Question

A monkey of mass 15 kg is climbing on a rope with one end fixed to the ceiling. If it wishes to go up with an acceleration of 1$m/s^2$, how much force should it apply to the rope ? If the rope is 5m long and the monkey starts from rest, how much time will it take to reach the ceiling ?

Answer 1

Given m = 15 kg

a = 1 $m/s^2$

From free body diagram,

T - [15g +15(1)] = 0

$\Rightarrow T=5(10+1)$

$\Rightarrow T=15\times 11=165N$

The monkey should apply 165 N force to the rope.
Initaial velocity , u = 0

Acceleration, a = 1 $m/s^2$

S = 5m

From $S=ut+\frac{1}{2}a{t}^2$

$5=0+\left(\frac{1}{2}\right)\times 1\times t^2$

$\Rightarrow t^2=5\times 2$

$\Rightarrow t=\sqrt{10}sec$

Hence time required is $\sqrt{10}sec.$