A student wants to measure the acceleration of gravity g by timing the free fall

Question

A student wants to measure the acceleration of gravity g by timing the free fall of a ball dropped from four different windows in a tall building. She assumes that air resistance is negligible and that the distance fallen is given by l = 1/2gt^2 . Using a tape measure and an electric stopwatch, she obtained the following set of data of the four separate drops:

Distance (m) : 15.43 17.37 19.62 21.68

Time (sec) : 1.804 1.915 2.043 2.149

(a) Copy these data and add a third row in which you put the corresponding acceleration, calculated as g = 2l/t^2 . Also give the best estimate g and its uncertainty in the standard format.

(b) Based on these results, what is her best estimate for g and its uncertainty, assuming that all errors are random? Show that this answer is inconsistent with the accepted value of g = 9.80 m/s^2 .

(c) Having checked her calculations, tape measure, stopwatch, she concluded (correctly) there must be some systematic error causing the value of g different from 9.80 m/s2 and she suggests that air resistance is probably responsible for this discrepancy. What is (are) the argument for this conclusion? How can we modify the experiment to reduce this systematic error?

Explanation / Answer

     Distance (m) :            15.43   17.37   19.62    21.68

      Time (sec) :                1.804   1.915    2.043    2.149

a) acceleration (m/s^2) : 9.482   9.473    9.401    9.388

b) her best estimate is g = 9.482 m/s^2

uncertainty = 9.80-9.482 = 0.318 m/s^2

c) there is some resistance offered by air in upward direction ..

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