Unit 1 A Physics Toolkit

1.1 Mathematics and Physics Physics depends on numerical results to support theoretical models.

SI Units Le Systeme International d’Unites –The International System of Units Builds units off of given base quantities Base QuantityBase UnitSymbol Lengthmeterm Masskilogramkg Timeseconds TemperaturekelvinK Amount of a substancemolemol Electric CurrentampereA Luminous Intensitycandelacd (Table 1-1 pp. 5)

Prefixes Used With SI (Table 1-2 pp 6) PrefixSymbolMultiplierSci. Not.Example femto-f femtosecond (fs) pico-p picometer (pm) nano-n nanometer (nm) micro-μ microgram ( μg) milli-m milliamps (mA) centi-c centimeter (cm) deci-d deciliter (dL) kilo-k kilometer (km) mega-M1,000, Megagram (Mg) giga-G1,000,000, gigameter (Gm) tera-T1,000,000,000, terahertz (THz)

Dimensional Analysis Use “Multiplicative Identity Property of One” to change from one unit to another. So,

Significant Digits Valid digits in the measurement of any value. Used to show precision NOT accuracy.

Rules for significant Digits 1. Any non-zero number in a measurement is significant m (4 s.f.) 2. Any zero between two s.f. is significant s (6 s.f.) 3. Zeroes placed at the END OF A NUMBER AFTER A DECIMAL are significant cd (5 s.f.) 4. Zeroes that space a decimal are NOT significant A (1 s.f.).002 m (1 s.f.)

Adding/Subtracting with S.F. You can only add or subtract to the least precise measurement m m m 41.1 m is the final answer. We get rid of the 9 because it is added to an unknown.

Multiplication with S.F. Your answer can only have as many s.f. as the multiplier with the least s.f (3 s.f) x 1.0(2 s.f) 2.3 is the answer not 2.34 The same goes for division.

Significant Figures do not apply when counting or dealing with exact numbers. A dozen = π = … These each have an infinite number of significant digits.

Measurement Comparing Results: (We look for) –Overlap in results. –Reproducibility These are signs of Precision –A degree of exactness in a measurement

Measuring Accuracy –When we are close to a known value. –How well the results “agree” with a known value.

The International Prototype Meter The probable uncertainty of the length of No. 27 at temperatures between 20°C and 25°C was estimated by BIPM to lie between ±0.1 μm and ±0.2 μm. International Bureau of Weights and Measures (BIPM) in Sevres, France

Accuracy and Precision Accurate, not precise Precise, not accurate Accurate and precise

Tolerance When measuring, the last significant digit is usually an estimate. –A table is measured at m long, and you are probably right to within 5 mm We can write it as: ±.005 m Or m ±.005 m It shows where the error lies. We will deal with them soon We call them “deviations”