First slide

Application of Newtons laws

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 ms^-2)

Moderate

A

105 N
B

108 N
C

10.5 N
D

100 N

Solution

If A is climbing with constant velocity, then
$\begin{array}{l} T^{'} = 5 g + T and T = 2 g \\ T^{'} = 5 g + 2 g = 7 g \end{array}$
Suppose A is climbing with acceleration a such that
$\begin{matrix} T = 30 N \\ T - 2 g = 2 a \\ 30 - 2 \times 10 = 2 a \\ or a = 5 {ms}^{- 2} \\ Again, T^{'} - T - 5 g = 5 a \\ or T^{'} = T + 5 g + 5 a \\ or T^{'} = (30 + 50 + 25) N \\ = 105 N \end{matrix}$

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