
What happens
51
Where does Kinetic Energy Come From
Once the car leans over the edge gravity pulls it down The ride is taking advantage of the gravitational attraction between the car and Earth to give the car kinetic energy and make it go faster as it falls
The kinetic energy the car is receiving is coming from another type of energy called potential energy
52
Where does Kinetic Energy Come From
Potential energy is energy stored in an object due to the objects position The roller coaster car on the previous slide had stored energy due to its height above the ground
There are two forms of potential energy that we will be looking at in this unit
Gravitational Potential Energy
and
Elastic Potential Energy
53
Gravitational Potential Energy
The potential energy due to elevated positions is called gravitational potential energy
Gravitational potential energy is stored energy and it can be used at a later time to cause an object to moveOnce the person steps off the diving board the gravitational potential energy is converted into kinetic energy and the person falls (moves)
54
Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
55
Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
56
h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
34
10 Which of the following situations has the least kinetic energy Be ready to explain your answer
A a man sitting still on a park bench
B a child riding a bike
C a woman driving a car
D it is impossible to tell
Answer
35
Calculating Kinetic Energy
Kinetic energy can be solved for by using the equation
12KE = mv2
Lets fill in the table below
variable unitsName
Kinetic Energy
mms
36
Example shy Calculating Kinetic Energy
A car which has a mass of 1000 kg is moving with a velocity of 5 ms How much kinetic energy does the car possess Calculate the cars kinetic energy
KE = mv2KE = (05)(1000 kg)(5 ms)2
KE = (05)(1000 kg)(25 m2s2)KE = 125000 J
12
Click on the box to see the solution
Teacher N
otes
37
11 A 10 kg snowball is rolling down a hill Just before reaching the bottom its velocity is measured to be 10 ms What is the kinetic energy of the ball at this position
Answer
38
12 A 100 kg running back in football is running with a velocity of 2 ms What is his kinetic energy
Answer
KE= 12 mv2KE= 12 (100 kg) (2 ms)2KE= 12 (100 kg) (4m2s2)KE= 200 J
39
13 A 2000 kg car with a velocity of 20 ms slows down and stops at a red light What is the change in kinetic energy
Answer
40
14 A 50 kg girl rode her 12 kg bicycle in a race She started from rest and peddled with a velocity of 10 ms What is the change in kinetic energy of the girl and her bicycle
Answer
41
Thinking Mathematically
KE = mv212
We have already said that mass is directly proportional to kinetic energy
This means that if the mass of the object doubles the
kinetic energy ___________ If the mass of the object increases by a
factor of 5 then the kinetic energy___________ by ______________
If the mass of the object decreases by half then the kinetic
energy will ____________ by ___________
doubles
increases a factor of 5
decrease half
42
15 If the mass of a wagon is doubled its kinetic energy
A increases
B decreases
Answer
43
16 If the mass of a wagon is doubled by what factor does the kinetic energy increase
Answer
44
Thinking Mathematically
Kinetic energy can be solved by using the equation
KE = mv212
From the equation we can see that the kinetic energy is also directly proportional to the square of the velocity
This means that if the velocity doubles the kinetic energy increases by a factor of 4
22=4
If the velocity is quadrupled then the kinetic energy increases by a factor of 16
42= 16
45
17 If the velocity of a wagon is tripled its kinetic energy
Answer
A increases
B decreases
46
18 If the velocity of a wagon is tripled by what factor does the kinetic energy increase
Answer
47
19 Two balls are moving with the same velocity ball A has a mass of 10 kg and ball B has a mass of 40 kg How much more kinetic energy does ball B have
Answer
48
20 A cart halves its mass and at the same time doubles its speed Does the kinetic energy increase or decrease By what factor does the kinetic energy change
A increase 2
B increase 4
C decrease 2
D decrease 4
Answer
bull half the mass gives 12 the KEbull double the speed gives 4 x KEbull therefore (12)(4)= 2
A
49
Stored Energy
Return to Tableof Contents
50
Where does Kinetic Energy Come From
Imagine a roller coaster car that is at the top of the first hill and is stopped
Does the car stay stopped at the top of the hill for the entire ride
What happens
51
Where does Kinetic Energy Come From
Once the car leans over the edge gravity pulls it down The ride is taking advantage of the gravitational attraction between the car and Earth to give the car kinetic energy and make it go faster as it falls
The kinetic energy the car is receiving is coming from another type of energy called potential energy
52
Where does Kinetic Energy Come From
Potential energy is energy stored in an object due to the objects position The roller coaster car on the previous slide had stored energy due to its height above the ground
There are two forms of potential energy that we will be looking at in this unit
Gravitational Potential Energy
and
Elastic Potential Energy
53
Gravitational Potential Energy
The potential energy due to elevated positions is called gravitational potential energy
Gravitational potential energy is stored energy and it can be used at a later time to cause an object to moveOnce the person steps off the diving board the gravitational potential energy is converted into kinetic energy and the person falls (moves)
54
Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
55
Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
56
h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
35
Calculating Kinetic Energy
Kinetic energy can be solved for by using the equation
12KE = mv2
Lets fill in the table below
variable unitsName
Kinetic Energy
mms
36
Example shy Calculating Kinetic Energy
A car which has a mass of 1000 kg is moving with a velocity of 5 ms How much kinetic energy does the car possess Calculate the cars kinetic energy
KE = mv2KE = (05)(1000 kg)(5 ms)2
KE = (05)(1000 kg)(25 m2s2)KE = 125000 J
12
Click on the box to see the solution
Teacher N
otes
37
11 A 10 kg snowball is rolling down a hill Just before reaching the bottom its velocity is measured to be 10 ms What is the kinetic energy of the ball at this position
Answer
38
12 A 100 kg running back in football is running with a velocity of 2 ms What is his kinetic energy
Answer
KE= 12 mv2KE= 12 (100 kg) (2 ms)2KE= 12 (100 kg) (4m2s2)KE= 200 J
39
13 A 2000 kg car with a velocity of 20 ms slows down and stops at a red light What is the change in kinetic energy
Answer
40
14 A 50 kg girl rode her 12 kg bicycle in a race She started from rest and peddled with a velocity of 10 ms What is the change in kinetic energy of the girl and her bicycle
Answer
41
Thinking Mathematically
KE = mv212
We have already said that mass is directly proportional to kinetic energy
This means that if the mass of the object doubles the
kinetic energy ___________ If the mass of the object increases by a
factor of 5 then the kinetic energy___________ by ______________
If the mass of the object decreases by half then the kinetic
energy will ____________ by ___________
doubles
increases a factor of 5
decrease half
42
15 If the mass of a wagon is doubled its kinetic energy
A increases
B decreases
Answer
43
16 If the mass of a wagon is doubled by what factor does the kinetic energy increase
Answer
44
Thinking Mathematically
Kinetic energy can be solved by using the equation
KE = mv212
From the equation we can see that the kinetic energy is also directly proportional to the square of the velocity
This means that if the velocity doubles the kinetic energy increases by a factor of 4
22=4
If the velocity is quadrupled then the kinetic energy increases by a factor of 16
42= 16
45
17 If the velocity of a wagon is tripled its kinetic energy
Answer
A increases
B decreases
46
18 If the velocity of a wagon is tripled by what factor does the kinetic energy increase
Answer
47
19 Two balls are moving with the same velocity ball A has a mass of 10 kg and ball B has a mass of 40 kg How much more kinetic energy does ball B have
Answer
48
20 A cart halves its mass and at the same time doubles its speed Does the kinetic energy increase or decrease By what factor does the kinetic energy change
A increase 2
B increase 4
C decrease 2
D decrease 4
Answer
bull half the mass gives 12 the KEbull double the speed gives 4 x KEbull therefore (12)(4)= 2
A
49
Stored Energy
Return to Tableof Contents
50
Where does Kinetic Energy Come From
Imagine a roller coaster car that is at the top of the first hill and is stopped
Does the car stay stopped at the top of the hill for the entire ride
What happens
51
Where does Kinetic Energy Come From
Once the car leans over the edge gravity pulls it down The ride is taking advantage of the gravitational attraction between the car and Earth to give the car kinetic energy and make it go faster as it falls
The kinetic energy the car is receiving is coming from another type of energy called potential energy
52
Where does Kinetic Energy Come From
Potential energy is energy stored in an object due to the objects position The roller coaster car on the previous slide had stored energy due to its height above the ground
There are two forms of potential energy that we will be looking at in this unit
