Calculating the error in a measurement In the

Calculating the error in a measurement In the first year physics a reasonable approximation is: A more correct approach is to use the standard deviation (but need enough observations for this to be reliable)

Absolute and fractional uncertainties These are two ways to present the uncertainty. In the first year physics lab you should present your final uncertainty as an absolute uncertainty. The absolute uncertainty is the uncertainty in the value presented with the same units as the value: The fractional uncertainty is the dimensionless ratio: The percentage uncertainty is just:

Calculating uncertainties when combining dependent variables If you add or subtract the values then you add the uncertainties (1) If you multiply or divide the values then you add the fractional errors to get the final fractional error (2)

Calculating uncertainties when combining independent variables If you add or subtract 2 independent variables, add their absolute errors in quadrature: (3) If you multiply or divide independent variables (2 in this example), add the fractional errors in quadrature, i. e. for or for (4)

What is the error on V, given d is the measured quantity? (5) How is a small change (infinitesimal) in V, d. V, related to a small (infinitesimal) change in d, dd? Differentiate equation 5: so that for small , (6) Equation 6 is the same as equation 2, the formula for calculating uncertainties for dependent variables (as it should be, since V depends on dxdxd). M and V are independent variables, so now we can use equation 4 to get the uncertainty on the density, rho.

Moodle resources: http: //moodle. telt. unsw. edu. au/mod/book/view. php? id=805463&chapterid=102938 Video: http: //www. animations. physics. unsw. edu. au/sf/toolkits/uncertainties. html