A monkey a mass 15 kg is climbing on a rope with one end fixed to the ceiling. If it whishes to go up with an acceleration of `1 m/s^2`, how much force should it apply to the rope? If the rope is 5 m long and the monkey starts from rest, how much time will it take to reach the ceiling?

Explanation

Given `m_1 = 100g= 0.1 kg
`m_2 = 500g=0.5kg`
` m_3 = 50g=0.05 kg`
From free body diagram -1
`T+ 0.5a-0.5=0` ……….i
From free body diagram -2 `T_1+0.05-0.05a=a` ……….ii.
Free body diagram -3
` T_1 + 0.1a-T+0.5g=0`……iii
From equation ii,
` T_1 = 0.05 kg + 0.05 a` .........iv.
From equation i.
`T_1 =0.5 g - 0.5 a`.................v.
Equation iii becomes,
`T_1 + 0.1a+T+0.05g=0`
From equations iv. and v we have `0.05g+0.05a+0.1a-0.5+0.5a+0.05g = 0`
` rarr 0.65a=0.4g`
`rarr a= 0.4/0.65 g`
` = 40/65g = 8/13 g` d(downward)
Acceleration of 500 gm block is `(8g)/13` downward.