Units andMeasurement

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What do you hear?

It is the standard for a SECOND. At National Institute of Standards and Technology (NIST) in Boulder Colorado, Atomic clocks set the standard for ‘1 second’.

Math and Units�SI Units – International System

� MKS�Meter m�Mass kg�Time s

�NIST (was called National Bureau of Standards)

�Prefixes

Measure the width of your palm

SI Unit Prefixes - Part I

Name Symbol Factor

tera- T 1012

giga- G 109

mega- M 106

kilo- k 103

hecto- h 102

deka- da 101

SI Unit Prefixes- Part II

Name Symbol Factordeci- d 10-1

centi- c 10-2

milli- m 10-3

micro- μ 10-6

nano- n 10-9

pico- p 10-12

femto- f 10-15

The Seven Base SI Units

Quantity Unit SymbolLength meter mMass kilogram kg

Temperature kelvin KTime second sAmount of Substance mole mol

Luminous Intensity candela cd

Electric Current ampere a

Derived SI Units (examples)

Quantity unit Symbol

Volume cubic meter m3

Density kilograms per cubic meter

kg/m3

Speed meter per second m/s

Newton kg m/ s2 N

Energy Joule (kg m2/s2) J

Pressure Pascal (kg/(ms2) Pa

SI Unit Prefixes for LengthName Symbol Analogygigameter Gm 109megameter Mm 106kilometer km 103decimeter dm 10-1centimeter cm 10-2millimeter mm 10-3micrometer μm 10-6nanometer nm 10-9picometer pm 10-12

Scientific NotationM x 10n

�M is the coefficient 1<M<10�10 is the base�n is the exponent or power of

10

Other Examples:�5.45E+6 or

�5.45 x 10^6

Numbers less than 1 will have a negative exponent.

A millionth of a second is:

0.000001 sec 1x10-6

1.0E-6 1.0^-6

Factor-Label Method of Unit Conversion � Example: Convert 5km to m:� Multiply the original measurement by a conversion

factor.

NEW UNIT85km x 1,000m = 85,000m

1kmOLD UNIT

�Example: Convert 789m to km:

789m x 1km =0.789km= _____??1000m

Convert 75.00 km/h to m/s 75.00 km x 1000 m x 1 h___ = 20.83m/s

h 1 km 3600 s

Limits of Measurement

�Accuracy and Precision

�Accuracy - a measure of how close a measurement is to the true value of the quantity being measured.

Example: Accuracy� Who is more accurate when measuring a book that has a true

length of 17.0cm?Susan:17.0cm, 16.0cm, 18.0cm, 15.0cm

Amy: 15.5cm, 15.0cm, 15.2cm, 15.3cm

�Precision – a measure of how close a series of measurements are to one another. A measure of how exact a measurement is.

Example: Precision

Who is more precise when measuring the same 17.0cm book?

Susan:17.0cm, 16.0cm, 18.0cm, 15.0cm

Amy: 15.5cm, 15.0cm, 15.2cm, 15.3cm

Example: Evaluate whether the following are precise, accurate or both.

Accurate

Not Precise

Not Accurate

Precise

Accurate

Precise

Vectors

VectorsHector is walking his dog (Fido) around the neighborhood. Upon arriving at Fidella's house (a friend of Fido's), Fido turns part mule and refuses to continue on the walk. Hector yanks on the chain with a 67.0 N force at an angle of 30.0� above the horizontal. Determine the horizontal and vertical components of the tension force.

Fx: 58.0 NFy: 33.5 N

A pack of three Artic wolves are fighting over the carcass of a dead polar bear. A top view of the magnitude and direction of the three forces is shown in the diagram to the right.

a. Determine the resultant or net force acting upon the carcass.b. Determine the acceleration of the 750-kg polar bear carcass.( Use F = ma)

a. 190 N at 23� south of east (or 337�)b. 0.25 m/s/s

At one moment during a walk around the block, there are four forces exerted upon Fido - a 10.0 kg dog. The forces are:

Fapp = 67.0 N at 30.0� above the horizontal (rightward and upward)Fnorm = 64.5 N, upFfrict = 27.6 N, leftFgrav = 98 N, downResolve the applied force (Fapp) into horizontal and vertical components, then add the forces up as vectors to determine the net force.

Fapp-horizontal: 58.0 N, rightFapp-vertical: 33.5 N, upFnet: 30.4 N, right