Gravitational Potential Energy
and
Elastic Potential Energy
53
Gravitational Potential Energy
The potential energy due to elevated positions is called gravitational potential energy
Gravitational potential energy is stored energy and it can be used at a later time to cause an object to moveOnce the person steps off the diving board the gravitational potential energy is converted into kinetic energy and the person falls (moves)
54
Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
55
Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
56
h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
36
Example shy Calculating Kinetic Energy
A car which has a mass of 1000 kg is moving with a velocity of 5 ms How much kinetic energy does the car possess Calculate the cars kinetic energy
KE = mv2KE = (05)(1000 kg)(5 ms)2
KE = (05)(1000 kg)(25 m2s2)KE = 125000 J
12
Click on the box to see the solution
Teacher N
otes
37
11 A 10 kg snowball is rolling down a hill Just before reaching the bottom its velocity is measured to be 10 ms What is the kinetic energy of the ball at this position
Answer
38
12 A 100 kg running back in football is running with a velocity of 2 ms What is his kinetic energy
Answer
KE= 12 mv2KE= 12 (100 kg) (2 ms)2KE= 12 (100 kg) (4m2s2)KE= 200 J
39
13 A 2000 kg car with a velocity of 20 ms slows down and stops at a red light What is the change in kinetic energy
Answer
40
14 A 50 kg girl rode her 12 kg bicycle in a race She started from rest and peddled with a velocity of 10 ms What is the change in kinetic energy of the girl and her bicycle
Answer
41
Thinking Mathematically
KE = mv212
We have already said that mass is directly proportional to kinetic energy
This means that if the mass of the object doubles the
kinetic energy ___________ If the mass of the object increases by a
factor of 5 then the kinetic energy___________ by ______________
If the mass of the object decreases by half then the kinetic
energy will ____________ by ___________
doubles
increases a factor of 5
decrease half
42
15 If the mass of a wagon is doubled its kinetic energy
A increases
B decreases
Answer
43
16 If the mass of a wagon is doubled by what factor does the kinetic energy increase
Answer
44
Thinking Mathematically
Kinetic energy can be solved by using the equation
KE = mv212
From the equation we can see that the kinetic energy is also directly proportional to the square of the velocity
This means that if the velocity doubles the kinetic energy increases by a factor of 4
22=4
If the velocity is quadrupled then the kinetic energy increases by a factor of 16
42= 16
45
17 If the velocity of a wagon is tripled its kinetic energy
Answer
A increases
B decreases
46
18 If the velocity of a wagon is tripled by what factor does the kinetic energy increase
Answer
47
19 Two balls are moving with the same velocity ball A has a mass of 10 kg and ball B has a mass of 40 kg How much more kinetic energy does ball B have
Answer
48
20 A cart halves its mass and at the same time doubles its speed Does the kinetic energy increase or decrease By what factor does the kinetic energy change
A increase 2
B increase 4
C decrease 2
D decrease 4
Answer
bull half the mass gives 12 the KEbull double the speed gives 4 x KEbull therefore (12)(4)= 2
A
49
Stored Energy
Return to Tableof Contents
50
Where does Kinetic Energy Come From
Imagine a roller coaster car that is at the top of the first hill and is stopped
Does the car stay stopped at the top of the hill for the entire ride
What happens
51
Where does Kinetic Energy Come From
Once the car leans over the edge gravity pulls it down The ride is taking advantage of the gravitational attraction between the car and Earth to give the car kinetic energy and make it go faster as it falls
The kinetic energy the car is receiving is coming from another type of energy called potential energy
52
Where does Kinetic Energy Come From
Potential energy is energy stored in an object due to the objects position The roller coaster car on the previous slide had stored energy due to its height above the ground
There are two forms of potential energy that we will be looking at in this unit
Gravitational Potential Energy
and
Elastic Potential Energy
53
Gravitational Potential Energy
The potential energy due to elevated positions is called gravitational potential energy
Gravitational potential energy is stored energy and it can be used at a later time to cause an object to moveOnce the person steps off the diving board the gravitational potential energy is converted into kinetic energy and the person falls (moves)
54
Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
55
Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
56
h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
37
11 A 10 kg snowball is rolling down a hill Just before reaching the bottom its velocity is measured to be 10 ms What is the kinetic energy of the ball at this position
Answer
38
12 A 100 kg running back in football is running with a velocity of 2 ms What is his kinetic energy
Answer
KE= 12 mv2KE= 12 (100 kg) (2 ms)2KE= 12 (100 kg) (4m2s2)KE= 200 J
39
13 A 2000 kg car with a velocity of 20 ms slows down and stops at a red light What is the change in kinetic energy
Answer
40
14 A 50 kg girl rode her 12 kg bicycle in a race She started from rest and peddled with a velocity of 10 ms What is the change in kinetic energy of the girl and her bicycle
Answer
41
Thinking Mathematically
KE = mv212
We have already said that mass is directly proportional to kinetic energy
This means that if the mass of the object doubles the
kinetic energy ___________ If the mass of the object increases by a
factor of 5 then the kinetic energy___________ by ______________
If the mass of the object decreases by half then the kinetic
energy will ____________ by ___________
doubles
increases a factor of 5
decrease half
42
15 If the mass of a wagon is doubled its kinetic energy
A increases
B decreases
Answer
43
16 If the mass of a wagon is doubled by what factor does the kinetic energy increase
Answer
44
Thinking Mathematically
Kinetic energy can be solved by using the equation
KE = mv212
From the equation we can see that the kinetic energy is also directly proportional to the square of the velocity
This means that if the velocity doubles the kinetic energy increases by a factor of 4
22=4
If the velocity is quadrupled then the kinetic energy increases by a factor of 16
42= 16
45
17 If the velocity of a wagon is tripled its kinetic energy
Answer
A increases
B decreases
46
18 If the velocity of a wagon is tripled by what factor does the kinetic energy increase
Answer
47
19 Two balls are moving with the same velocity ball A has a mass of 10 kg and ball B has a mass of 40 kg How much more kinetic energy does ball B have
Answer
48
20 A cart halves its mass and at the same time doubles its speed Does the kinetic energy increase or decrease By what factor does the kinetic energy change
A increase 2
B increase 4
C decrease 2
D decrease 4
Answer
bull half the mass gives 12 the KEbull double the speed gives 4 x KEbull therefore (12)(4)= 2
A
49
Stored Energy
Return to Tableof Contents
50
Where does Kinetic Energy Come From
Imagine a roller coaster car that is at the top of the first hill and is stopped
Does the car stay stopped at the top of the hill for the entire ride
What happens
51
Where does Kinetic Energy Come From
Once the car leans over the edge gravity pulls it down The ride is taking advantage of the gravitational attraction between the car and Earth to give the car kinetic energy and make it go faster as it falls
The kinetic energy the car is receiving is coming from another type of energy called potential energy
52
Where does Kinetic Energy Come From
Potential energy is energy stored in an object due to the objects position The roller coaster car on the previous slide had stored energy due to its height above the ground
There are two forms of potential energy that we will be looking at in this unit
Gravitational Potential Energy
and
Elastic Potential Energy
53
Gravitational Potential Energy
The potential energy due to elevated positions is called gravitational potential energy
Gravitational potential energy is stored energy and it can be used at a later time to cause an object to moveOnce the person steps off the diving board the gravitational potential energy is converted into kinetic energy and the person falls (moves)
54
Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
55
Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
56
h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
38
12 A 100 kg running back in football is running with a velocity of 2 ms What is his kinetic energy
Answer
KE= 12 mv2KE= 12 (100 kg) (2 ms)2KE= 12 (100 kg) (4m2s2)KE= 200 J
39
13 A 2000 kg car with a velocity of 20 ms slows down and stops at a red light What is the change in kinetic energy
Answer
40
14 A 50 kg girl rode her 12 kg bicycle in a race She started from rest and peddled with a velocity of 10 ms What is the change in kinetic energy of the girl and her bicycle
Answer
41
Thinking Mathematically
KE = mv212
We have already said that mass is directly proportional to kinetic energy
This means that if the mass of the object doubles the
kinetic energy ___________ If the mass of the object increases by a
factor of 5 then the kinetic energy___________ by ______________
If the mass of the object decreases by half then the kinetic
energy will ____________ by ___________
