George of the Jungle, with mass m, swings on a light vine hanging from a station

Question

George of the Jungle, with mass m, swings on a light vine hanging from a stationary tree branch. A second vine of equal length hangs from the same point, and a gorilla of larger mass M swings in the opposite direction on it. Both vines are horizontal when the primates start from rest at the same moment. George and the gorilla meet at the lowest point of their swings. Each is afraid that one vine will break, so they grab each other and hang on. They swing upward together, reaching a point where the vines make an angle of 29.8° with the vertical. Find the value of the ratio m/M.

Explanation / Answer

in the givenproblem each object swings down according to m gR = (1 / 2) m v12 M gR = (1 / 2) M v12 v1 = v(2 g R) duringthe collision - mv1 + M v1 = (m + M)v2 v2= [(M - m) / (M + m)] v1 onsolving we get that (1/ 2) (M + m) v22 = (M + m) g R (1 -cos29.8o) v2= v[2 g R (1 - cos29.8o)] v[2g R (1 - cos29.8o)] (M + m) = (M - m) v(2 gR) solvefor m / M There you go.

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