Physics and Measurement
• Model• Theory• Observation• Law• Empirical Law
What is physics?Why do we study it?
Significant Digits• 23.21 m• 0.062 m• 8200 m
26.2x10 m
Scientific notation helps!!!
2Area 0.062 m 23.21 m 1.43902 m
• The final result of multiplication or division can have only as many significant digits as the component factor with the least number of significant figures
• The final result for addition or subtraction can have no more decimal places than the term with the least number of decimal places
2Area 1.4 m
Perimeter = 46.54 m
Base Units
Redefining the meter:
In 1792 the unit of length, the meter, was defined as one-millionth the distance from the north pole to the equator.
Later, the meter was defined as the distance between two finely engraved lines near the ends of a standard platinum-iridium bar, the standard meter bar. This bar is placed in the International Bureau of Weights and Measures near Paris, France.
In 1960, the meter was defined to be 1 650 763.73 wavelengths of a particular orange-red light emitted by krypton-86 in a discharge tube that can be set anywhere in the world.
In 1983, the meter was defined as the length of the path traveled by light in a vacuum during the time interval of 1/299 792 458 of a second. The speed of light is then exactly 299 792 458 m/s.
Typical Lengths
Typical Masses
What is Density?V
m
Typical Times
Three unit systems
Physical Quantity
Dimensional Symbol
UnitSystem
SI MKS SI CGS USCustomary
Length [L] m cm ft
Mass [M] kg g
Time [T] s s s
Three unit systems
Physical Quantity
Dimensional Symbol
UnitSystem
SI MKS SI CGS USCustomary
Length [L] m cm ft
Mass [M] kg g slug
Time [T] s s s
Unit conversion
A BA
1B
C 1 C
1 kg 2.2 lb 1 kg1
2.2 lb
1 kg200 lb 90.9 kg
2.2 lb
Metric Prefixes
Dimensional (unit) Analysis
21x at
2
22
1 L[L] [ ][T ] [L]
2 T
If your units do not work out, your answer cannot be correct!
Sometimes you can figure out the correct equation merely by making the units work!
Estimating
• Often we are looking for order of magnitude numbers.
• Is the number 1, 10, 100, 1000, 10000?• Make assumptions. We will have some
standard assumptions:– Surfaces are frictionless (at first)– Strings have no mass– Objects are all treated as if their mass is at a point in
space– Pulley wheels have no mass– Forces from springs are linear with displacement
Example
• Enrico Fermi • Nothing to do with Physics• Shows the power of order of magnitude estimates
• How many piano tuners are in San Francisco?
(800,000 people in San Francisco)
Lab Data Recording
And Calculating
Uncertainty
• Precision = Repeatability• Accuracy = Correctness
measurement = best measured value uncertainty
uncertaintypercent uncertainty = 100%
best measured value
uncertaintyfractional uncertainty =
best measured value
Propagating Uncertainty
• Addition/Subtraction: Add the uncertainty in the individual terms
• Multiplication/Division:– Add the fractional uncertainties of the factors
– Use extreme values of factors and subtract
If C=A+B, Then C= A+ B
C A BIf C=AB, Then = +
C A B
If C=AB, Then C= A+ A B+ B A - B
What does it mean to agree?
5.0
0.5
0.5
4.8
0.25
0.25
Measurement A Measurement B
Do Measurements A and B agree?
What does it mean to agree?
5.0
0.5
0.5
4.2
0.25
0.25
Measurement A Measurement B
Do Measurements A and B agree?
What does it mean to agree?
5.0
0.5
0.5
4.6
0.25
0.25
Measurement A Measurement B
Do Measurements A and B agree?
What does it mean to agree?
5.0
0.5
0.5
4.4
0.25
0.25
Measurement A Measurement B
Do Measurements A and B agree?
Recommended
