An Introduction to the Uncertainties and Errors as used in Physical Measurement

1. Topic 1 – Physical Measurements 1.2b – Uncertainties and Errors

3. Whenever you actually measure something then you are always comparing it against a standard and there is always a chance that you can make an error.

5. Systematic – these are errors usually brought about by the measuring equipment (or its operator) e.g. a calliper that does not actually read zero when it should.

8. Accuracy is improved by reducing systematic errors

9. Precision is improved by reducing random errors.

10. Accuracy and Precision

12. A value quoted as 5.00 kJ (3sf) suggests an answer between 4995 J and 5005 J i.e. a range of just 10 J or 0.01kJ

15. Calculate 605N x 12m

16. Calculate 4.05m + 3.54 mm

19. The error (by precision) is just ±1Ω BUT the mean of the results is 1472Ω.

22. Human reaction time is approximately 0.3 s. You can check yours online if you want. http://faculty.washington.edu/chudler/java/redgreen.html

23. Therefore the time is 5.46 ± 0.3 s

25. The unit always follows the uncertainty not the measurement

27. A percentage uncertainty is found by using:

29. 1.56 ± 1.28% m x 4.53 ± 1.10% m

30. 7.0668 ± 2.38% m 2

31. 7.0668 ± 0.1681 m 2

32. 7.07 ± 0.17 m 2 which could become 7.1 ± 0.2 m 2

35. Sin 44 = 0.694 (-0.011)

36. Sin 46 = 0.719 (+0.012)

37. Sin 45 = 0.707± 0.012 OR 0.71 ± 0.01

42. The bottom left corner of data point 1 is joined to the top right corner of data point n

43. The gradients of these two lines are then calculated and the one with the largest deviance from the line of best fit is quoted as the uncertainty.

44. Graphing Uncertainties Line of Best Fit Line of Max Gradient Line of Min Gradient

46. In order to make use of these sorts of graphs we often use logarithms. Error bars are not needed on log graphs

49. i.e. a straight line graph of log x versus log (y-c) of gradient n and ordinate intercept of log k