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AP Physics Chapter 1
Measurement
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AP Physics
Turn in Contract/Signature Lecture Q&A Website: http://www.mrlee.altervista.org
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Measurement and Units
Physics is based on measurement. International System of Units (SI unit)
– Fundamental (base)quantities: more intuitive
– Derived quantities: can be described using fundamental quantities.
length, time, mass …
Speed = length / time Volume = length3
Density = mass / volume = mass / length3
Two kinds of quantities:
– Created by French scientists in 1795.
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Units
Unit: a measure of the quantity that is defined to be exactly 1.0.
Fundamental (base) Unit: unit associated with a fundamental quantity
Derived (secondary) Unit: unit associated with a derived quantity– Combination of fundamental units
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Standard Units
Standard Unit: a unit recognized and accepted by all.
Quantity Unit Name Unit Symbol
Length Meter m
Time Second s
Mass kilogram kg
– Standard: a reference to which all other examples of the quantity are compared.
– Standard and non-standard are separate from fundamental and derived.
Some SI standard base units
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Length
Standard unit: meter (m) Standard meter bar: International Bureau of Weights
and Measures near Paris Secondary standards: duplicates In 1983:
The meter is the length of the path traveled by light in vacuum during a time interval of 1/299,792,458 of a second.
Other (nonstandard) units: cm, km, ft, mile, …
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Time
Standard unit: second (s) One second is the time taken by 9,192,631,770
vibrations of the light (of a specified wavelength) emitted by a cesium-133 atom.
Other nonstandard units: min, hr, day, …
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Mass
Standard unit: kilogram (kg) Standard kilogram cylinder: International
Bureau of Weights and Measures near Paris Other nonstandard units: g, Lb, ounce, ton, ..
Atomic mass unit (amu, u)
1 u = 1.6605402 10-27 kg
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Changing Unit: Conversion Factors
Conversion factor: a ratio of units that is equal to one.
160
min1
s1
min1
60
s s60min1 and
So two conversion factors:
s60
min1min1
60sand
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A few equalities (conversion Factors) to remember
1 m = 100 cm 1 inch = 2.54 cm 1 mile = 1.6 km 1 hr = 60 min 1 min = 60 s 1 hr = 3600 s
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Question?
Two conversion factors from each identity, but which one to use?
Depends on the unit we want to cancel. – If the unit we want to cancel is on the top with the
numerator, then for the conversion factor we must put that unit at the bottom with the denominator.
– If the unit we want to cancel is at the bottom with the denominator, then for the conversion factor we must put that unit on the top with the numerator.
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Example: 5 min = ___ s
60
min
s
300s
5min 5min 1
min cannot be cancelled out. Not good conversion factor.
Good conversion factor.
Does not work!
5min 5min
5min min
60s
1min 60s
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Practice:
Convert 12.3 m to cm
10012.3 12.3 1230
1
cmm m cm
m
1 100m cm
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Chain-link Conversion
60min
hr
60
min
s
Convert: 2 hr = ____ s
2 2hr hr 7200s
1 60min
1min 60
hr
s
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Practice:
12 m = ___ inch
10012 12 472
1 2.54
cm inchm m inch
m cm
1 100
1 2.54
m cm
inch cm
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Still simple? How about…
2 mile/hr = __ m/s
Chain Conversion
2 2mile mile
hr hr 1600m
mile
1
3600
hr
s
0.89m
s
1 1600
1 3600
mile m
hr s
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More practice:
2.54cm
inch
2232.cm
5 inch2 = _____ cm2
2 2.545 5
cminch inch inch
inch
2.54cm
inch
2 232.258 32.cm cm
2 25 5inch inch
1 2.54inch cm
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When reading the scale,
Estimate to 1/10th of the smallest division
6 7 cm.5
6.3 cm
– Draw mental 1/10 divisions– However, if smallest division is already too small,
just estimate to closest smallest division.
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Uncertainty of Measurement
All measurements are subject to uncertainties.
Uncertainties in measurement cannot be avoided, although we can make it very small.
Uncertainties are not mistakes; mistakes can be avoided.
Uncertainty
– External influences: temperature, magnetic field– Parallax: the apparent shift in the position of an
object when viewed from various angles.
experimental error
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Precision
Precision: the degree of exactness to which a measurement can be reproduced.
The precision of an instrument is limited by the smallest division on the measurement scale.
