Name: Conservation of Linear Momentum
Uploaded: 2019-07-19
Duration: 3 min 5 s
Description: In their study of natural phenomena over many centuries, scientists have identified certain fundamental laws. One such law is the law of conservation of mome...

Question

The monkey $B$ shown in figure given below 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 monkey $A$ 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 $g = 10 m s^{- 2}$ .

Accepted Answer

Let the monkey $A$ applies a force $T$ on the rope due to which the rope also applies the same tension on the monkey. To remain in equilibrium, this tension should balance the weights of both the monkeys.

Hence, $T = (5 + 2) \times 10 = 70 N$ .

This is the smallest value of the force that should be applied by the monkey holding the rope, so as to remain stationary.

To move upwards, the tension should be greater than $70 N$ . Let the tension in the rope be $T'$ and the acceleration of both the monkeys be $a$ upwards. Then,

$T' - 70 = 7 a$

But, the limiting tension in the tail of the monkey $A$ is $30 N$ . Hence, the value of the acceleration should be such that the tension in the tail of the monkey does not exceed this limiting value.

Hence, the maximum allowed acceleration for both the monkeys is given by writing the force equation for the lower monkey.

$30 - 2 \times 10 = 2 a \Rightarrow a = 5 m s^{- 2}$ .

Hence, the maximum acceleration allowed for both the monkeys to climb the rope is $5 m s^{- 2}$ .

Since, the force applied by the upper monkey on the rope and hence, the tension in the rope depends on the acceleration, the maximum allowed magnitude of the force to be applied by the upper monkey on the rope is $T' - 70 = 7 \times 5 \Rightarrow T' = 105 N$ .

Hence, monkey $A$ should apply a force of magnitude $70 N < T' < 105 N$ .

Important Questions on Newton's Laws of Motion

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