Transcript Measurement - College of Arts & Sciences

Physics 1710—Section 4
Instructor—Matteson
Session #2
Chapter 1 Measurement
Physics 1710—Chapter 1 Measurement
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1/14/02
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Physics 1710—Chapter 1 Measurement
Fact:
The earth has a circumference of approximately
40 million meters (4. X 107 m). How fast must one
move on average to travel around the world in 80
days?
Physics 1710—Chapter 1 Measurement
1′ Lecture
• First 3 Fundamental Units:
–Time, measured in seconds = 1/86 400 of m.s. day
–Length, measured in meters = c (1/299 792 458 sec)
–Mass, measured in kilograms = specimen
• Prefixes scale units to convenient size.
• Density is mass per unit volume. [kg/m3 ]
• Avogadro’s number is the number of atoms
in a mole of an element, NAvogadro = 6.022x1023
• Significant figures tell the tale.
• Scientific notation saves ink.
Physics 1710—Chapter 1 Measurement
Q&A:
Q: Is this class mainly for engineers? I ask this because I
am pre-med. Does this course apply to my field?
A(s): No, it is for scientists as well.
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Yes, it does apply to your field.
You will learn facts about how things move,
e.g. consider muscles, joints, blood, air.
You will grow an understanding of dynamics,
e.g. energy, momentum and trauma.
You will develop analytical and qualitative skills,
e.g. think about diagnosis and drug dosing.
This course is for all scientists and engineers.
Physics 1710—Chapter 1 Measurement
Laboratory Introduction
Physics 1730
Dr. John Prince
Physics 1710—Chapter 1 Measurement
Matteson’s Dicta Numbers 1 & 2:
1. Physics is that branch of science concerned
with the interaction of matter-energy in spacetime.
2. The physical universe consists of only matter
and energy and the vacuum.
• Late breaking news: what about “dark matter”
and “dark energy?” They are 95% of universe
and we don’t yet know what they are.
Physics 1710—Chapter 1 Measurement
Measurement is the quantitative comparison
of a physical parameter to a standard unit.
“Existential Physics” Activity:
Measure the width of the top of
your desk in “hands.”
Physics 1710—Chapter 1 Measurement
Why did we observe a variety of values
in our measurement?
Measurement is the quantitative comparison
of a physical parameter to a standard unit.
‽ A “hand” is not a standard unit.
Our measurement is subject to error.
Our measurement is coarse.
Physics 1710—Chapter 1 Measurement
Measurement is the quantitative comparison of
a physical parameter to a standard unit. Therefore
we need standards.
Accuracy is the difference of a measurement
from the (unknown) true value. All measurement
contain experimental error.
Precision is the “fineness” of the division of the
scale used to compare to the standard unit.
Precision limits our knowledge.
Physics 1710—Chapter 1 Measurement
80/20Precision
is the fineness of a
measurement.
80/20Accuracy is the correspondence of a
measurement to an (unknown) true
value.
Measurement
Less precise
Standard
Less accurate
Physics 1710—Chapter 1 Measurement
Significant figures:
What numbers one writes down reveals one’s
knowledge (and ignorance) of the actual true
(but unknown) value.
Example:
2. 2.0 2.01 2.0085 2.00852 represent
the values of a measurement at various levels of
precision.
Physics 1710—Chapter 1 Measurement
Rules for Computing
with Significant Figures:
•When multiplying (or dividing) numbers, round
result to same number of significant figures as the
factor with least number of significant figures.
•When adding (or subtracting), first round to same
decimal place as contribution with the least
precision, then compute.
Physics 1710—Chapter 1 Measurement
Rules for Rounding
• If remainder is less than 5, truncate,
i.e. round down.
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Example: 3.1415927… ~ 3.14
• If remainder is larger than 5, round up.
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Example: 3.1415927… ~3.1416
• If remainder is exactly 5, round up or down to
leave last digit even.
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Example: 31½ = 31.5000… ~32.
