Phys 250 Ch1 p1

Measurement, Models and Analysis

Physics: knowledge of nature

Model: an idealized description of a physical system or natural phenomena

idealized how?

simplifications?

Measurements and Models

qualitative vs. quantitative descriptions

interplay between observation (measurements) and the development/refinement of model:

the “scientific method”

Phys 250 Ch1 p2

Units and Standards of Measurement

How big is ...

A quantity has dimensions if the answer depends upon the units (inches, feet, cm, etc.)

Basic Units or Fundamental Units are the standards by which measurement results are described

Quantity Unit Length Time Mass Temperature Electric Current

meter (m) second (s) kilogram (kg) kelvin (K) ampere (A)

See also table 1.1

Symbols for units can be used to help with dimensional analysis by treating unit symbols algebraically:

mss

ms

s

ms

s

m505050510

Phys 250 Ch1 p3

Prefixes for units are convenient shorthand for scientific notationPrefix Abbre-

viation Power of Ten

femto pico nano micro milli centi kilo mega giga

f p n µ m c k M G

10-15

10-12

10-9

10-6

10-3

10-2

103

106

109

1/1,000,000,000,000,000 1/1,000,000,000,000 1/1,000,000,000 1/1,000,000 1/1,000 1/100 1,000 1,000,000 1,000,000,000

check out http://www.wordwizz.com/pwrsof10.htmhttp://microcosm.web.cern.ch/Microcosm/P10/english/P0.html

Phys 250 Ch1 p4

Examples:

A soccer field is supposed to be at least 100m x 64 m. What is the area (in kilometers squared) of the smallest legal field?

What is the volume of a sheet of paper that is 21.6 cm by 27.9 cm and 8.6E-3 cm?

Phys 250 Ch1 p5

Consistency of units

Algebraic equations must always be dimensionally consistent.

You can’t add apples and oranges!

cminchcm

ftinches

ftft

inchcm

cminch

48.30540.212

11

1540.2540.21

converting units

treat units as algebraic quantities

multiplying or dividing a quantity by 1 does not affect its value

s5sm

2m10

time speed distance

vtd

Phys 250 Ch1 p6

Some Useful Conversion factors:1 inch = 2.54 cm1 m = 3.28 ft1 mile = 5280 ft

Examples:

How many kilometers are in one mile?

If an automobile has a speed of 25 mi/h, what is its speed in km/s?

Phys 250 Ch1 p7

Significant Figures: common way of implicitly indicating uncertainty

number is only expressed using meaningful digits (sig. figs.)

last digit (the least significant digit = lsd) is uncertain

3 one digit

3.0 two digits (two significant figures = 2 sig. figs.)

3.00 three digits,etc. (300 how many digits?)

Combining numbers with significant digits

Addition and Subtraction: least significant digit determined by decimal places (result is rounded)

.57 + .3 = .87 =.9 11.2 - 17.63 = 6.43 = 6.4

Multiplication and Division: number of significant figures is the number of sig. figs. of the factor with the fewest sig. figs.

1.3x7.24 = 9.412 = 9.4 17.5/.3794 = 46.12546 = 46.1

Integer factors and geometric factors (such as ) have infinite precision

x 3.762 = 44.4145803 = 44.4

Phys 250 Ch1 p8

Examples:

Calculate the volume of an cylindrical oatmeal box with a diameter of 10.2 cm and a height of 18.4 cm

Phys 250 Ch1 p9

Estimates and Order of magnitude calculations

an order of magnitude is a (rounded) 1 sig fig calculation, whose answer is expressed as the nearest power of 10.

Estimates should be done “in your head”

check against calculator mistakes!Example

Estimate the volume of rubber worn from automobile tires each year in the United States. The average radial tire has a useful tread depth of 5/16 in and can be driven 35,000 mi before it is worn out.

Phys 250 Ch1 p10

Succeeding in Physics:

Physics is about applying principles to solve problems!

learn definitions

do problems

Problem solving strategies

Read the entire problem carefully

draw a (simple) diagram

identify what is given

explicit information

implicit information

find mathematical relation(s) between known and unknown quantities

solve the equations (and watch units!)

reality check!