Question

Tarzan spies a 35kg chimpanzee in severe danger, so he swings to the rescue. He adjusts his strong, but very light, vine so that he will first come to rest 4.0 s after beginning his swing, at which time his vine makes a 12 degree angle with the vertical. (a) How long is Tarzan's vine, assuming that he swings at the bottom end of it? (b) What are the frequency and amplitude (in degrees) of Tarzan's swing? (c) Just as he passes through the lowest point in his swing, Tarzan nabs the chimp from the ground and sweeps him out of the jaws of danger. If Tarzan's mass is 65 kg, find the frequency and amplitude (in degrees) of the swing with Tarzan holding onto the grateful chimp.

Answer 1

(a) For the length L of the vine, use the fact that the period of oscillation (back and forth) is
P = 8.0 s = 2 pi sqrt(L/g)
g is the acceleration of gravity. Solve gor L
b) Picking up the chimp will not affect the frequency/period of vibration, and it will be an inelastic collision process with momentum conserved. The two of them will have their speed at the bottom of the swing reduced by a ratio 65/100. The kinetic energy will be reduced by a (100/65)(65/100)^2 = 0.65 factor

This will reduce the swing amplitude so that
1 - cos theta) is 65% of what it was before, since maximum potential energy is proportional to (1 - cos theta)

Original 1 - cos theta = 0.0219
Final 1 - cos theta = 0.0142
cos theta = 0.9858
theta = 9.7 degrees.