Physics 1710—Chapter 1 Measurement
Scientific Notation
Number = Mantissa x 10 Exponent = _._____ E__
Big Numbers:
1.234567 x 10 3 = 1234.567
Small Numbers:
1.234567 x 10 –2 = 0.01234567
Physics 1710—Chapter 1 Measurement
Know Your Calculator
Activity:
Enter: “1.234567” ; “EXP” or “EE”; “03”
Display should read:
“1.234567 03” or “1.234567E03”
Enter: “1.234567”; “EXP”; “03” ;
“+/-” or “⇄” or “(-)”
Display should read: “
“1.234567-03” or “1.234567E-03”
Physics 1710—Chapter 1 Measurement
Fundamental Units
• Système International de Metrique (SI)— “Metric System”
• First introduced in France in 1799—(on Napoleon’s coup)
1770
1780
1790
1800
1810
La
$
American Rev French Rev
US Constitution Napoleon
Physics 1710—Chapter 1 Measurement
Time Standard:
second [s]
• (1/60)(1/60)(1/24) =1/86,400 mean solar day
• 9,192,631,770 (exactly) times the period
of vibration of a Cesium-133 atomic clock.
• Time Demonstration
Physics 1710—Chapter 1 Measurement
Length standard: meter [m]
• Meter defined in 1799, by Napoleon’s
Republic.
• 1/107 quadrant of Earth; C= 4.00x 107 m
• Distance light travels in 1/299,792,458 sec
• Meter Demonstration
Physics 1710—Chapter 1 Measurement
Derived Units of area and volume
• Area: 10 m x 10 m = 100 m 2 = 1 are
100 ares = 1 hectare = 1x104 m2
1 US acre = 0.4046 ha
• Volume: m x m x m = m 3 = 1000 liter = 1000 l
e.g. 1000 cm 3 = 1 liter
1 US gallon = 3.7854118 liters ~ 3.8 l
Physics 1710—Chapter 1 Measurement
Mass Standard : kilogram [kg]
• kilo = 1000, 1 kg = 1000 gram
• 1 kg is the mass of approximately
1/1000 m3 (=1 liter) of water
• Mass is a fundamental property of all matter.
• Each atom has a mass of ~1.66 x 10-27 kg times its
“atomic mass number”
Physics 1710—Chapter 1 Measurement
Mass Standard : kilogram [kg]
•1 kg weighs on earth about 2.2 pounds.
Physics 1710—Chapter 1 Measurement
Amedo Avogadro
(1776-1856)
• Italian Physicist
• Proposed Avogadro’s Law
(1811)
22.8 liters
= 1 mole of gas
= 6.022 x1023 molecules or atoms
12 g C = 1 mole
Physics 1710—Chapter 1 Measurement
Avogadro’s Number
NA = 6.0221367(28) x 10 23 atoms/mole
Atomic mass unit = u
u = 1.660 540 2(10) x 10 –27kg
(~ 1 2/3 yoctogram)
NA ‧ u = 1.00 x 10 –3 kg = 1.00 gram
NA is the number of atoms in one “gram molecular
weight” of an element.
Physics 1710—Chapter 1 Measurement
Practice:
How much does a 5 US Gal can of water weigh?
Density of water = 1.0 kg/l
M = ρ V = (1.0 kg/l )(5 gal x 3.8 l/gal) = 19. kg
W = 2.2 lbs/kg x 19. kg = 42. lbs
Physics 1710—Chapter 1 Measurement
Summary
•Fundamental Dimensions and Units
Time, measured in seconds;
Length, measured in meters;
Mass, measured in kilograms.
• Prefixes scale units to convenient size.
k =1000, M = 1 000 000
c = 1/100, m = 1/1000, μ =1/1 000 000
• Density is mass per unit volume.
ρ = m/V [kg/m3 ]
• Avogadro’s number is the number of atoms
in a mole of an element. 6.022 x1023 atom/mole
Physics 1710—Chapter 1 Measurement
1′ Essay
• What was that about?
• An “Aha!”
• A Question
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