physics unit 0: foundations
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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
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