doubles
increases a factor of 5
decrease half
42
15 If the mass of a wagon is doubled its kinetic energy
A increases
B decreases
Answer
43
16 If the mass of a wagon is doubled by what factor does the kinetic energy increase
Answer
44
Thinking Mathematically
Kinetic energy can be solved by using the equation
KE = mv212
From the equation we can see that the kinetic energy is also directly proportional to the square of the velocity
This means that if the velocity doubles the kinetic energy increases by a factor of 4
22=4
If the velocity is quadrupled then the kinetic energy increases by a factor of 16
42= 16
45
17 If the velocity of a wagon is tripled its kinetic energy
Answer
A increases
B decreases
46
18 If the velocity of a wagon is tripled by what factor does the kinetic energy increase
Answer
47
19 Two balls are moving with the same velocity ball A has a mass of 10 kg and ball B has a mass of 40 kg How much more kinetic energy does ball B have
Answer
48
20 A cart halves its mass and at the same time doubles its speed Does the kinetic energy increase or decrease By what factor does the kinetic energy change
A increase 2
B increase 4
C decrease 2
D decrease 4
Answer
bull half the mass gives 12 the KEbull double the speed gives 4 x KEbull therefore (12)(4)= 2
A
49
Stored Energy
Return to Tableof Contents
50
Where does Kinetic Energy Come From
Imagine a roller coaster car that is at the top of the first hill and is stopped
Does the car stay stopped at the top of the hill for the entire ride
What happens
51
Where does Kinetic Energy Come From
Once the car leans over the edge gravity pulls it down The ride is taking advantage of the gravitational attraction between the car and Earth to give the car kinetic energy and make it go faster as it falls
The kinetic energy the car is receiving is coming from another type of energy called potential energy
52
Where does Kinetic Energy Come From
Potential energy is energy stored in an object due to the objects position The roller coaster car on the previous slide had stored energy due to its height above the ground
There are two forms of potential energy that we will be looking at in this unit
Gravitational Potential Energy
and
Elastic Potential Energy
53
Gravitational Potential Energy
The potential energy due to elevated positions is called gravitational potential energy
Gravitational potential energy is stored energy and it can be used at a later time to cause an object to moveOnce the person steps off the diving board the gravitational potential energy is converted into kinetic energy and the person falls (moves)
54
Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
55
Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
56
h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
39
13 A 2000 kg car with a velocity of 20 ms slows down and stops at a red light What is the change in kinetic energy
Answer
40
14 A 50 kg girl rode her 12 kg bicycle in a race She started from rest and peddled with a velocity of 10 ms What is the change in kinetic energy of the girl and her bicycle
Answer
41
Thinking Mathematically
KE = mv212
We have already said that mass is directly proportional to kinetic energy
This means that if the mass of the object doubles the
kinetic energy ___________ If the mass of the object increases by a
factor of 5 then the kinetic energy___________ by ______________
If the mass of the object decreases by half then the kinetic
energy will ____________ by ___________
doubles
increases a factor of 5
decrease half
42
15 If the mass of a wagon is doubled its kinetic energy
A increases
B decreases
Answer
43
16 If the mass of a wagon is doubled by what factor does the kinetic energy increase
Answer
44
Thinking Mathematically
Kinetic energy can be solved by using the equation
KE = mv212
From the equation we can see that the kinetic energy is also directly proportional to the square of the velocity
This means that if the velocity doubles the kinetic energy increases by a factor of 4
22=4
If the velocity is quadrupled then the kinetic energy increases by a factor of 16
42= 16
45
17 If the velocity of a wagon is tripled its kinetic energy
Answer
A increases
B decreases
46
18 If the velocity of a wagon is tripled by what factor does the kinetic energy increase
Answer
47
19 Two balls are moving with the same velocity ball A has a mass of 10 kg and ball B has a mass of 40 kg How much more kinetic energy does ball B have
Answer
48
20 A cart halves its mass and at the same time doubles its speed Does the kinetic energy increase or decrease By what factor does the kinetic energy change
A increase 2
B increase 4
C decrease 2
D decrease 4
Answer
bull half the mass gives 12 the KEbull double the speed gives 4 x KEbull therefore (12)(4)= 2
A
49
Stored Energy
Return to Tableof Contents
50
Where does Kinetic Energy Come From
Imagine a roller coaster car that is at the top of the first hill and is stopped
Does the car stay stopped at the top of the hill for the entire ride
What happens
51
Where does Kinetic Energy Come From
Once the car leans over the edge gravity pulls it down The ride is taking advantage of the gravitational attraction between the car and Earth to give the car kinetic energy and make it go faster as it falls
The kinetic energy the car is receiving is coming from another type of energy called potential energy
52
Where does Kinetic Energy Come From
Potential energy is energy stored in an object due to the objects position The roller coaster car on the previous slide had stored energy due to its height above the ground
There are two forms of potential energy that we will be looking at in this unit
Gravitational Potential Energy
and
Elastic Potential Energy
53
Gravitational Potential Energy
The potential energy due to elevated positions is called gravitational potential energy
Gravitational potential energy is stored energy and it can be used at a later time to cause an object to moveOnce the person steps off the diving board the gravitational potential energy is converted into kinetic energy and the person falls (moves)
54
Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
55
Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
56
h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
40
14 A 50 kg girl rode her 12 kg bicycle in a race She started from rest and peddled with a velocity of 10 ms What is the change in kinetic energy of the girl and her bicycle
Answer
41
Thinking Mathematically
KE = mv212
We have already said that mass is directly proportional to kinetic energy
This means that if the mass of the object doubles the
kinetic energy ___________ If the mass of the object increases by a
factor of 5 then the kinetic energy___________ by ______________
If the mass of the object decreases by half then the kinetic
energy will ____________ by ___________
doubles
increases a factor of 5
decrease half
42
15 If the mass of a wagon is doubled its kinetic energy
A increases
B decreases
Answer
43
16 If the mass of a wagon is doubled by what factor does the kinetic energy increase
Answer
44
Thinking Mathematically
Kinetic energy can be solved by using the equation
KE = mv212
From the equation we can see that the kinetic energy is also directly proportional to the square of the velocity
This means that if the velocity doubles the kinetic energy increases by a factor of 4
22=4
If the velocity is quadrupled then the kinetic energy increases by a factor of 16
42= 16
45
17 If the velocity of a wagon is tripled its kinetic energy
Answer
A increases
B decreases
46
18 If the velocity of a wagon is tripled by what factor does the kinetic energy increase
Answer
47
19 Two balls are moving with the same velocity ball A has a mass of 10 kg and ball B has a mass of 40 kg How much more kinetic energy does ball B have
Answer
48
20 A cart halves its mass and at the same time doubles its speed Does the kinetic energy increase or decrease By what factor does the kinetic energy change
A increase 2
B increase 4
C decrease 2
D decrease 4
Answer
bull half the mass gives 12 the KEbull double the speed gives 4 x KEbull therefore (12)(4)= 2
A
49
Stored Energy
Return to Tableof Contents
50
Where does Kinetic Energy Come From
Imagine a roller coaster car that is at the top of the first hill and is stopped
Does the car stay stopped at the top of the hill for the entire ride
What happens
51
Where does Kinetic Energy Come From
Once the car leans over the edge gravity pulls it down The ride is taking advantage of the gravitational attraction between the car and Earth to give the car kinetic energy and make it go faster as it falls
The kinetic energy the car is receiving is coming from another type of energy called potential energy
52
Where does Kinetic Energy Come From
Potential energy is energy stored in an object due to the objects position The roller coaster car on the previous slide had stored energy due to its height above the ground
There are two forms of potential energy that we will be looking at in this unit
Gravitational Potential Energy
and
Elastic Potential Energy
53
Gravitational Potential Energy
The potential energy due to elevated positions is called gravitational potential energy
Gravitational potential energy is stored energy and it can be used at a later time to cause an object to moveOnce the person steps off the diving board the gravitational potential energy is converted into kinetic energy and the person falls (moves)
54
Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
