Physics and Physical
Measurement
The Realm of physics
Measurement and uncertainties
Scale Video
• http://www.youtube.com/watch?v=Bz9D6xba
9Og&list=PL772556F1EFC4D01C&index=1&fea
ture=plpp_video
Why does that matter?
• Must have a consistent set of units agreed
upon. (SI system)
– SI has 7 fundamental units w/ lots of
combinations.
• How far off were you?
– Need an appreciation for the magnitude of things.
(masses, time, distances, forces…)
1.1.2 State the ranges of magnitude of distances, masses and
times that occur in the universe, from smallest to greatest.
Distances
• Sub-nuclear particles = 10-15m
• Extent of the visible universe = 1025m
• Distance from Earth to Moon = 3.84 x 105km
• Radius of Earth = 6380km = 107m
• Diameter of a nucleus = 10-15m
1.1.2 State the ranges of magnitude of distances, masses and
times that occur in the universe, from smallest to greatest.
Masses
• Rest mass of and electron = 10-30kg
• The universe = 1050kg
• Mass of the Earth = 5.97 x 1024kg
• Mass of the Moon = 7.35 x 1022kg
• Mass of an electron = 9.11 x 1031kg
1.1.2 State the ranges of magnitude of distances, masses and
times that occur in the universe, from smallest to greatest.
Times
• Passage of light across a nucleus = 10-23s
• Age of the universe = 1018s
• Light to travel from Sun to Earth = 8min = 102s
• Period for one orbit of Earth = 365day = 107s
• Time between vibrations of Cesium = 10-10s
1.1.2 State the ranges of magnitude of distances, masses and
times that occur in the universe, from smallest to greatest.
• Range of magnitudes of quantities in our
universe:
– Visible universe= 1026 m
– The age of the universe= 1018 s
– The total mass of the universe= 1050 kg
• The atom:
– The diameter of an atom = 10-10 m
– The diameter of the nucleus = 10-15 m
Upper and lower measurements
•
•
•
•
Size of proton 10-17 m (lower)
Speed of light in a vacuum 3 x108 m/s
Age of universe 1017s
If quarks are the fundamental unit then their
mass would give us the lower limit, but they
hide in protons and our best guess is 10-30 kg.
This is also the approximate mass of an
electron at rest.
1.1.3 Stating ratios of quantities as differences of orders of
magnitude
• 10-10m/ 10-15 m= 105
• 105 is known as a difference of five orders of
magnitude.
The ratio of the diameter of the hydrogen atom
to its nucleus is about 100000 times or 105
times, or a difference of 5 orders of magnitude.
1.1.3 Stating ratios of quantities as differences of orders of
magnitude
Example
• The rest mass of a proton is about 1.67x10-27kg.
The rest mass of an electron is about 9.1x1031kg.
How many orders of magnitude bigger is the
mass of the proton than that of the electron?
1.1.3 Stating ratios of quantities as differences of orders of
magnitude
Example
• Solution
1x10-27kg and 10x10-31kg (1x10-30kg)
-27- -30 = 3 orders of magnitude
Realize that the proton is not 3 times more massive it is
103 times more massive or 1000 times more massive.
1.1.3 Stating ratios of quantities as differences of orders of
magnitude
Practice 2
• The length of a football pitch is about 100m. The
distance from the earth to the moon is about
384x106m. How many orders of magnitude larger
is the distance from earth to the moon than the
length of a football pitch?
1.1.3 Stating ratios of quantities as differences of orders of
magnitude
Practice 2 solution
• Football pitch = 102
• Earth to moon = 108
• 8-2 = 6 orders of mag
Or
1,000,000 times larger
1.1.3 Stating ratios of quantities as differences of orders of
magnitude
Practice 3
• The mass of the Sun is 1.99 x 1030kg. The mass of
the Earth is 5.98x1024kg. How many orders of
magnitude more massive is the Sun than the
Earth?
1.1.3 Stating ratios of quantities as differences of orders of
magnitude
Practice 3 Solution
• Sun = 1030
• Earth = 1025
• 30-25 = 5 orders of magnitude
1.1.4 Estimate approximate values of everyday quantities to
one or two significant figures and/or to the nearest order of
magnitude.
– How high is a two storey house in meters?
– What is the diameter of your pupil?
– How many times does your heart beat in an hour
when you are relaxed?
– What is the weight of an apple in Newtons?
