PHYSICS UNIT 0: FOUNDATIONS

MEASUREMENT Units of Measure - Metric System (SI)

Fundamental Units: defined by scientistsDimension Unit Symbollength meter mmass kilogram kgtime second s current ampere Atemperature Kelvin K Derived Units: combinations of fundamental

units ex: area measured in m2, density measured

in g/cm3

Measurement Important Ranges of Magnitudes to

remember Distances – size of a nucleus(10^-15

m) to size of the universe (10^25 m) Masses – mass of an electron(10^-30

kg) to mass of the universe (10^53 kg) Times – time for light to pass a nucleus

(10^-23 s) to age of the universe (10^18 s)

So what are the order of magnitude differences?

MEASUREMENT prefixes: for larger or smaller quantities

Prefix Symbol Value ExampleGiga G 109 30 Gb = 30,000,000,000 b

mega M 106 2.1 Mm = 2,100,000 mkilo k 103 3.5 kg = 3500 gdeci d 10–1 8.7 dL = 0.87 Lcenti c 10–2 5.9 cs = 0.059 s milli m 10–3 7.2 mmol = 0.0072

molmicro 10–6 4.4 m = 0.0000044 m nano n 10–9 9.0 ng = 0.000000009

g

MEASUREMENT conversions from one prefix to

another:mega kilo none deci centi milli micro

nano1000 1000 10 10 10 1000 1000

larger units smaller units divide multiply

MEASUREMENT conversion factors - multipliers that change

units without changing equation’s overall value(factors have a value of 1) ex: 1 in = 2.54 cm factors:

in 1

cm 54.2

cm 54.2

in 1

mi

ft

1

5280

ft

in

1

12

in

cm

1

54.2

cm

m

100

1

m

km

1000

1km 60.1mi 1

set up so units cancel ex: find the kilometers in 1 mile

MATHEMATICS Scientific Notation: shorthand for

large & small numbers form: 0.00 × 10 0 (number ≥ 1 & <

10 × power of 10) ex: 450,000,000 = 4.5 ×

100,000,000 = 4.5 × 108

0.0000036 = 3.6 × 0.000001 = 3.6 × 10–6

MATHEMATICS Scientific Calculators

4.5 × 108 is entered and may appear as or

3.6 × 10–6 is entered and may appear as or

some calculators use instead of

3 . 6 EE +/- 6

4 . 5 EE 8

4.5 08 4.5 08

3.6 -06 3.6 -06

EXP EE

UNCERTAINTY Significant Figures

shorthand way of showing precision & uncertainty

number of sig. fig's = # of digits BUT don't count beginning zeroes AND don't count ending zeroes unless there is a decimal.234.15 14.080 560,000 0.00282 5.6 × 105

UNCERTAINTY Significant Figures

calculations cannot be more exact than measurements:

a. round off to least number of sig. fig's ex:(1.05)(39.04)(251,000)

(0.0044)=45271.565round off to 2 sig. fig's = 45,000

b. round off once, at the end of all calculations

c. when in doubt, round to 3 sig. fig's

PHYSICS

UNIT 0: FOUNDATIONS

The 2 Major Types of Error in Experimental Physics

Systematic Error- Errors inherent in the system of data taking. (Can not be cancelled with lots of data)

Example – using an uncalibrated scale.

Random Error- are inherently unpredictable. (Can be cancelled out with lots of data)

Example – stopping a stop watch too early sometimes and too late other times.

Systematic Error

There are 3 major types of systematic error human error: mistakes in reading & recording

make repeat measurements (Do not include in lab write up, instead fix human problem).

method error: mistakes in measurement methods choose the best method & use it consistently.

instrument error: mistakes due to damaged instruments

check instrument calibration, use carefully.

UNCERTAINTY Accuracy- the degree of closeness of

experimental result with theoretical result. (Low systematic error)

Assessing accuracy: percent error (if you know what the measurement should have been by other methods)

% Error = |O – A|

A ×100=|observed – accepted|

accepted ×100

UNCERTAINTY Precision: limitations of a measuring

instrument (Sensitivity) the more digits you can read, the more

precision (less uncertainty) A precise measuring device will take

repeated measurements that are close to each other.

GRAPHING

title graph dependent variable: y, independent

variable:x Uncertainty in data should be included on

graph Include the equation that best fits the data

purpose: finding patterns & relationships

drawing graphs: choose & show scale on each axis - fit all data

label each axis: measured quantity & units

Distance Fallen vs. Timey = 5x2

0

100

200

300

400

500

0 2 4 6 8 10

Time (s)

Dist

ance

Falle

n (m

)

GRAPHING graph interpretation:

linear relationship: as x increases, y increases (y x)

y = mx+b m: slope, b:y-intercept Said “The distance

traveled by a car moving at constant speed is directly proportional to the time travelled.”.

GRAPHING graph

interpretation: quadratic relationship:

as x increases, y increases (y x2)

y = kx2

k: appropriate constant Said “The bacteria

population grew exponentially with time.”

GRAPHING graph interpretation:

inverse relationship: as x increases, y decreases (y 1/x)

y = k/x k: appropriate constant Said “For any given

constant force acting on an object there is an inverse relationship between and object’s mass and it’s acceleration”

UNIT 0 QUIZ PREVIEW Concepts Covered:

metric system: units, prefixes & conversions

accuracy, precision & significant figures math skills – algebra, scientific notation,

estimation, types of graphs. What’s On The Quiz:

__ multiple choice/matching __ problems

Equations for Propagating Error

B

B

A

ABABBAA

B

B

A

ABABBAA

BABABBAA

BABABBAA

%100%100)()()(

%100%100)()()(

)()()()(

)()()()(Sum

Difference

Product

Quotient