55
Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
56
h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
41
Thinking Mathematically
KE = mv212
We have already said that mass is directly proportional to kinetic energy
This means that if the mass of the object doubles the
kinetic energy ___________ If the mass of the object increases by a
factor of 5 then the kinetic energy___________ by ______________
If the mass of the object decreases by half then the kinetic
energy will ____________ by ___________
doubles
increases a factor of 5
decrease half
42
15 If the mass of a wagon is doubled its kinetic energy
A increases
B decreases
Answer
43
16 If the mass of a wagon is doubled by what factor does the kinetic energy increase
Answer
44
Thinking Mathematically
Kinetic energy can be solved by using the equation
KE = mv212
From the equation we can see that the kinetic energy is also directly proportional to the square of the velocity
This means that if the velocity doubles the kinetic energy increases by a factor of 4
22=4
If the velocity is quadrupled then the kinetic energy increases by a factor of 16
42= 16
45
17 If the velocity of a wagon is tripled its kinetic energy
Answer
A increases
B decreases
46
18 If the velocity of a wagon is tripled by what factor does the kinetic energy increase
Answer
47
19 Two balls are moving with the same velocity ball A has a mass of 10 kg and ball B has a mass of 40 kg How much more kinetic energy does ball B have
Answer
48
20 A cart halves its mass and at the same time doubles its speed Does the kinetic energy increase or decrease By what factor does the kinetic energy change
A increase 2
B increase 4
C decrease 2
D decrease 4
Answer
bull half the mass gives 12 the KEbull double the speed gives 4 x KEbull therefore (12)(4)= 2
A
49
Stored Energy
Return to Tableof Contents
50
Where does Kinetic Energy Come From
Imagine a roller coaster car that is at the top of the first hill and is stopped
Does the car stay stopped at the top of the hill for the entire ride
What happens
51
Where does Kinetic Energy Come From
Once the car leans over the edge gravity pulls it down The ride is taking advantage of the gravitational attraction between the car and Earth to give the car kinetic energy and make it go faster as it falls
The kinetic energy the car is receiving is coming from another type of energy called potential energy
52
Where does Kinetic Energy Come From
Potential energy is energy stored in an object due to the objects position The roller coaster car on the previous slide had stored energy due to its height above the ground
There are two forms of potential energy that we will be looking at in this unit
Gravitational Potential Energy
and
Elastic Potential Energy
53
Gravitational Potential Energy
The potential energy due to elevated positions is called gravitational potential energy
Gravitational potential energy is stored energy and it can be used at a later time to cause an object to moveOnce the person steps off the diving board the gravitational potential energy is converted into kinetic energy and the person falls (moves)
54
Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
55
Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
56
h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
42
15 If the mass of a wagon is doubled its kinetic energy
A increases
B decreases
Answer
43
16 If the mass of a wagon is doubled by what factor does the kinetic energy increase
Answer
44
Thinking Mathematically
Kinetic energy can be solved by using the equation
KE = mv212
From the equation we can see that the kinetic energy is also directly proportional to the square of the velocity
This means that if the velocity doubles the kinetic energy increases by a factor of 4
22=4
If the velocity is quadrupled then the kinetic energy increases by a factor of 16
42= 16
45
17 If the velocity of a wagon is tripled its kinetic energy
Answer
A increases
B decreases
46
18 If the velocity of a wagon is tripled by what factor does the kinetic energy increase
Answer
47
19 Two balls are moving with the same velocity ball A has a mass of 10 kg and ball B has a mass of 40 kg How much more kinetic energy does ball B have
Answer
48
20 A cart halves its mass and at the same time doubles its speed Does the kinetic energy increase or decrease By what factor does the kinetic energy change
A increase 2
B increase 4
C decrease 2
D decrease 4
Answer
bull half the mass gives 12 the KEbull double the speed gives 4 x KEbull therefore (12)(4)= 2
A
49
Stored Energy
Return to Tableof Contents
50
Where does Kinetic Energy Come From
Imagine a roller coaster car that is at the top of the first hill and is stopped
Does the car stay stopped at the top of the hill for the entire ride
What happens
51
Where does Kinetic Energy Come From
Once the car leans over the edge gravity pulls it down The ride is taking advantage of the gravitational attraction between the car and Earth to give the car kinetic energy and make it go faster as it falls
The kinetic energy the car is receiving is coming from another type of energy called potential energy
52
Where does Kinetic Energy Come From
Potential energy is energy stored in an object due to the objects position The roller coaster car on the previous slide had stored energy due to its height above the ground
There are two forms of potential energy that we will be looking at in this unit
Gravitational Potential Energy
and
Elastic Potential Energy
53
Gravitational Potential Energy
The potential energy due to elevated positions is called gravitational potential energy
Gravitational potential energy is stored energy and it can be used at a later time to cause an object to moveOnce the person steps off the diving board the gravitational potential energy is converted into kinetic energy and the person falls (moves)
54
Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
55
Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
56
h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
43
16 If the mass of a wagon is doubled by what factor does the kinetic energy increase
Answer
44
Thinking Mathematically
Kinetic energy can be solved by using the equation
KE = mv212
From the equation we can see that the kinetic energy is also directly proportional to the square of the velocity
This means that if the velocity doubles the kinetic energy increases by a factor of 4
22=4
If the velocity is quadrupled then the kinetic energy increases by a factor of 16
42= 16
45
17 If the velocity of a wagon is tripled its kinetic energy
Answer
A increases
B decreases
46
18 If the velocity of a wagon is tripled by what factor does the kinetic energy increase
Answer
47
19 Two balls are moving with the same velocity ball A has a mass of 10 kg and ball B has a mass of 40 kg How much more kinetic energy does ball B have
Answer
48
20 A cart halves its mass and at the same time doubles its speed Does the kinetic energy increase or decrease By what factor does the kinetic energy change
A increase 2
B increase 4
C decrease 2
D decrease 4
Answer
bull half the mass gives 12 the KEbull double the speed gives 4 x KEbull therefore (12)(4)= 2
A
49
Stored Energy
Return to Tableof Contents
50
Where does Kinetic Energy Come From
Imagine a roller coaster car that is at the top of the first hill and is stopped
Does the car stay stopped at the top of the hill for the entire ride
What happens
51
Where does Kinetic Energy Come From
Once the car leans over the edge gravity pulls it down The ride is taking advantage of the gravitational attraction between the car and Earth to give the car kinetic energy and make it go faster as it falls
The kinetic energy the car is receiving is coming from another type of energy called potential energy
52
Where does Kinetic Energy Come From
Potential energy is energy stored in an object due to the objects position The roller coaster car on the previous slide had stored energy due to its height above the ground
There are two forms of potential energy that we will be looking at in this unit
Gravitational Potential Energy
and
Elastic Potential Energy
53
Gravitational Potential Energy
The potential energy due to elevated positions is called gravitational potential energy
Gravitational potential energy is stored energy and it can be used at a later time to cause an object to moveOnce the person steps off the diving board the gravitational potential energy is converted into kinetic energy and the person falls (moves)
54
Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
55
Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
56
h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
44
Thinking Mathematically
Kinetic energy can be solved by using the equation
KE = mv212
From the equation we can see that the kinetic energy is also directly proportional to the square of the velocity
This means that if the velocity doubles the kinetic energy increases by a factor of 4
22=4
If the velocity is quadrupled then the kinetic energy increases by a factor of 16
42= 16
45
17 If the velocity of a wagon is tripled its kinetic energy
Answer
A increases
B decreases
46
18 If the velocity of a wagon is tripled by what factor does the kinetic energy increase
Answer
47
19 Two balls are moving with the same velocity ball A has a mass of 10 kg and ball B has a mass of 40 kg How much more kinetic energy does ball B have
Answer
48
20 A cart halves its mass and at the same time doubles its speed Does the kinetic energy increase or decrease By what factor does the kinetic energy change
