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elementis0
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Homework Statement
Heres is the problem I am trying to solve:
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 the vine will break, so they grab each other and hang on.
They swing upward together, reaching a point where the vine makes an angle of 35 degrees with the vertical.
The question is to find the ratio m/M
Homework Equations
No equations, just use the concepts of linear momentum and energy.
The Attempt at a Solution
I've been at this problem about an hour and have not found what works..
Heres what I tried, which is probably totally wrong.
First I looked at the momentum by saying that before the collision the momenum of this system is the following:
p_initial = mv1 + Mv2
and when they collide at the lowest point I said
P_final = (m+M)vf
Using conservation of momentum I got:
mv1 + Mv2 = (m+M)vf
I also looked at the energy of the system and said that right when they collide the only energy will be kinteic in the system so
E_initial = 0.5mvf + 0.5Mvf = (1/2)(m + M)vf
and then after they reach that given angle of 37, I interpreted the question as that being their max height of the swing so the only energy would be the potential which I modeled as
E_final = (m+M)g(L-Lcos(theta)) where L-Lcos(theta) is their height above the lowest point of the swing.
So my since energy is conserved I got:
Energy: (1/2)(m + M)vf = (m+M)g(L-Lcos(theta))But when trying to manipulate that system of eqn's I fail to be able to reasonably find the ratio of m/M which should come out to being an actual number...
Help Por favor?