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Chapter 1.2

Chapter 1.2. Measurements and Uncertainties. 1.2.1 SI Units. 7 fundamental SI units m length kg mass s second A electric current K Temperature Cd intensity of light. 1.2.2 Derived SI Units. Derived SI Units- combinations of the fundamental SI units

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Chapter 1.2

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  1. Chapter 1.2 Measurements and Uncertainties

  2. 1.2.1 SI Units • 7 fundamental SI units • m length • kg mass • s second • A electric current • K Temperature • Cd intensity of light

  3. 1.2.2 Derived SI Units • Derived SI Units- combinations of the fundamental SI units • N, J, W, Pa, Hz, C, V, T, Wb, Bq • Example 1:

  4. 1.2.3 Convert units to SI • Examples 2 (conversion):

  5. 1.2.4 Know Common SI Prefixes • Question 3: • Accepted SI units: ms-2 not m/s2 • 1.2.5 Values must be stated in scientific notation • Example: 5.0 x 10-16 nm with appropriate prefixes

  6. 1.2.6 Uncertainty and error in measurement • Random errors= if readings of a measurement are above and below the true value with equal probability then errors are random. • Examples: changes in experimental conditions, such as temperature, pressure, humidity • Different person reading instrument • Malfunction of the apparatus

  7. Systematic error= due to the system or apparatus being used. • Examples: observer consistently making the same mistakes -apparatus calibrated incorrectly • Random errors can be reduced by repeating measurement many times and taking the average but not systematic errors.

  8. 1.2.7 • Precise= getting same answer over and over • Accurate= getting equally close to the answer you want. • Example: Dart Board 4 Graph Possibilities • A measurement may have great precision yet may be inaccurate.

  9. 1.2.8 • Measurements are accurate if systematic error is small. They are precise if random error is small. • Random errors can be reduced by taking many readings (measurements) and taking the average.

  10. 1.2.9 Significant Figures • Give measurements with numbers that can be guaranteed (measurement of a paper) • Should reflect precision of the value or input data to a calculation • Multiplication and division number of significant figures in a result should not exceed the least precise value upon which it depends.

  11. Example: assume reading error is half smallest division on instrument on a ruler. Interval is 1mm; half is .5mm • Measurement would be 14.54 +/- .05cm

  12. Uncertainties in calculated results 1.2.10 • Absolute uncertainty= error in measured time to show uncertainty. Drop a ball= uncertainty due to reaction time. • Example: Measured time= 1.0s, uncertainty= +/- .1 s • Uncertainty can also be shown as a fraction or a percentage. • +/- .1s or 1/10 or 10%

  13. 1.2.11 Determine Uncertainties in Results • Example pg. 34 Tsokos • To determine maximum uncertainties: • addition/subtraction= absolute uncertainties may be added • Mult/division/exponential= percentage uncertainties may be added • Trig fxns/other fxns= mean of highest/lowest possible answers may be calculated to determine uncertainty.

  14. 1.2.11 Determine Uncertainties in results • Can throw out outliers • Square root= percentage uncertainty is halved • Uncertainties in graphs - Excel example of how to calculate and draw error bars on graphs

  15. 1.2.12 • Uncertainty values must always be shown at the top of data tables as +/- sensible values • Represented as error bars on graph (only need to be considered when uncertainty in one or both plotted quantities is significant) • Do not have to have error bars for trig or log fxns. • Question 4: How to draw minimum and maximum gradients

  16. Excel Example with Error Bars • Best fit line must pass through error bars. If it doesn’t, point must be labeled as an outlier. • To determine uncertainty in gradient and intercept of straight line graph, error bars only need to be added to the first and last data points.

  17. Significant Figures Handout • Review significant figures and do several examples

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