A increase 2
B increase 4
C decrease 2
D decrease 4
Answer
bull half the mass gives 12 the KEbull double the speed gives 4 x KEbull therefore (12)(4)= 2
A
49
Stored Energy
Return to Tableof Contents
50
Where does Kinetic Energy Come From
Imagine a roller coaster car that is at the top of the first hill and is stopped
Does the car stay stopped at the top of the hill for the entire ride
What happens
51
Where does Kinetic Energy Come From
Once the car leans over the edge gravity pulls it down The ride is taking advantage of the gravitational attraction between the car and Earth to give the car kinetic energy and make it go faster as it falls
The kinetic energy the car is receiving is coming from another type of energy called potential energy
52
Where does Kinetic Energy Come From
Potential energy is energy stored in an object due to the objects position The roller coaster car on the previous slide had stored energy due to its height above the ground
There are two forms of potential energy that we will be looking at in this unit
Gravitational Potential Energy
and
Elastic Potential Energy
53
Gravitational Potential Energy
The potential energy due to elevated positions is called gravitational potential energy
Gravitational potential energy is stored energy and it can be used at a later time to cause an object to moveOnce the person steps off the diving board the gravitational potential energy is converted into kinetic energy and the person falls (moves)
54
Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
55
Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
56
h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
45
17 If the velocity of a wagon is tripled its kinetic energy
Answer
A increases
B decreases
46
18 If the velocity of a wagon is tripled by what factor does the kinetic energy increase
Answer
47
19 Two balls are moving with the same velocity ball A has a mass of 10 kg and ball B has a mass of 40 kg How much more kinetic energy does ball B have
Answer
48
20 A cart halves its mass and at the same time doubles its speed Does the kinetic energy increase or decrease By what factor does the kinetic energy change
A increase 2
B increase 4
C decrease 2
D decrease 4
Answer
bull half the mass gives 12 the KEbull double the speed gives 4 x KEbull therefore (12)(4)= 2
A
49
Stored Energy
Return to Tableof Contents
50
Where does Kinetic Energy Come From
Imagine a roller coaster car that is at the top of the first hill and is stopped
Does the car stay stopped at the top of the hill for the entire ride
What happens
51
Where does Kinetic Energy Come From
Once the car leans over the edge gravity pulls it down The ride is taking advantage of the gravitational attraction between the car and Earth to give the car kinetic energy and make it go faster as it falls
The kinetic energy the car is receiving is coming from another type of energy called potential energy
52
Where does Kinetic Energy Come From
Potential energy is energy stored in an object due to the objects position The roller coaster car on the previous slide had stored energy due to its height above the ground
There are two forms of potential energy that we will be looking at in this unit
Gravitational Potential Energy
and
Elastic Potential Energy
53
Gravitational Potential Energy
The potential energy due to elevated positions is called gravitational potential energy
Gravitational potential energy is stored energy and it can be used at a later time to cause an object to moveOnce the person steps off the diving board the gravitational potential energy is converted into kinetic energy and the person falls (moves)
54
Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
55
Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
56
h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
46
18 If the velocity of a wagon is tripled by what factor does the kinetic energy increase
Answer
47
19 Two balls are moving with the same velocity ball A has a mass of 10 kg and ball B has a mass of 40 kg How much more kinetic energy does ball B have
Answer
48
20 A cart halves its mass and at the same time doubles its speed Does the kinetic energy increase or decrease By what factor does the kinetic energy change
A increase 2
B increase 4
C decrease 2
D decrease 4
Answer
bull half the mass gives 12 the KEbull double the speed gives 4 x KEbull therefore (12)(4)= 2
A
49
Stored Energy
Return to Tableof Contents
50
Where does Kinetic Energy Come From
Imagine a roller coaster car that is at the top of the first hill and is stopped
Does the car stay stopped at the top of the hill for the entire ride
What happens
51
Where does Kinetic Energy Come From
Once the car leans over the edge gravity pulls it down The ride is taking advantage of the gravitational attraction between the car and Earth to give the car kinetic energy and make it go faster as it falls
The kinetic energy the car is receiving is coming from another type of energy called potential energy
52
Where does Kinetic Energy Come From
Potential energy is energy stored in an object due to the objects position The roller coaster car on the previous slide had stored energy due to its height above the ground
There are two forms of potential energy that we will be looking at in this unit
Gravitational Potential Energy
and
Elastic Potential Energy
53
Gravitational Potential Energy
The potential energy due to elevated positions is called gravitational potential energy
Gravitational potential energy is stored energy and it can be used at a later time to cause an object to moveOnce the person steps off the diving board the gravitational potential energy is converted into kinetic energy and the person falls (moves)
54
Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
55
Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
56
h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
47
19 Two balls are moving with the same velocity ball A has a mass of 10 kg and ball B has a mass of 40 kg How much more kinetic energy does ball B have
Answer
48
20 A cart halves its mass and at the same time doubles its speed Does the kinetic energy increase or decrease By what factor does the kinetic energy change
A increase 2
B increase 4
C decrease 2
D decrease 4
Answer
bull half the mass gives 12 the KEbull double the speed gives 4 x KEbull therefore (12)(4)= 2
A
49
Stored Energy
Return to Tableof Contents
50
Where does Kinetic Energy Come From
Imagine a roller coaster car that is at the top of the first hill and is stopped
Does the car stay stopped at the top of the hill for the entire ride
What happens
51
Where does Kinetic Energy Come From
Once the car leans over the edge gravity pulls it down The ride is taking advantage of the gravitational attraction between the car and Earth to give the car kinetic energy and make it go faster as it falls
The kinetic energy the car is receiving is coming from another type of energy called potential energy
52
Where does Kinetic Energy Come From
Potential energy is energy stored in an object due to the objects position The roller coaster car on the previous slide had stored energy due to its height above the ground
There are two forms of potential energy that we will be looking at in this unit
Gravitational Potential Energy
and
Elastic Potential Energy
53
Gravitational Potential Energy
The potential energy due to elevated positions is called gravitational potential energy
Gravitational potential energy is stored energy and it can be used at a later time to cause an object to moveOnce the person steps off the diving board the gravitational potential energy is converted into kinetic energy and the person falls (moves)
54
Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
55
Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
56
h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
48
20 A cart halves its mass and at the same time doubles its speed Does the kinetic energy increase or decrease By what factor does the kinetic energy change
A increase 2
B increase 4
C decrease 2
D decrease 4
Answer
bull half the mass gives 12 the KEbull double the speed gives 4 x KEbull therefore (12)(4)= 2
A
49
Stored Energy
Return to Tableof Contents
50
Where does Kinetic Energy Come From
Imagine a roller coaster car that is at the top of the first hill and is stopped
Does the car stay stopped at the top of the hill for the entire ride
What happens
51
Where does Kinetic Energy Come From
Once the car leans over the edge gravity pulls it down The ride is taking advantage of the gravitational attraction between the car and Earth to give the car kinetic energy and make it go faster as it falls
The kinetic energy the car is receiving is coming from another type of energy called potential energy
52
Where does Kinetic Energy Come From
Potential energy is energy stored in an object due to the objects position The roller coaster car on the previous slide had stored energy due to its height above the ground
There are two forms of potential energy that we will be looking at in this unit
Gravitational Potential Energy
and
Elastic Potential Energy
53
Gravitational Potential Energy
The potential energy due to elevated positions is called gravitational potential energy
Gravitational potential energy is stored energy and it can be used at a later time to cause an object to moveOnce the person steps off the diving board the gravitational potential energy is converted into kinetic energy and the person falls (moves)
