The "rising chimp" problem


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Can you solve Martin Gardner's "coin of the realm" puzzle?

I’m more worried about the other kind of rising chimp problem.


OK, I’ll bite. Assuming it’s perfect equilibrium with no friction and no rope weight, shouldn’t they arrive simultaneously?


I’m going to say the weight. I think pulling on the rope to raise himself will basically raise the weight.

Note: I nearly failed physics in high school and then again in college


Only one way to settle this… packing up my frictionless pulley and negligible-weight rope and heading to the zoo.


I’m going to say weight. Because he’s pulling the rope toward himself and the added weight of that extra rope makes his side heavier.


I say the chimp gets to the top first, since the weight on both sides of the wheel does not change the wheel should not turn and therefore the chimp should simply be able to climb up to the wheel.


The pulley! No…the rope! Wait, wait…turtles?


Yes, by symmetry. But also, when Bonzo climbs the rope, he’s not just making the distance shorter - he’s exerting a force. That force gets evenly distributed between 4.5 kg of lead and 4.5 kg of ape. F=mA, so they move at the same velocity until little Bonzo’s fingers go into the pulley.


I think you’re right and I was wrong.


The monkey arrives first, with no net movement of the weight.

The monkey is already hanging at equilibrium with the weight, and can’t apply a net unbalanced force on the rope. Depending on how much the monkey swings its rope around, there will be some oscillation, but the monkey will not pull the weight any closer to the pulley.


“I’d sooner be a rising ape than a falling angel” - Terry Pratchett.

So I guess what he was saying was that if we replace the weight with an angel weighing exactly 10 kg, it would hit the floor before the chimp hit the ceiling?

Which means that no matter the counterweight, only the chimp can make it to the top.



I’d say the chimp, since it is reaching up to climb, therefore shortening the distance.


Yes, and what also floats?


The rope has negligible weight…



*Death (he of the robe, scythe and bony countenance) speaks in all caps.


Yes, they move in the same velocity relative to the rope. The rope is not fixed though. The rope can move on the pulley depending on which side weighs more. And the monkey gathering rope weighs more that the weight just tied off to the other end.


Your conclusion is correct, but the proper quotation to cite is:

“A rising chimp lifts all primates” - John F. Kennedy

Obviously the weight is not a primate; therefore only the chimp can make it to the top.


I think the chimpanzee gets to the top first, but only briefly.

Each time the chimpanzee pulls itself up, the weight will be held by inertia. But once the chimpanzee is higher than the weight, then the pulley is imbalanced, and this causes the weight to rise secondarily.

But perhaps that principle only holds with levers, not pulleys?


I’m just happy there isn’t a chimp uprising!