–
•
•
•
•
About 6m
about 2-4mm / 4-8mm
about 60-100 beats/min
about 1N
1.1.4 Estimate approximate values of everyday
quantities to one or two significant figures and/or to
the nearest order of magnitude.
Practice 7
• Estimate the thickness of a page in your book.
Fundamental Units
•
•
•
•
•
•
•
Meter
Kilogram
Second
Ampere
Kelvin
Mole
Candela
m
kg
s
A
K
mol
cd
length
mass
time
electric current
temperature
amount of matter
intensity of light
Mechanics and Derived Units
• Mechanics is the study of matter, forces, and
energy. With combinations of the first three base
units (m, kg, and s), all other units for mechanics
can be developed.
• Name one not listed….
• Newton
N
force or weight
kg m s-2
• Joule
J
energy or work
kg m2 s-2
• Watt
W
power
kg m2 s-3
• Pascal
Pa pressure
kg m-1 s-2
Derived Units
Find the symbol, concept, and broken down
base units for each of the following:
• Hertz
• Coulumb
• Ohm
• Tesla
• Weber
• Becquerel
•
•
•
•
•
•
Hertz
Coulomb C
Ohm
Ω
Tesla
T
Weber Wb
Becquerel Bq
Hz
frequency
s-1
Electric charge
As
electrical resistance
kg m2 s-3 A-2
magnetic flux
Wb m-2
magnetic flux
(T m2) or kg m-2 s-2 A
radioactivity
s-1
•
•
•
•
•
•
Hertz
Coulomb C
Ohm
Ω
Tesla
T
Weber Wb
Becquerel Bq
Hz
frequency
s-1
Electric charge
As
electrical resistance
kg m2 s-3 A-2
magnetic flux
Wb m-2
magnetic flux
(T m2) or kg m-2 s-2 A
radioactivity
s-1
Problems
1. Give units for the following expressed as
derived and base units:
a. Force
b. Kinetic energy
2. Check if these equations work by substituting
units into them.
a. Power= work/time or energy/time
b. Power = force x velocity
Answers
1.
a. N or kg m s-2
b. J or kg m2 s-2
2.
a. W: J s-1 or W: (kg m2 s-2 )s-1 or W: kg m2 s-3
b. W: N x (m s-1 ) or W: (kg m s-2 )x (m s-1 ) or
W: kg m2 s-3
Problems
3. Which one of the following units is a unit of
energy?
a. eV b. W s-1 c. W m-1 d. N m s-1
4. Which on of the following lists a derived unit
and a fundamental unit?
A
Ampere
Second
B
Coulomb
Kilogram
C
Coulomb
Newton
D
Meter
kilogram
Answers
3. eV
4. B
Other Units
Name
Symbol
Concept
Liter
L
volume
Minute, hour, year, etc.
Min, h, y, etc.
Time
Kilowatt-hour
kWh
Energy
Electronvolt
eV
Energy
Degrees celsius
oC
temperature
Decibel
dB
Loudness
Unified atomic mass unit
U
Mass of nucleon
Problem
5. Convert these units to SI:
a. Year
b. 100 oC
c. kWh
d. eV
Modifying SI Units
• SI units can be modified by the use of prefixes.
Prefix
Abbreviation
Value
Tera
T
1012
Giga
G
109
Mega
M
106
Kilo
k
103
centi
c
10-2
milli
m
10-3
micro
μ
10-6
nano
n
10-9
pico
p
10-12
femto
f
10-15
Problems
6. Change 2360000J to scientific notation and
MJ.
7. A popular radio station has a frequency of
1090000Hz. Change this to scientific
notation and MHz.
8. The average wavelength of white light is
5.0x 10-7 m. What would this be in
nanometers?
9. The time taken for light to cross a room is
about 1 x10-8 s. Change this into
microseconds.
Answers
6.
7.
8.
9.
2.36 x 106 J or 2.36 MJ
1.09 x 106 Hz or 1.09 MHz
500 nm
0.01 μs
10.Estimate the speed with which human hair
grows.
11.If all the people on earth were to hold hands
in a straight line, how long would the line be?
How many times would it wrap around the
earth?
12.How many revolutions do the wheels of a car
make before it is junked (wheel radius is
30cm,250,000km total)
Answers
• About 4 x 10-9 m/s
• About 9 x 109m, about 200 times
• About 108
Uncertainty and Error
• There are two types of errors:
• Random and systematic
• Random errors can be reduced by repeating
measurement many times.
• Systematic errors can be reduced by repeating
measurement using a different method or
different apparatus and comparing the results.