Post on 02-May-2018
Physics, Page 1
Chapter 8. Potential EnergyChapter 8. Potential Energyand Conservation of Energyand Conservation of Energy
Potential Energy (U)
중력 U, 탄성 U, 전자기 U, …..
Conservative Force ( 보존력)
Energy Conservation (에너지보존)
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Work: Transfer of Energy by Force• WF = |F| |S| cosθ
Kinetic Energy (Energy of Motion) • K = 1/2 mv2
Work-Kinetic Energy Theorem:• ΣW = ΔK
Review
θ
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QuestionQuestionImagine that you are comparing three different ways of having a ball move down through the same height. In which case does the ball reach the bottom with the highest speed?
1. Dropping2. Slide on ramp (no friction)3. Swinging down4. All the same
ball A is the only one without any tension or friction acting on it
In all three cases, the work done by the gravitational force is the same since the change in vertical distance is the same
1 2 3correct
it has the most distance to acceleratehas tension and gravity as forces, causing the greater acceleration
Wrong: all have same acceleration due to gravity
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QuestionQuestionImagine that you are comparing three different ways of having a ball move down through the same height. In which case does the ball get to the bottom first?
1. Dropping2. Slide on ramp (no friction)3. Swinging down4. All the same 1 2 3
correct
It has the most direct path.
They each have only gravitational force acting on them so they fall at the same speed. Since they are at the same height, they will hit at the same time.
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QuestionQuestionWhich of the following statements correctly define a Conservative Force (보존력):
1. A force is conservative when the work it does on a moving object is independent of the path of the motion between the object's initial and final positions.
2. A force is conservative when it does no net work on an object moving around a closed path, starting and finishing at the same point.
correct3. Both of the above statements are correct.
4. Neither of the above statements is correct.
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Suppose the initial kinetic and potential energies of a system are 75J and 250J respectively, and that the final kinetic and potential energies of the same system are 300J and -25J respectively. How much work was done on the system by non-conservative forces?
1. 0J 2. 50J 3. -50J 4. 225J 5. -225J
Wnc = Ef - Ei=(KEf + PEf) - (KEi + PEi) =(300J -25J) - (75J + 250J) =275J - 325J= -50J
correct
The change in kinetic energy plus the change in potential energy equals the work done on the system by non-conservative forces
QuestionQuestion
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GalileoGalileo’’s Pendulum ACTs Pendulum ACTHow high will the pendulum swing on the other side now?
A) h1 > h2 B) h1 = h2 C) h1 < h2
h1 h2
m
Conservation of Energy
0= ΔK + Δ UKinitial + Uinitial = Kfinal+Ufinal0 + mgh1 = 0 + mgh2
h1 = h2
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- Conservative force : Work is independent of the path. - Non-conservative force : Work is dependent of the path.
보존력과보존력과 비보존력비보존력
W = 0
(Conservative force) (Non-conservative force)
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Potential energyPotential energy어떤힘이보존력이면, 그힘에대한 potential energy의정의가능 !
Conservative force(보존력) : 중력, 탄성력, 전기력(Non-conservative force : 쓸림힘, 끌림힘) => 확인
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Potential energy Potential energy 구하기구하기
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일과일과 potential energypotential energy
ΔU > 0
W (< 0)
W (> 0)
ΔU < 0
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ΔU > 0
W < 0
ΔU < 0W > 0
ΔK < 0
ΔK > 0
평형점
(a) 수축시
(b) 이완시
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역학에너지역학에너지 보존보존
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Em = U + K = 일정
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(보기문제 8-3)
수직힘은
수직힘,
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(보기문제)
Sample problem 8-4 : Report
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Physics, Page 19
E = U + K = 5 J
E = U + K = 4 J
(X2, X3, X4, 0~X0, X5~)
(X2, X4)
(X3)
Potential energy Potential energy 곡선읽기곡선읽기
(X1)되돌이점 (x1)
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외부외부 힘이힘이 계에계에 한한 일일
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(보기문제)
30o N)
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Energy is Conserved !Energy is Conserved !
• Energy is “Conserved” meaning it can not be created nor destroyed.–Can change the form–Can be transferred
• Total Energy does not change with time.
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에너지에너지 보존보존
마찰력마찰력 ((비비 보존력보존력))이이 있는있는 경우경우
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(보기문제)
h2
ΔE
Physics, Page 25
Skiing Example (no friction)A skier goes down a 78 meter high hill with a variety of slopes. What is the maximum speed should can obtain if she starts from rest at the top?
Conservation of energy:
Ki + Ui = Kf + Uf
½ m vi2 + m g yi = ½ m vf
2 + m g yf
0 + g yi = ½ vf2 + g yf
vf2 = 2 g (yi-yf)
vf = sqrt( 2 g (yi-yf))
vf = sqrt( 2 x 9.8 x 78) = 39 m/s26
0 = Kf-Ki + Uf - Ui
Physics, Page 26
Pendulum ExampleAs the pendulum falls, the work done by the string is
1) Positive 2) Zero 3) Negative
How fast is the ball moving at the bottom of the path?
W = F d cos θ. But θ = 90 degrees so Work is zero.
h
Conservation of Energy
0= ΔK + Δ U0 = Kf - Ki + Uf- Ui
Ki + Ui = Kf+Uf0 + mgh = ½ m v2
f + 0vf = sqrt(2 g h)
30
“Why mass doesn't matter when you drop something?”
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θ
h
i
j
Total Energy
mghmvUKE g +=+= 202
1
At y = 0
mghmvmvE +== 202
1221
jvivv ˆsinˆcos 000 θθ +=
θ= cosvv:i x 0
gtsinvv:j y −θ= 0
gghsinvsinv
t
gttsinvhy
2
022
00
221
0
+θ+θ=
=−⋅θ+=
ghsinvvy 2220 +θ−=
ghvv 220 +=
θ++θ=+= 220
220
22 2 cosvghsinvvvv yx
ghv 220 +=
(보기문제)
v at y = 0?
vo
에너지보존법칙이용
등가속운동법칙이용
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m2m1
θR
Total Energy of m1 ffii UKUKE +=+=1
( ) ( ) ( )oifif gRmvmUUKK θcos1 12
121 +−−=⇒−−=−
( ) ( )ogmRvmamgmTF θθ cos120 1
2
111 −===−==
( )ogmT θcos231 −=
gmT 2>If , it lift up m2 . In this case, 12 2mm =
( ) gmgmgm o 121 2cos23 =>− θ
(보기문제)
What is the minimum of the initial angle θοfor lifting m2 (= 2m1) at θ = 0?
21cos <oθ Therefore, If θο > 60°, it lifts up m2 .
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(a) No Friction
tE
0
30sin
221
21
221
+=
==
+=
f
ii
mv
mgdmgd
mgymvo
glv f =(b) Friction coefficient μk
HUKUKE ffiit ++=+=Heat LossH = fk·d = μkmg cos30°·d
mgcosθ
mgdmvmgd kf μ232
21
21 +=
( )gdv kf μ31−=
(보기문제)vf ? (a) without friction, (b) with friction (μk)
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SummarySummary
Conservative Forces• Work is independent of path• Define Potential Energy U
– Ugravity = m g y– Uspring = ½ k x2
Work – Energy Theorem
internalEUKEW total Δ+Δ+Δ=Δ=