Question

PROPAGATING UNCERTAINTY - MULTIPLICATION AND DIVISION To learn how to propagate uncertainty when dividing, read the following example: EXAMPLE 2: You are trying to determine the speed of a person who is running. You measure the distance they run to be x = 80.0 m and the time it took them to be t = 9.0 s. Your measurements have an uncertainty of Ox=2.0 m and or=0.2 s. That is: x = 80.0 + 2.0 m t = 9.0 + 0.2 s Finding the speed is easy: v=8.88888... m/s Finding the uncertainty is a little more involved. We can't do what we did before to find the uncertainty, we will have to use the percent uncertainty. First convert the absolute uncertainti into percent uncertainties. x=80.0 m + 2.5% t= 9.0 s +2.2% Now add the two percent errors from both x and t. % = %ox + %ot % = 2.5% + 2.2% %or= 4.7% This gives us the uncertainty as a percentage of the speed: v=8.88888... m/s + 4.7% But we still need to convert the percent uncertainty into an absolute uncertainty! %ov=- - 100% calculated speed Op 4.7% = - - 100% 8.88888. m/s Ov= 0.4 m/s This gives a final value of: v=8.9 + 0.4 m/s Vhen we multiply or divide two measured values, we add their percent ncertainties to find the uncertainty in the calculated value. ust like before we have a rule in equation form:

the whole thing. I think I figured out the first part, just having trouble with second part. I am not sure that they correlate to one another.

Answer 1

v alue of spead hom above speed AV=0-4Mls (oR) abso lute eaos O.4mls V in speed b AV 1oO. X 1007 4.49% Answe a 1 Y