Using an apparatus where a freely falling body is attached to a strip of special

Question

Using an apparatus where a freely falling body is attached to a strip of special sensitized paper and allowed to fall through a spark generator that marks the paper every 1/60 of a second: A student from Sidney, Australia compares the distance he obtained from the 1-st spark mark to the 20-th spark mark, with the similar result of a student who did the experiment in Gaithersburg, Maryland. Both students operated identical setups powered with 60 Hz AC, reported no missing spark marks, and certified precision of their measurements in four significant figures. A student in Europe performs the same experiment, but the AC frequency there is 50 Hz. How different length of sensitized tape will he need in order to get 20 spark marks, compared to the length of your tape for the same number of marks? Give the result in centimeters. g in Maryland= 9.810424 m/s^2 g in Sydney= 9.7967134

Explanation / Answer

time period = 20 / 50

= 0.4 sec

For 60 Hz, time period = 20/60

= 0.333 sec

difference = (0.5 * t12 * a1)-(0.5 * t22 * a2)

= (0.5*(0.42)*(9.81)-(0.5 * (0.3332)*9.797 )

= 0.2405 m = 24.05 cm

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