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 Quantity Base Unit SymbolLength meter m

Mass kilogram kg

Time second s

Temperature kelvin K

Amount of a substance mole mol

Electric Current ampere A

Luminous Intensity candela cd

(Table 1-1 pp. 5)

Prefixes Used With SI(Table 1-2 pp 6)

Prefix Symbol Multiplier Sci. Not. Examplefemto- f .000000000000001 10-15 femtosecond (fs)

pico- p .000000000001 10-12 picometer (pm)

nano- n .000000001 10-9 nanometer (nm)

micro- μ .000001 10-6 microgram (μg)milli- m .001 10-3 milliamps (mA)

centi- c .01 10-2 centimeter (cm)

deci- d .1 10-1 deciliter (dL)

kilo- k 1000 103 kilometer (km)

mega- M 1,000,000 106 Megagram (Mg)

giga- G 1,000,000,000 109 gigameter (Gm)

tera- T 1,000,000,000,000 1012 terahertz (THz)

Dimensional Analysis• Use “Multiplicative Identity Property of One”

to change from one unit to another.

1=1kg

1000gSo, 1.34kg

1000g1kg

⎛⎝⎜

⎞⎠⎟=1340g

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. 456.2 m (4 s.f.)

• 2. Any zero between two s.f. is significant.604.301 s (6 s.f.)

• 3. Zeroes placed at the END OF A NUMBER AFTER A DECIMAL are significant. 43.200 cd (5 s.f.)

• 4. Zeroes that space a decimal are NOT significant. 4000 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. 34.89 m + 6.2 m 41.09 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.

2.34 (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 = 12.0000000000000000000

• π = 3.1415926535…

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 1.638 m long, and

you are probably right to within 5 mm

• We can write it as: 1.638 ± .005 mOr 1.638 m ± .005 m

It shows where the error lies. We will deal with them soonWe call them “deviations”