A person has a mass of 80 kg and is climbing a massless rope that is thrown over

Question

A person has a mass of 80 kg and is climbing a massless rope that is thrown over a tree limb and attached to a 100 kg rock. There is effectively no friction between the tree limb and the rope. If the person is climbing the rope accelerating at 3.5 m/s2, what is the acceleration of the rock? If, after the rock has been raised off the ground, the person stops and hangs onto the rope, what will his acceleration and the tension in the rope now be? What is the maximum acceleration the person can climb such that the rock stays on the ground?

Explanation / Answer

FOR MAN: T-mg= ma T-800= 80*3.5 T= 280+800= 1080N FOR ROCK: T>mg so rock will lift from ground T-mg= ma 1080-1000=100a a.) a= 0.8m/s^2 b.) FOR ROCK: mg-T = ma and T-mg= ma 200= (180)*a a= 200/180= 1.11 m/s^2 c.) for rock to rest T= 1000N 1000-800= 80*a a= 20/8= 2.5m/s^2

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