A horizontal tree branch is directly above another horizontal tree branch. The e

Question

A horizontal tree branch is directly above another horizontal tree branch. The elevation of the higher branch is 8.78 m above the ground, and the elevation of the lower branch is 6.17 m above the ground. Some children decide to use the two branches to hold a tire swing. One end of the tire swing's rope is tied to the higher tree branch so that the bottom of the tire swing is 0.48 m above the ground. This swing is thus a restricted pendulum. Starting with the complete length of the rope at an initial angle of 14.2° with respect to the vertical, how long does it take a child of mass 29.9 kg to complete one swing back and forth?

Explanation / Answer

The time taken by the swing to go back:
T = (2**(l1/g))/4 + (2**(l2/g))/4

l1= pendulum length before hitting the lower brach = 8.78-0.48 = 8.3

l2=pendulum length after hitting the lower brach = 6.17-0.48 = 5.69

=> T= 2.63s

The time taken for back and forth = 2*T =5.27 s

Ans : 5.27s

NOTE: since the given angle is small (14.2), I have taken the time period of simple harmonic motion which is 2**(l1/g). This is an approximated equation for small amplitudes. Hence it may be slightly different from the actual answer.

Hope this helped!!

CHEERS!!

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