1. Measurements and Uncertainties
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 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 /- .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