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 rope? (See Figure)
Hint: Assume that this is a perfect machine—the pulley is frictionless,
and the mass of the rope and pulley is negligible.
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.
Solution: 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.
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