#### theKingPin

##### Member

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- Jul 29, 2014

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- 2017

I was practicing some physics questions from Australian Physics Olympiads Online and came across a question that I had not seen before. The answer is given however I do not completely understand it. Could someone explain it.

Thanks

Question:

Lucy is measuring the acceleration due to gravity in Melbourne by dropping a ball through a vertical distance 1.00 m and timing how long it takes.

The ball starts at rest, and Lucy times its fall four times. The results are: 0.47 s, 0.42 s, 0.48 s and 0.41 s. The uncertainty in her distance measurement is 1 cm and the uncertainty in the timer is 0.01 s. What is the uncertainty in the value of g that Lucy calculates?

Select one:

a. at least 0.01 ms−2 and at most 0.03ms−2.

b. more than 0.03 ms−2but at most ms−2.

c. more than 0.1 ms−2 but at most 0.4 ms−2.

d. more than 0.4 ms−2 but at most 0.6 ms−2.

e. more than 0.6ms−2 but at most 2ms−2.

Correct Answer: E

A value of t = 0.45 ± 0.04 s just covers the range of measured values.

Alternative 1: Use this value and the range in possible distance measurements to calculate the largest and smallest possible values of the acceleration due to gravity.

Alternative 2 (using fractional errors): t has approximately 9% fractional error. The fractional error in the distance is 1%, so the fractional error in g is (2 × 9 + 1)% = 19% which gives an absolute uncertainty of around 2 ms−2.

http://csma31.csm.jmu.edu/physics/Courses/P140L/appendices/Combining Uncertainties in Experimental Results.htm