54
Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
55
Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
56
h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
49
Stored Energy
Return to Tableof Contents
50
Where does Kinetic Energy Come From
Imagine a roller coaster car that is at the top of the first hill and is stopped
Does the car stay stopped at the top of the hill for the entire ride
What happens
51
Where does Kinetic Energy Come From
Once the car leans over the edge gravity pulls it down The ride is taking advantage of the gravitational attraction between the car and Earth to give the car kinetic energy and make it go faster as it falls
The kinetic energy the car is receiving is coming from another type of energy called potential energy
52
Where does Kinetic Energy Come From
Potential energy is energy stored in an object due to the objects position The roller coaster car on the previous slide had stored energy due to its height above the ground
There are two forms of potential energy that we will be looking at in this unit
Gravitational Potential Energy
and
Elastic Potential Energy
53
Gravitational Potential Energy
The potential energy due to elevated positions is called gravitational potential energy
Gravitational potential energy is stored energy and it can be used at a later time to cause an object to moveOnce the person steps off the diving board the gravitational potential energy is converted into kinetic energy and the person falls (moves)
54
Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
55
Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
56
h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
50
Where does Kinetic Energy Come From
Imagine a roller coaster car that is at the top of the first hill and is stopped
Does the car stay stopped at the top of the hill for the entire ride
What happens
51
Where does Kinetic Energy Come From
Once the car leans over the edge gravity pulls it down The ride is taking advantage of the gravitational attraction between the car and Earth to give the car kinetic energy and make it go faster as it falls
The kinetic energy the car is receiving is coming from another type of energy called potential energy
52
Where does Kinetic Energy Come From
Potential energy is energy stored in an object due to the objects position The roller coaster car on the previous slide had stored energy due to its height above the ground
There are two forms of potential energy that we will be looking at in this unit
Gravitational Potential Energy
and
Elastic Potential Energy
53
Gravitational Potential Energy
The potential energy due to elevated positions is called gravitational potential energy
Gravitational potential energy is stored energy and it can be used at a later time to cause an object to moveOnce the person steps off the diving board the gravitational potential energy is converted into kinetic energy and the person falls (moves)
54
Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
55
Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
56
h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
51
Where does Kinetic Energy Come From
Once the car leans over the edge gravity pulls it down The ride is taking advantage of the gravitational attraction between the car and Earth to give the car kinetic energy and make it go faster as it falls
The kinetic energy the car is receiving is coming from another type of energy called potential energy
52
Where does Kinetic Energy Come From
Potential energy is energy stored in an object due to the objects position The roller coaster car on the previous slide had stored energy due to its height above the ground
There are two forms of potential energy that we will be looking at in this unit
Gravitational Potential Energy
and
Elastic Potential Energy
53
Gravitational Potential Energy
The potential energy due to elevated positions is called gravitational potential energy
Gravitational potential energy is stored energy and it can be used at a later time to cause an object to moveOnce the person steps off the diving board the gravitational potential energy is converted into kinetic energy and the person falls (moves)
54
Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
55
Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
56
h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
52
Where does Kinetic Energy Come From
Potential energy is energy stored in an object due to the objects position The roller coaster car on the previous slide had stored energy due to its height above the ground
There are two forms of potential energy that we will be looking at in this unit
Gravitational Potential Energy
and
Elastic Potential Energy
53
Gravitational Potential Energy
The potential energy due to elevated positions is called gravitational potential energy
Gravitational potential energy is stored energy and it can be used at a later time to cause an object to moveOnce the person steps off the diving board the gravitational potential energy is converted into kinetic energy and the person falls (moves)
54
Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
55
Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
56
h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
53
Gravitational Potential Energy
The potential energy due to elevated positions is called gravitational potential energy
Gravitational potential energy is stored energy and it can be used at a later time to cause an object to moveOnce the person steps off the diving board the gravitational potential energy is converted into kinetic energy and the person falls (moves)
54
Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
55
Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
56
h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
54
Gravitational Potential Energy
Work is required to elevate objects against Earths gravity
For example work is done on the truck to elevate it off the ground The amount of work done on the truck is equal to the trucks gravitational potential energy at this new height
55
Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
56
h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
55
Gravitational Potential EnergyGravitational potential energy is determined by three factors mass gravitational acceleration and height All three factors are directly proportional to energy
Mass The heavier the object is the _______ gravitational potential energy the object has
Gravitational Acceleration The larger the g the _________ gravitational potential energy the object has Since gravity on Earth is considered a constant this will not change
Height The higher the object is off the ground the _________ gravitational potential energy the object has
more
more
more
56
h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
56
h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture the mass of a tennis ball was doubled when it was at the same height off of the ground
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare for the two objects
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
57
h = 2 m h = 2 m
m = 2 kg m = 1 kg Mass doubledGravitational Acceleration stayed the same no changeHeight stayed the same no change
Since the only thing that changed was the mass which doubled the gravitational potential energy also doubled
How Does Mass Affect Gravitational Potential Energy
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
58
h = 4 m
h = 2 m
In this picture a tennis ball is lifted to a height that is twice as high
How Does Height Affect Gravitational Potential Energy
How would the gravitational potential energy compare at the
higher height
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
59
h = 4 m
h = 2 m
Mass stayed the same no changeGravitational Acceleration stayed the same no changeHeight doubled
Since the only thing that changed was the height which doubled the gravitational potential energy also doubled
How Does Height Affect Gravitational Potential Energy
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
60
21 A bowling ball which has a mass that is 30 times larger than a softball is lifted to the same height as the softball How does the gravitational potential energy of the bowling ball compare to the softball
A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
D
Answer
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
61
22 Two balloons are floating in the sky If one balloon is floating at a height of 30 m and the other identical balloon is floating at a height of 45 m how much larger is the gravitational potential energy of the higher balloon compared to the lower one
A half as large
B they are the same
C 15 times larger
D twice as large
Answer
C
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
62
Calculating Gravitational Potential Energy
Gravitational potential energy can be solved by using the equation
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mghLets fill in the table below
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
63
Example shy Calculating Gravitational Potential Energy
A basketball with a mass of 05 kg is held at a height of 2 m above the ground How much gravitational potential energy does the basketball possess
GPE = mghGPE = (05 kg)(98 ms2)(2 m)
GPE = 98 J
Click on the box to see the solution
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
64
23 A 50 kg diver is standing on top of a 10 m platform How much gravitational potential energy does he have
