# Pulley

Question:

A rope passes through a pulley. On one end of the rope is an iron weight. At the other end of the rope hangs a monkey of equal weight. What happens if the monkey starts to climb up the rop?

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C

A

P

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A

I

N

I

N

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E

R

V

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W

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Solution: Start by considering the initial equilibrium situation, before the monkey starts to try to climb. The monkey’s weight acts downward, pulling the rope with a force w, and the rope transfers this force directly to the weight on the other end of the rope, pulling the weight upward with a force w. However, the weight also pulls downward with an equal force w, which pulls the rope with a force w, which acts on the monkey. Therefore both the weight and the monkey are pulled downward by their own weights and pulled upward by the rope with equal forces. This is why the situation is in equilibrium, and is why neither the monkey nor the weight move. Another way of saying all this is to say that the monkey balances the weight, so they don’t move. Let a candidate who paid attention in physics class explain the rest:

Now, what happens when the monkey tries to climb the rope? The monkey exerts an additional force on the rope, so it pulls the rope down with a force that is now greater than w. How is this possible? In exactly the same way as any person would climb any rope—when the person hangs from a rope, the rope is pulled by the person’s weight, but when the person climbs it, he or she pulls the rope with a larger force. Hopefully, whatever is supporting the rope is strong enough not to break under this extra force and the person can climb the rope. This exertion of a greater force than one’s weight happens every time someone does a chin-up, or in fact, just stands up from the sofa.

The monkey pulls the rope. On the other end of the rope, the weight is now pulled upward not just by the monkey’s weight w, but by its climbing force too. It is only pulled downward by its own weight, w, though, so the net force is upward. Therefore the weight will accelerate upward.

Answer: The monkey is pulling down on the rope hard enough to pull itself up. This pulling action increases the effective weight of the monkey. The tension in the rope increases just enough to cause the weight to rise at the same rate as the monkey.