A monkey A (mass = 5 kg) is climbing up a rope tied to a rigid support. The monkey B (mass=2kg) is holding on the tail of monkey A. If the tail can tolerate a maximum tension of 30N, what maximum force should monkey A apply on the rope in order to carry monkey B with it? `(g=10ms^(-1))`

Explanation

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 ltbRgt `30-2g-2a=0` …….ii.
Form equation i. and ii, we have
`rarr T=105 N (max.)`
and `a=5 m/s^2`
So, A can apply a maximum forc eof 105 N in the rope to carry the monkey B with it.
For minimum force there is no acceleration of monkey A and B.
`rarr a=0`
From equation ii,
`T_1 -2g=0`
`rarr T_1 = 20 N` (weight of monkey B)
From equation i.
` T-5g-20=0`
`as T_1 =20`
`rarr T-5g-20=0`
` T=70N`
`:.` The monkey A should apply force betwen 70 N and 105 N to carry the monkey B with it.