Question

Kids at a swimming hole swing over the water on a tire swing (essentially a simple pendulum) and then drop in the water. If the tire+kid takes 2.7·s to swing from the launching point to its farthest point over the water, how long will it take the empty tire to return for the next kid? s Assuming the tire is launched without a push from its highest point, what is the frequency of the tire-swing-pendulum (unloaded)? Hz. How long is the rope? m

Answer 1

Part A.

We know that time period of simple pendulum is given by:

T = 2*pi*sqrt (L/g)

Since time period does not depend on the mass of pendulum, So empty tire will also take same time to return to the next kid, as it take with kid

Time taken by the empty tire to return for the next kid = 2.7 sec

Part B.

Since given that time taken from highest point to next highest point is 2.7 sec, So

total time period of pendulum = 2.7 sec*2 = 5.4 sec

frequency = 1/time period

f = 1/5.4 = 0.185 Hz

Part C.

Since

T = 2*pi*sqrt (L/g)

L = g*T^2/(4*pi^2)

L = 9.81*5.4^2/(4*pi^2)

L = 7.25 m = length of rope

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