Question

A monkey of mass 15 kg is climbing a rope fixed to a ceiling. If it wishes to go up with an acceleration of 1 m/s², how much force should it apply on the rope? If the rope is 5 m long and the monkey starts from rest, how much time will it take to reach the ceiling?

Answer 1

Mass of the monkey, m = 15 kg,
Acceleration of the monkey in the upward direction, a = 1 m/s²

The free-body diagram of the monkey is shown below:


From the free-body diagram,
T − [15g + 15(a)] = 0
T − [15g + 15(1)] = 0
⇒ T = 5 (10 + 1)
⇒ T = 15 × 11 = 165 N
The monkey should apply a force of 165 N to the rope.

Initial velocity, u = 0
s = 5 m
Using, $s=ut+\frac{1}{2}a{t}^2$, we get:
$$\begin{gathered} 5=0+\left(\frac{1}{2}\right)\times 1\times t^2 \\ \Rightarrow t^2=5\times 2 \\ \Rightarrow t=\sqrt{10}\mathrm{s} \end{gathered}$$
Hence, the time required to reach the ceiling is $\sqrt{10}\mathrm{s}$.