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 2.6 seconds 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

Here,

Time taken , t = 2.6 s

as this is a simple pendulum , the period is not dependent on the mass or initial velocity

hence , for the only tire , the time taken to come back is 2.6 s

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if it is launched with initial speed , the time period will be same

Frequency = 1/time period

Frequency = 1/(2 * 2.6)

Frequency = 0.192 Hz

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let the length of the rope is L

T = 2pi * sqrt(L/g)

5.2 = 2pi * sqrt(L/9.8)

solving for L

L = 6.71 m

the length of rope is 6.71 m