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 9.68 m above the ground, and the elevation of the lower branch is 6.44 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 0.46 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*p*v(l1/g))/4 + (2*p*v(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

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