Question

An athlete grips a light rope that passes over a low friction pulley attached to the ceiling of a gym. A sack of sand precisely equal in weight to the athlete is tied to the other end of the rope. Both the sand and the athlete are initially at rest. The athlete climbs the rope, sometimes speeding up and showing down as he does so. What happens to the sack of sand? Explain.

Short answer

The sack of the sand will move the same distance than the athlete and in the same direction towards the pulley. So the distance between the athlete and the sack of the sand will not change.

Step-by-step solution

Tension on the rope:

Tension force is defined as the force that is transmitted by a rope, string, or wire when pulled by forces acting from opposite sides. The pulling force is directed along the length of the wire, pulling energy evenly onto the bodies at the ends.

The sack of the sand will not change:

There are two forces acting over the athlete and the sack of the sand, the tension of the rope and their own weight, since the weight of the athlete and the sack of the sand is the same system is in equilibrium and none of them will move until they break the equilibrium, to do that the athlete pulls the rope downwards, so he is exerting a force over the rope and by third Newton’s law, the rope will exert the same force in the opposite direction over the athlete.

This means that the tension of the rope will increase which means that,

$\mathrm{T}>\mathrm{m}*\mathrm{g}$

And the athlete will have an acceleration upward and they move the same distance in the same direction since they have the same mass.