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?Vm

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 kg 12.2 lb

1 kg200 lb 90.9 kg2.2 lb

Metric Prefixes

Dimensional (unit) Analysis

21x at2

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?