Sneak preview of tomorrow’s puzzle post: Take an ordinary jet airliner and place it on a giant treadmill…
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Here is a solution:
http://www.activityworkshop.net/puzzlesgames/monkey/solution.html
tl;dr: They get to the top at the same time
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In this kind of problem, the standard unrealistic simplifications become irritating because they’re exactly the sorts of thing the answer hinges on.
If we consider it in a completely po-faced way, and assume a weightless inelastic chain, frictionless pulley, no air resistance etc., then the “right” answer is that they both get there at the same time because the monkey cannot move without accelerating, and cannot accelerate without imparting the same (vertical component of) acceleration to the weight. But it’s a dull answer because the problem’s setup rules out any connection to what would really happen.
I would take that as an invitation to try to break the puzzle. For example: the monkey swings over and stands on the weight, then hauls on its original rope until it gets to the top. Or: the monkey jumps to the other rope, then jumps back in time to grab the bottom end of its original rope; it now has a headstart and can reach the top first. In this vein, we can conclude that— because monkeys are naughtier and cleverer than whiteboard-marker addicts— the monkey will in general get there first, last or whenever it chooses to.
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Allow me to present the “rising tedium” problem:
Imagine that there is an even two-dimensional, massless cable draped over a completely frictionless, one-dimensional point-wheel. Equal lengths of the cable descend from either side. One both sides are perfectly equal point-masses balanced at exactly equal heights.
When you give a signal, a magical, sourceless force of acceleration pulls the cable down through the right-hand point-mass. Which point-mass reaches the top of the point-wheel first?
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in that case it’s the right hand object but only by a fraction of a nano second as the information about it’s change in position would travel at the speed of light before the forces providing equilibrium of the two objects can act.
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Ah, my apologies
I am, however left wondering whether the 60-odd answers before you represent BB-ers who prefer to work things out on their own or BB-ers too dumb/lazy to look up a well-known problem.
It depends on how hard the monkey yanks the rope. When I climb a rope really fast, at times I am not even pulling the rope at all - yet, I am still rising, due to inertia. The weight, being completely bound to the rope, will not move the same way. And I have long monkey like arms, too, which extend far past my center of gravity.
As @Ratel already pointed out, if you make the question inutterably boring by removing all real world considerations it’s a simple problem.
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Exactly. So, logically, if she weighs the same as a duck… ?
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Here is the practical application of a somewhat similar problem, with the chimp’s part being played by an angry motorcyclist…
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Wow, bright spark there.
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Then how would it climb?
In the event of a simian takeover, I intend to go “The Full Armando/MacDonald” and collaborate with the apes. What good is pride when one is being pummeled by so much chimpanzee poo?
This isn’t about Trump? click
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It’s essentially just a set of scales. The two sides will remain balanced.
The rope of negligible weight will be immediately shorn or unwoven by the violence of the monkey’s simple locomotion and the lead in the monkey’s enclosure will put the facility out of compliance. The case can never exist and we must consider instead the endless tumbling of isolated monkey and weight; the weight will more persistently fight against its demise, never being entertained that it is a fast weight.
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I’m afraid I must turn down this honor and retract my retraction. I now think I was right all along, but in a ‘Gladwell Blink’ sort of way. I intuited the answer correctly but lost confidence when reading smart sounding conflicting analyses. But only if we’re going with the spherical chimp paradigm.
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The monkey is a very stubborn monkey. It isn’t gonna climb any dumb rope just because you said so.
Instead it just hangs there, silently mocking you. For a long time. Even though it’s at rest, it’s burning some calories. And the humidity is low, so the monkey is also losing some water weight. Eventually the monkey is lighter than the 10 kg weight; the 10 kg weight drops while the monkey rises. At last the monkey reaches the pulley. You miss it, though, because you long ago got bored and went out to have a beer. The monkey still feels like it beat you at your game.
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Seymour Papert addresses this problem in Mindstorms: Children, Computers, and Powerful Ideas.
And once one thinks of the monkey and the rock as linked objects, similar to the ones we worked with in the Turtle microworld, it is obvious that they must both undergo the same changes in state. Since they start with the same velocity, namely zero, they must therefore always have the same velocity. Thus, if one goes up, the other goes up at the same speed.
Papert, Seymour. Mindstorms: Children, Computer, and Powerful Ideas. New York: Basic Books, 1993.
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One more scenario: If we include rotational inertia of the pulley, the money is on the monkey.
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