Person climbing rope on pulley with equal mass box

[Tibriel]

Homework Statement

person and a box of equal masses are hanging off of the same pulley. The rope is considered massless. The person and the box are separate from each other. (The person is NOT standing on the box.)

Homework Equations

How far does the box move if the person starts climbing and moves a distance x relative to the rope.

The Attempt at a Solution

In an attempt to get a solution I tried to analogize it to a person and a block on a frictionless plane with a rope between them. With no outside forces the CG would have to remain constant. So if the person pulled through 10 feet of rope the movement, relative to the ground, would be split evenly between the two. However on a frictionless plane they would keep going until they hit each other. In the pulley system would they just stop when the person stopped climbing?

 

[andrewkirk]

Yes I think you're right. The person and the box will both move upwards at the same rate. They'll both travel upwards by x/2.

Under this scenario, the CG moves upwards. The force that provides that is that of the bracket holding the axle of the pulley, which will be pulling upwards with a force greater than the weight of person+box while the person is trying to climb.

When the person stops climbing, they momentarily apply a force to the rope that is less than their weight, thereby allowing gravity to decelerate them back to a stationary state. The resulting reduced tension in the rope also causes the block to stop rising. They'll come to a standstill at the same height as one another, but both higher than before.