measurement what is physics the metric system metric prefixes dimensional analysis significant...

MEASUREMENTWHAT IS PHYSICS

THE METRIC SYSTEM

METRIC PREFIXES

DIMENSIONAL ANALYSIS

SIGNIFICANT FIGURES

CONVERSION OF UNITS

ORDER OF MAGNITUDE

NOTATION

TRIGONOMETRY

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Physics is the study of how physical quantities are related. It isconcerned with the understanding of the natural universe.

Physics is based on experimental observation.

Physics is organized into a set of physical laws havingmathematical expressions.

PHYSICS:Mechanics

Thermodynamics

Electromagnetism

Relativity

Quantum Mechanics

THE METRIC SYSTEM:

The fundamental physical quantities of the metricsystem are:

length, mass, and time.

Metric system basic units:

length: the meter

mass: the gram

time: the second

Metric prefixes are based on powers of 10.

prefix power abbreviation

tera 10 12 Tgiga 10 9 Gmega 10 6 Mkilo 10 3 K- 10 0 -milli 10 -3 m

micro 10 -6 nano 10 -9 npico 10 -12 p

MASS:

Mass in kg:

Universe 1052 (?)

Milky Way Galaxy 7x1041

Earth 6x1024

Human 7x101

Bacterium 1x10-15

Electron 9x10-31

Lengths and Distances in m:

Distance to most remote Quasar 1x1026

Distance to nearest Galaxy 1x1022

Distance to nearest Star 4x1016

Mean orbital radius of Earth 4x1011

Length of a housefly 5x10-3

Size of a living cell 1x10-5

Diameter of a proton 1x10-15

Time Intervals in s:

Age of Universe 5x1017

Age of earth 1x1017

Average of college student 6x108

One day 9x104

Period of audible sound wave 1x10-3

Period of visible light wave 2x10-15

Time for light to cross a proton 3x10-24

Dimensional Analysis:

Physical units combine algebraically .

a = acceleration [a] = L/T 2

x = distance [x] = L

t = time interval [t] = T

x = at2/2

L = (L/T2)T2 = L

EXAMPLE: Using the variables v and r for speed (meters per second) and distance (meters), combine them algebraically to form an acceleration, a (meters per second squared).

2va

r

EXAMPLE: Using the variables v and r for speed (meters per second) and distance (meters), combine them algebraically to form an acceleration, a (meters per second squared).

Significant Figures:

Significant figures includes the first estimated digit.

Multiplication or Division: 1. Calculate the result2. The result has the same number of significant

figures as the factor with the fewest.

Zeros immediately to the right of a decimal point are notsignificant unless they are by themselves.

Zeros on the end of a number (5200) may or may not besignificant. 5200. or 5.2x103

Adding and Subtracting: The result has the same numberof decimal places as the value with the fewest.

Conversion of Units:

All conversion factors begin with an equation: x = y.

All conversion factors are equal to 1 (unity).

If x = y, then x/y = 1 and y/x = 1.

Chose the ratio that eliminates the original unit.

100 cm = 1 m

52 cm = 52 cm x 1m/100cm = 0.52 m

EXAMPLE: Convert 67 miles per hour to meters per second.

1 mile = 1609 meters 1 hour = 3600 seconds

EXAMPLE: Convert 3525.00 cm2 to m2.

EXAMPLE: Convert 67 miles per hour to meters per second.

1 mile = 1609 meters 1 hour = 3600 seconds

EXAMPLE: Convert 3525.00 cm2 to m2.

67.00 mi/hr

1 mi

1609 m 1 hr

36 00 s

= 29.95 m/s

3525.00 cm2

(100 cm)2

(1 m)2

= 0.3525 m2

Order of Magnitude Calculation:

An order of magnitude calculation is done by selectingreasonable sized values to substitute into an equation. Thepurpose is to determine the size of the real calculation result.

EXAMPLE: How much tire tread is worn off a tire for every mile driven?

EXAMPLE: How much tire tread is worn off a tire for every mile driven?

A tire lasts about 40,000 miles and takes off about 1 cm of tread. Thus about 2.5x10-7 m/mile of tread is removed. The important value is the power of 10.

NOTATION:

means change in.

means sum of.

2 1 f ix x x or v v v

1 2 3 ...x x x x

Trigonometry:

c

b

a

sin sin

cos cos

tan

bb c

ca

a ccb

a

The trigonometric functions are most easily understood as ratios of the lengths of the sides of a right triangle.

2 2 2

1tan

c a b

b

a

Solve the triangle for the unknown sides.

40o

8

X= ______

Y= _____

Solve the triangle for the unknown sides.

40o

8

X= ______

Y= _____

6.128

5.142

Problem Solving:

Read the problem carefully.

Draw a diagram or sketch of the problem, don’t bean artist.

Identify given information.

Select basic relationship that applies.

Substitute data and calculate result.