Question

The monkey B shown in figure is holding on to the tail of the monkey A which is climbing up a rope. The masses of the monkeys A and B are 5 kg and 2 kg respectively. If A can tolerate a tension of 30 N in its tail, what force should it apply on the rope in order to carry the monkey B with it ? Take g = 10 $m/s^2$.

Answer 1

Suppose A moves upward with acceleration a, such that in the tail of a maximum tension 30 N produced.

T - 5g -30-5a = 0 ....(i)

30 -2g -2a = 0 .....(ii)

From equations (i) and (ii), we have

$\Rightarrow$ T = 105 N (max)

and a = 5 $m/s^2$

So, A can apply a maximum force of 105 N in the rope carry the monkey B with it. For minimum force there is no acceleration of monkey A and B.

$\Rightarrow$ a = 0

From equation (ii),

$T_1-2g=0$

$\Rightarrow$ $T_1=20N$ (weight of monkey B)

From equation (i),

T - 5g -20 = 0

as $T_1=20$

$\Rightarrow$ T- 5g -20 = 0

$\Rightarrow$ T = 70N

$\therefore$ The monkey A should apply force between 70 N and 105 N to carry the monkey B with it.