Physics and Measurement What is physics? Why do we study it? • • • • • Model Theory Observation Law Empirical Law Significant Digits • 23.21 m • 0.062 m • 8200 m 6.2x102 m Scientific notation helps!!! Area 0.062 m 23.21 m 1.43902 m 2 • 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 Area 1.4 m 2 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? m V Typical Times Three unit systems Physical Dimensional Quantity Symbol Unit System SI MKS SI CGS Length [L] m cm Mass [M] kg g Time [T] s s US Customary ft s Three unit systems Physical Dimensional Quantity Symbol Unit System SI MKS SI CGS Length [L] m cm US Customary ft Mass [M] kg g slug Time [T] s s s Unit conversion AB 1 kg 2.2 lb A 1 B 1 kg 1 2.2 lb C 1 C 1 kg 200 lb 90.9 kg 2.2 lb Metric Prefixes Dimensional (unit) Analysis 1 2 x at 2 1 L [L] [ 2 ][T 2 ] [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 uncertainty fractional uncertainty = best measured value uncertainty percent uncertainty = 100% best measured value Propagating Uncertainty • Addition/Subtraction: Add the uncertainty in the individual terms If C=A+B, Then C=A+B • Multiplication/Division: – Add the fractional uncertainties of the factors C A B If C=AB, Then = + C A B – Use extreme values of factors and subtract If C=AB, Then C= A+A B+B -AB What does it mean to agree? 0.5 5.0 0.5 0.25 4.8 0.25 Measurement A Measurement B Do Measurements A and B agree? What does it mean to agree? 0.5 5.0 0.5 0.25 4.2 Measurement A 0.25 Measurement B Do Measurements A and B agree? What does it mean to agree? 0.5 5.0 0.5 0.25 4.6 0.25 Measurement A Measurement B Do Measurements A and B agree? What does it mean to agree? 0.5 5.0 0.5 0.25 4.4 0.25 Measurement A Measurement B Do Measurements A and B agree?