– Uncertainty is one-tenth of the smallest division.– Last digit of measurement is uncertain, the
measurement can be anywhere within ± one increment of last digit. Meter stick: smallest division = 1 mm = 0.001 m uncertainty is 0.0001 m
1.2345m: 1.2344m -1.2346m3 digits after decimal pt4 digits after
decimal pt
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Uncertainty and Precision
What is the uncertainty of the meterstick?0.0001m
What is the precision of the meterstick?0.001m
How precise is the meterstick?0.001m
estimate
certain
certain
Sometimes, when not strictly:
precision = uncertainty
Both the uncertainty and precision of a meterstick is 0.0001m
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Uncertainty and Precision
What is the uncertainty and precision of 1.234?
Uncertainty = 0.001
Precision = 0.01 or 0.001 (loosely)
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More precise = smaller uncertainty
Which is more precise, 12.34 or 2.345?
12.34: uncertainty = 0.01
2.345: uncertainty = 0.001
So, 2.345 is more precise.
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Accuracy
Accuracy: how well the result agrees with an accepted or true value
Accuracy and Precision are two separate issues.
ExampleAccepted (true) value is 1.00 m. Measurement #1 is 1.01 m, and Measurement #2 is 1.200 m.
Which one is more accurate? #1, closer to true value.
Which one is more precise? #2, precise to 0.001m, compared to 0.01m of #1
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Significant Figures (Digits)
1. Nonzero digits are always significant.2. The final zero is significant when there is a decimal
point.3. Zeros between two other significant digits are always
significant.4. Zeros used solely for spacing the decimal point are not
significant.
Example: 1.002300
0.004005600 7 sig. fig’s
7 sig. fig’s 12300 3 sig. fig’s
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Practice:
How many significant figures are there ina) 123000
b) 1.23000
c) 0.001230
d) 0.0120020
e) 1.0
f) 0.10
3
64
6
2
2
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Operation with measurements
In general, no final result should be “more precise” than the original data from which it was derived.
Too vague.
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Addition and subtraction with Sig. Figs
The sum or difference of two measurements is only as precise as the least precise one.
Example:16.26 + 4.2 = 20.46
Which number is least precise? 4.2
Precise to how many digits after the decimal pt? 1 So the final answer should be rounded-off (up or down) to how many digits after the decimal pt? 1
=20.5
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Practice:
1) 23.109 + 2.13 = ____
2) 12.7 + 3.31 = ____
3) 12.7 + 3.35 = ____
4) 12. + 3.3= ____
1) 23.109 + 2.13 = 25.239 = 25.24
2) 12.7+3.31 = 16.01 = 16.0Must keep this 0.
3) 12.7+3.35 = 16.05 = 16.1
4) 12. + 3.3 = 15.3 = 15. Keep the decimal pt.
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Multiplication and Division with Sig. Figs
The number of significant digits in a product or quotient is the number in the measurement with the least number of significant digits
Example:2.33 5.5 = 12.815
Which number has the least number of sig. figs? 5.5
How many sig figs? 2 So the final answer should be rounded-off (up or down) to how many sig figs? 2
=13.
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Practice:
2.33/3.0 = ___
2.33 / 3.0 = 0.7766667 = 0.78
2 sig figs 2 sig figs
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What about exact numbers?
Exact numbers have infinite number of sig. figs.
If 2 is an exact number, then 2.33 / 2 = __
2.33 / 2 = 1.165 = 1.17
Note: 2.33 has the least number of sig. figs: 3
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Prefixes Used with SI Units
Prefix Symbol Fractions
nano n × 10-9
micro × 10-6
milli m × 10-3
centi c × 10-2
kilo k × 103
mega M × 106
giga G × 109
1 m = 1 × 10-6 m 1 mm = 1 × 10-3 m
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Dimensional Analysis
What is the dimension of K if ?21
2K mv
21
2K mv
2K m v
[x] = dimension of quantity x
Ignore
mass 2
length
time
2
2
lengthmass
time
2
2
MLor
T
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l
r l
r
When angle in unit of radian
radian 180o
1' 60"
1 60 'o
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1 AU
1 pc1”
61 92.9 10AU miles
180
1 60 '
1' 60"
o
o
rad
1" radx
1
1
AU
pc
1 1AU x rad pc x pc
1 ly = distance traveled by light in one year
HW 57
speed time
186,000 1mile
yrs
186,000 smile
ys
Convert 1 syr y
Conversion factor to convert61 92.9 10AU miles ly