Answer
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
65
24 A 3000 kg hot air balloon is hovering at a height of 100 m above Earths surface How much gravitational potential energy does it possess
Answer GPE= mgh
= 3000 kg(98 ms2)(100 m)= 294000000 J
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
66
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
GPE = mgh
Thinking Mathematically
If any of these decrease then the GPE decreases by the same factor
We know that GPE is directly proportional to mass to gravity and to height This means that as any of these increase the GPE increases by the same factor
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
67
25 A ball is at a height of 30 m It is then moved to a height of 60m By what factor does the GPE increase
Answer 2
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
68
26 A 3 kg object and a 9 kg object are elevated from the same height Which has more GPE
A 3 kg object
B 9 kg object
Answer
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
69
27 A 3 kg object and a 9 kg object are dropped from the same height How much less is the GPE of the 3 kg object than the 9 kg object
Answer 13
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
70
28 An object is 5 m above the ground The object triples its mass and doubles its height By what factor does the objects GPE change
Answer 6
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
71
Elastic Potential Energy
Another type of stored energy is called elastic potential energy
Looking at the picture to the right can you come up with an idea about what elastic potential energy is
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
72
Elastic potential energy is determined by two factors the elasticity of the material and how far it is stretched or compressed
Elastic Potential Energy
Think about what you know about rubber bands
Do you think elasticity and distance stretched are directly proportional or indirectly proportional to the energy
Talk about this at your table
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
73
Elasticity The more elastic a material is the more elastic potential energy the object has
Distance of stretch (or compression) The larger the distance the elastic material is stretched (or compressed) the more elastic potential energy it has
Elastic Potential Energy
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
74
What is the Difference Between Stretching and Compression in a Spring
Think about a slinky sitting on a desk A spring has no potential energy stored in it if it is neither stretched nor compressed This relaxed state is shown in figure (a)
Stretching a spring is caused when the spring is pulled increasing the length of the spring compared to the relaxed length as shown in figure (b)
(a) (b) (c)
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
75
What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed This causes a decrease in the length of the spring compared to the relaxed length as shown in figure (c)
The stretched and compressed spring below store the same elastic potential energy because both springs are displaced the same distance x
(a) (b) (c)
relaxed stretched compressed
no EPE stored
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
76
How Does Elastic Potential Energy Depend Upon Compression and Stretching
Both pictures to the right show a spring which is an elastic material
In the top picture the spring is stretched from its relaxed state
In the bottom picture the spring is compressed from its relaxed state
For each case is elastic potential energy stored in the spring
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
77
29 A child jumps on a trampoline When will the trampoline have more elastic potential energy
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after jumping
D The trampoline will always have the same elastic potential energy
Answer
C
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
78
Calculating Elastic Potential Energy
Elastic potential energy can be solved by using the equation
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (Nm) x = distance of stretch or compression (m)
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
79
Spring Constant
The energy and distance variables in this equation are likely familiar
12EPE = kx2
But what is the spring constant (k) Look at the two springs to the right Which do you think would be easier to stretch
Every spring has a different degree of stretchiness and that is what the spring constant represents
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
80
Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents
Can you explain what Newtons per Meter (Nm) means
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
81
Example shy Calculating Elastic Potential Energy
A spring that has a spring constant of 10 Nm is stretched a distance of 1 m from its relaxed length How much elastic potential energy is stored in the spring
EPE = kx2
EPE = ( )(10 Nm)(1 m)2
EPE = ( )(10 Nm)(1 m2)EPE = (5 Nm)EPE = 5 J
1212
12
Click on the box to see the solution
Teacher N
otes
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
82
30 A child bouncing on a pogo stick compresses the spring by 025 m If the spring constant of the spring on the bottom of the pogo stick is 200 Nm what is the elastic potential energy stored in the spring when it is compressed
Answer
EPE= 12 kx2= 12 (200 Nm) (025 m) 2= 12 (200 Nm)(00625 m2)= 100 Nm (00625 m2)EPE = 625 J
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
83
31 A rubber band with a spring constant of 40 Nm is pulled back 05 m How much elastic potential energy is stored in the elastic band
Answer
EPE= 12 kx2= 12 (40 Nm) (05 m)2= 20 Nm (025 m2)EPE = 5 J
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
84
32 Which of the following would you expect to have the smallest spring constant
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
Answer
C
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
85
Thinking Mathematically
EPE = kx212
12KE = mv2
Notice that the equation for EPE is similar to the equation for KE Remember that in the equation for KE energy was directly proportional to the mass and it was also directly proportional to the square of the velocity
What do you think the relationship is between EPE and the spring constant k
What do you think is the relationship between EPE and the distance x the spring is stretched or compressed
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
86
Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant
EPE is _________________________ to the square of the
distance the spring is compressed or stretched
directly proportional
directly proportional
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
87
33 If the spring constant k is tripled by what factor does the EPE increase
Answer
3
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
88
34 If the spring constant k is halved by what factor does the EPE decrease
Answer
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
89
35 If the distance a spring is stretched is increased by a factor of 6 by what factor is the EPE increased
Answer
36
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
90
Conservation of Energy
Return to Tableof Contents
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
91
What we have looked at so far is that an object has kinetic energy if the object is in motion The faster that the object is going the more
kinetic energy it has
In order for an objects kinetic energy to increase it must get energy from somewhere But where would it get that energy
Conservation of Energy
Hint think back to the roller coaster What kind of energy did it have at the
top of the hill
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
92
This is called the Conservation of Energy
initial Total Energy = final Total Energy
TEi = TEf
In order for an objects kinetic energy to increase it must take energy from its stored energy which we call potential energy When this happens the potential energy that an object possesses decreases
Even though kinetic and potential energy are changing the Total Energy (TE) in that closed system contains does not change
Conservation of Energy
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
93
When energy is conserved no energy is added or taken away from the system The total energy you start with is the total energy you end with
TEi = TEf
In other words energy can not be created or destroyed It can only be transformed from one form to another
Conservation of Energy
Click here to see conservation of energy explained in roller coasters
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
94
When looking at the mechanical energy of a system the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together Therefore another way to write conservation of energy is like this
(PE + KE)i = (PE + KE)f
Conservation of Energy
When would PE be zero
bull the object is on the ground (GPE)
bull when a spring or other elastic material is not
stretched or compressed (EPE)
When would KE be zero
bull the object is not moving
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
95
Conservation of EnergyLets see if we can determine the total energy of a ball that is dropped from rest The figure below shows the ball at different positions as it falls starting with when its at rest at 1 m before being dropped Use the idea of conservation of energy to determine the missing values
