Physics and Physical Measurement

1. Physics and Physical Measurement The Realm of physics Measurement and uncertainties

2. Extra Book Physics: for use with the IB Diploma Program By Michael J Dickinson ISBN: 9781475130010

3. Hertz Hz frequency s-1 • Coulomb C Electric charge As • Ohm Ω electrical resistance kg m2 s-3 A-2 • Tesla T magnetic flux Wb m-2 • Weber Wb magnetic flux (T m2) or kg m-2 s-2 A • Becquerel Bq radioactivity s-1

4. Uncertainty and Error • There are two types of errors: • Random and systematic • Random errors can be reduced by repeating measurement many times. • Systematic errors can be reduced by repeating measurement using a different method or different apparatus and comparing the results.

5. Sources of random errors • the readability of the instrument • the observer being less than perfect • the effects of a change in the surroundings.

6. Sources of systematic errors • an instrument with zero error • an instrument being wrongly calibrated • the observer being less than perfect in the same way every measurement.

7. Accuracy and precision • Accuracy is how close to the “correct” value • Precision is being able to repeatedly get the same value • Measurements are accurate if the systematic error is small • Measurements are precise if the random error is small.

8. Three Basic Rules • Non-zero digits are always significant. • 523.7 has ____ significant figures • Any zeros between two significant digits are significant. • 23.07 has ____ significant figures • A final zero or trailing zeros if it has a decimal, ONLY, are significant. • 3.200 has ____ significant figures • 200 has ____ significant figures

9. Uncertainties • All measurement involves readability error. If we use a graduated cylinder to find the volume of a liquid, the best estimate is 73cm3, but we know that it is not exactly this value(73.00000000000cm3). Uncertainty range is ± 5cm3. We say volume = 73± 5cm3.

10. Uncertainties in Calculations • Random errors can be taken into account by use of an uncertainty range. • An analogue scale is +/-half of the limit of reading. • Rulers, scales with moving pointers. • A digital scale is +/-the limit of reading. • Ex. Top-pan balances, Digital meters

11. Uncertainties Examples

12. We can express this uncertainty in one of three ways- using absolute, fractional, or percentage uncertainties • Absolute uncertainties are constants associated with a particular measuring device. • (Ratio) Fractional uncertainty = absolute uncertainty measurement • Percentage uncertainties = fractional x 100%

13. Example • A meter rule measures a block of wood 28mm long. • Absolute = 28mm +/- 0.5mm • Fractional = 0.5mm = 28mm +/- 0.0179 28mm • Percentage = 0.0179 x 100% = 28mm +/- 1.79%

14. Graphs • error bars. • Since error bars represents the uncertainty range, the ‘best-fit’ line of the graph should pass through all of the rectangles created by the error bars. • The best fit line is included by all error bars in the first two graphs. This is not true of the last graph. Systematic and random errors can often be recognized from a graph of the results.

15. The best fit line is included by all error bars in the first two graphs. This is not true of the last graph. Systematic and random errors can often be recognized from a graph of the results.