Question

A monkey is climbing on a rope that goes over a smooth light pulley and supports a block of equal mass at thr other end Figure. Shoe that whatever force the monkey exerts on the rope, the monkey and the block move in the same direction with equal acceleration. If initially both were at rest, their separation will not change as time passes.

Answer 1

Suppose the monkey accelerate upward with acceleration 'a' and the block accelerates downward with acceleration $a_1$. Let force exerted by monkey is equal to 'T'. From the free body diagram of monkey

T - mg - ma = 0 ....(i)

$\Rightarrow$ T = mg+ma

Again, from the free body diagram of block,

$T+m{a}_1-mg=0$

mg+ ma+ma_1-mg = 0 [From (i)]

$\Rightarrow ma=-m{a}_1$

$\Rightarrow a_1$= -a

Acceleration '-a' downward, i.e. 'a' upward. The block and the monkey move in the same direction with equal acceleration.

If initially they are at rest (no force is exerted by monkey), motion of monkey of block occurs as they have same weight (same mass). Their separation will not change as the passes.