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
Remember that the total mechanical energy at that position is the sum of the two individual energies (PE + KE)
TE = 05 JPE = 05 J KE = 0 J TE = 05 J
PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
96
At position A in the diagram below the roller coaster car has 40 J of total energy and has a velocity equal to 0 ms
40 J
15 J25 J
How much kinetic energy does the car possess at Point A
0 J
How much gravitational potential energy does the car possess at Point A
40 J
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
97
At position B in the diagram below the roller coaster car has a gravitational potential energy equal to 15 J
40 J
15 J25 J
How much total energy does the car possess at Point B
40 J
How much kinetic energy does the car possess at Point B
25 J
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
98
At position C in the diagram below the roller coaster car has a gravitational potential energy equal to 25 J
40 J
15 J25 J
How much total energy does the car possess at Point C
40 J
How much kinetic energy does the car possess at Point C
15 J
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
99
36 At what position in the diagram below does the object have only gravitational potential energy
A W
B X
C Y
D Z
E None of the above h = 0 m
Answer
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
100
37 At what position in the diagram below does the object have only kinetic energy
A W
B X
C Y
D Z
E None of the above
h = 0 m
Answer
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
101
38 At what position in the diagram below does the object have both gravitational potential and kinetic energy Choose all that apply
A W
B X
C Y
D Z
E None of the aboveh = 0 m
Answer
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
102
Transfer of Kinetic Energy to Potential Energy
The total energy of the object must always be the same due to conservation of energy Lets look at the ball that is dropped from 1 m again Suppose the ball bounces after it hits the ground What will happen to the KE
Just as potential energy can be transferred to kinetic energy kinetic energy can be transferred into potential energy
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
103
Transfer of Kinetic Energy to Potential Energy
The kinetic energy at the bottom will be transferred to gravitational potential energy as the ball gains height Because of conservation of energy the total energy stays the same
v= 0 msHeight = 1 m
Height = 05 m
Height = 0 m
TE = 05 JPE = 05 J KE = 0 J
TE = 05 J PE = 025 JKE = 025 J
TE = 05 J PE = 0 JKE = 05 J
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
104
Transfer of Kinetic Energy to Potential Energy
In reality the ball will not bounce as high as it was dropped Does this mean energy was lost
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 05 J PE = 025 JKE = 015 J
TE = 05 JPE = 04 J KE = 0 J
Sound Energy
No It just means that some of the KE that the ball had when it first hits the ground was transferred to the ground as heat and sound energy (aka NonshyMechanical Energy) If we consider the ball and the ground to be a closed system then the systems total energy stays the same
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
105
Transfer of Kinetic Energy to Potential Energy
Conservation of energy of still applies which means the total energy remains constant
Lets consider a system that is composed of a block and a spring as shown to the right
Kinetic energy can also be transferred to elastic potential energy
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
106
Transfer of Kinetic Energy to Elastic Potential Energy
In the top picture the block is travelling at 10 ms meaning that it has kinetic energy The spring is relaxed and therefore has no elastic potential energy The total energy of the blockshyspring system is entirely due to the KE of the block right now
In the bottom picture the block has compressed the spring and is no longer moving The block has transferred its kinetic energy to elastic potential energy in the spring The total energy of the blockshyspring system is entirely due to the elastic potential energy in the spring
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
107
39 In which position of the block would the system have only EPE
A B C Answer
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
108
40 In which position of the block would the system have both KE and EPE
A B C Answer
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
109
41 In which position of the block would the system have only KE
A B C
Answer
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
110
If the total amount of energy that we start with Ei does not equal the total amount of energy that we end up with Ef then energy was not conserved
TEi TEf
This means that there was an outside force that acted on the system Lets look at the dropping ball again Last time we considered the ball and the ground as the system together What if we just considered the ball as the system by itself
What if the Total Energy is not equal at the beginning and the end
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
111
v= 0 msHeight lt 1 m
TE = 05 J PE = 0 JKE = 05 J
NME = 010 J NME=010 J
TE = 04 J PE = 025 JKE = 015 J
TE = 04 JPE = 04 J KE = 0 J
Sound Energy
TE = 05 J
The total energy of the ball before the bounce and after the bounce would be different This is because the ground would now be an outside force acting on the system the ball
What if the Total Energy is not equal at the beginning and the end
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
112
Types of Energy Resources
Return to Tableof Contents
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
113
Electrical energy can be produced through the conservation of energy by using the mechanical energy contained in energy resources
Energy resources can be broken down into two categories Renewable and NonshyRenewable
Renewable Energy Resources are natural resources that can replenish themselves over time
NonshyRenewable Energy Resources are natural energy resources that exist in limited supply and cannot be replenished in a timely manner
Energy Resources
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
114
Types of Energy Resources
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
115
Energy Production from the Sun
Solar energy is a renewable form of energy that is produced when photons that are contained in sunlight are absorbed by specially designed plates that are angled towards the sun
When the photons hit the solar panels charged particles are free to move which causes a current to be produced This current is converted to usable electricity by the home
Solar energy is converted to electrical energy
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
116
Energy Production from the Wind
Wind is a renewable energy resource that is used to create electricity by wind turbines such as in the Alta Wind Energy Center in California the worlds largest wind farm
As the wind blows past the blades of the turbine the kinetic energy of the wind is transferred to the blades Inside the column of the turbine there is a drive shaft which is connected to a generator
As the blades spin it spins the drive shaft that is connected to a generator The generator converts the kinetic energy (mechanical energy) into electrical energy
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
117
Energy Production From Water Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam
Gravitational potential energy is stored in elevated water When the water is released downward towards a turbine the GPE is converted to kinetic energy and spins the turbine
The turbine is connected to a generator that converts this mechanical energy to electrical energy
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
118
Energy Production from Fossil Fuels
Fossil fuels are a nonshyrenewable energy resource that can be used to produce electricity when it is burned
Fossil fuels include natural gas oil and coal (shown to the right)
When the fuel is burned the heat turns water into steam which turn the blades of a turbine (kinetic energy) The turbine is connected to a generator that converts the mechanical energy into electrical energy
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
119
Effects of Using Fossil Fuels As An Energy Resource
Fossil fuels are nonshyrenewable energy resources due to how long it takes for them to be produced compared to how much is used to create energy
Fossil fuels take millions of years to be produced
Fossil fuels are also not considered Clean energy resources as they produce Carbon Dioxide (CO2) when burned Carbon dioxide is considered a greenhouse gas which many believe is a cause global warming
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
120
42 Which of the following is not considered a renewable energy resource
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
Answer
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
121
43 The production of energy by wind water the sun and fossil fuels relies on the principle of conservation of energy
True
False
Answer
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
122
44 The spinning of a generator in wind turbines and hydroelectric dams converts nonshymechanical energy into electrical energy
True
False
Answer
FALSE
they convert mechanical energy into electrical energy
Attachments
watchwebloc
Attachments
watchwebloc
