A monkey is sitting on a wood plate attached to a rope whose other end is passed

Question

A monkey is sitting on a wood plate attached to a rope whose other end is passed over a tree branch, as shown in the figure. The monkey holds the rope and tries to pull it down. The combined mass of the monkey and the wood plate is 112 kg.

(a) What is the minimum force the monkey has to apply to lift off the ground?

(b) What applied force is needed to move the monkey with an upward acceleration of 1.75 m/s2?

(c) Explain how the answers would change if a second monkey on the ground pulled on the rope instead.

Explanation / Answer

When the monkey is applying the force on the rope, the rope is applying a tension on the monkey which is being reflected in the force which is pulling the plank up as tension too. So the if we consider the monkey+plank as a system then the normal force between them is not taken. Now the system has two forces 2 Tensions in upward direction, and a combined mass*g in downward direction, and to achieve an acceleration of a in upward direction the equation comes out to be: 2T=Mg+Ma this M=combined mass the Ma is coming the downward direction because the acceleration causes an pseudo force in the opposite direction to which it is being applied. So for a lift off a=0 therefore (a) Force applied by the monkey is T so T=Mg/2=(112Kg*9.8m/s*s)/2 (b) for a=1.75 T=(Mg+Ma)/2=112*(9.8+1.75)/2 (c) Earlier there were 2 tensions acting on the system which was facilitating the motion, but as now the second monkey is pulling the system so now there is only one tension acting on system so they '/2' in the tension equation will not be there. Now the answers would be (a-1) T=Mg=112Kg*9.8m/s*s (b-1) T=Mg+Ma=112*(9.8+1.75) The answers are doubled.

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