Monkey business!!!

Please donot flame if you feel this has to go to Sci.Physics.

Hanging over a pulley there is a rope, with a weight at one end. At the other end hangs a monkey of equal weight. What happens if the monkey starts to ascend the rope? Assume that the mass of the rope and pulley are negligible, and the pulley is frictionless.

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I'm tempted to guess - look how careful and perhaps completely wrong I am - that the monkey and the weight will reach the pulley at the same time: each time the monkey pulls himself up, his own inertia will cause some of the work to be used to lift the weight. Of course, if the monkey does a *very* gentle climbing, he could reach the top without displacing the weight. On the other hand, in an ideal world, the higher the monkey gets, the less he is attracted to the earth, so his weight will decrease. So as soon he has climbed just a little bit, he will get pulled up automatically by the heavier weight. But that is purely theoretical and very probably not measurable in practice.

Open for debate

Dirk Vdm

Monkey's answer: The system has no externally applied force, so the resultant momentum of the system stays at zero. The downward motion of the weight must therefore mirror the upward motion of the monkey. This is wrong, because the monkey forgot that the pulley has to be attached to an indefinitely large mass which can absorb any momentum with its own acceleration tending to zero in the limit.

My answer: The rope has to exert an upward force (as a reaction to the force the monkey exerts on the rope) on the monkey. The tension on the rope is the same everywhere, so at the other end, the rope exerts an equal upward force on the weight. The monkey and the weight therefore move upwards with identical accelerations, both starting from rest. They reach the pulley simultaneously.

If the variation in g with height is taken into account, the answer would be that if the monkey moves upward by an infinitesimal amount, he would be infinitesimally lighter than the weight and would automatically continue upwards towards the pulley whilst the weight moves down through an equal distance. Achieving this feat would imply truly ideal circumstances in the experiment.

This is a standard homework question. Was it so in this case?

Franz Heymann

Not with a perfect rope and frictionless pulley, though.

This is how the monkey can get to the top.

He climbs half way up so that the weight is level with him. Then he stands on the weight mometarily and uses his knees to give himself a push upwards and the weight downward. Having given the balanced system a motion, it will then continue.

Remember this in case you are ever stuck down an 'ole!

.......and when the monkey gets to the top his fingers go round the pulley with the rope. Remember the barrel of bricks!

<SNIP> <SNIP>

No, No!! Not a home work, just office work)

<SNIP> <SNIP> Why only theoritical, I was thinking this could be practically possible too. OK, let me visualise this.... Monkey climbs up say 10 cm upwards, the shift in the weight on the monkey's side should make the weight on the other side pull the monkey up. Actually when the monkey takes two of its limbs off the rope to hold on the higher side , that should itself pull the weight on the other side , cuz for a second or a fraction of it the weight on the monkey's side reduces. Is that not???

Yes, the arms movement would result in raising his center of gravity that would in turn result in reducing the weight. Theoretically. So the monkey doesn't even have to do any climbing at all Nice.

Dirk Vdm

... which is wat I was telling next: 'in an ideal world....'

In fact not needed since we can assume he starts at the same height as the weight.

That would probably work. If we can assume that he can reach the weight, which is quite reasonable.

I'll remember when I'm stuck in an 'ole. Let's hope the pulley will not be too rusty

Dirk Vdm

Monkey, weight and pulley converge.

Monkey, weight and pulley converge.