Posted by Sarah on .
I was just a little confused with this problem and was hoping for some help or a nudge since the only value given is 27 degrees. Thanks for your time!
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 27.0° with the vertical.
(a) Find the value of the ratio m/M.
Actually the question gives more information than meets the eye.
0. The primates had the collision on Earth, where the acceleration due to gravity is g=9.8 m/s².
1. The masses are m for George, and M for the Gorilla, where M>m.
2. The vines are of equal length, say r.
3. They both start from the same elevation on the same horizontal line.
Thus the velocity v0 just before impact can be calculated from energy considerations.
4. Consequent to #3, they have equal speeds, v0, just prior to collision.
5. They collide inelastically, i.e. they stick to each other after the impact, and travelled with the same velocity v1.
Work is done during an inelastic impact, thus energy is not conserved.
The law of conservation of momentum applies before and after impact.
6. At an angle of 27 degrees with the vertical, the common velocity is 0.
Thus the velocity v1 can be calculated from energy considerations from the moment right after the inelastic impact.
In fact, what you would need to do is to calculate v0, and v1. Apply them to the law of conservation of momentum which will give you the ratio of m/M.
Can you take it from here? Post your result for verification if you wish, or tell us where you are stuck if that's the case.