Question

20. A chimpanzee is swinging on a vine that can withstand a tension of 1860. N. The mass of the chimpanzee is 56.8 kg and the length of the vine is 12.6 m. What is the greatest speed the chimp can have at the bottom of the swing before the vine breaks?

Answer 1

For circular motion, centripetal force=mv2/r, where m is mass, v is velocity and r is radius of the circular trajectory.

Now, there are 2 vertical forces on the chimpanzee at the bottom of the swing:

i)Gravitational force =mg downwards, where m is mass and g is gravitational acceleration.

ii)Tension T upwards.

So, T-mg = mv2/r.

Here,T=1860 N, m=56.8 kg, r=12.6 m.

So, 1860 - 56.8*9.8 = 56.8v2/12.6

=>1303.36 = 56.8v2/12.6

=>v2 = 1303.36*12.6/56.8 = 289.1256

=>v = 17 m/s