Having trouble with this question? Tarzan spies a 38 kg chimpanzee in severe dan

Question

Having trouble with this question? Tarzan spies a 38 kg 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 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 of Tarzan's swing?

C. What are the amplitude (in degrees) of Tarzan's swing?

D. 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 67 kg , find the frequency of the swing with Tarzan holding onto the grateful chimp.

E. If Tarzan's mass is 67 kg , find the amplitude (in degrees) of the swing with Tarzan holding onto the grateful chimp.

Explanation / Answer

a)

time, t/2= 4 s

t= 8 s

for simple pendulum,

t= 2(L/g)

8= 2(L/9.8)

L= 15.9 m

b) frequency, f= 1/t= 1/8=0.25 Hz

c) amplitude= 12 deg

d) frequency is dependent only on length of wire and acceleration due to gravity

f= 0.25 Hz

e) momentum at bottom=67*sqrt(2*9.8*15.9*(1-cos 12))=174.844 kgm/s2

applying conservation of momentum

new velocity=174.844/(67+38)=1.6652 m/s

now,

2*9.8*15.9*(1-cos x)=1.6652^2

x=7.649 degree

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