(cough)
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I think you are correct as far as the basic physics. In practice, the monkey reaches up with his hand before climbing (an action that doesnât exert any force on the rope, so he would reach up and touch the pulley first.)
That mostly depends whether it is a physics or biology questions. Given the title of the book, your answer is probably more correct.
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Hey!
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The chimp, because she will reach with her adorable little hand before transferring her weight.
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Thatâs true. I guess then it was a mistake to focus on the continuity and skip over the main problem with that argument, which is mistaking what actually moves the weight. Itâs never just that the chimp is above it. Two equal weights could hang from a pulley at any heights and no force needs to show up to equalize them*. Itâs the act of pulling, the reaction and the tension of the rope, that causes all the movement.
* For people who want to say attraction between the chimp and weight, consider that there are also differences in gravitational force from one being closer to the earth. Then consider the magnitude of these effects and if it makes any sense to bring them up after saying we can neglect the extra weight of rope on one side.
That suit alone is many times too heavy to be balanced up by a 10 kg weight. Weâre already talking about a very small chimp here, I donât think we can suppose itâs laden with more than a coconut or two.
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Actually, I think reaching upward would exert a force on the rope, since it would require shifting the monkeyâs center of mass upwards. But it would probably still hit the pulley first since the armâs mass would be small relative to the rest of the monkey.
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Monkeys arenât dumb. The monkey puts its foot on the weight, pulls up on the ropeâŚ
Monkey wins. Pinches fingers in the pulley. Yelps, lets go, plunges. Weight follows. OOooooooâŚ
Thereâs a song something like this about a guy and a barrel of bricks.
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Well, it could be a spherical cow, but they donât have hands so climbing the rope would be much more difficult.
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The weight and the chimp will reach the pulley at the same time. Any force the chimp exerts on the rope will be transferred to the weight by the pulley. Since both have identical weight, and the weight of the rope is negligible, both will move up at the same speed and reach the pulley at the same time.
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If it makes you feel better, I always think youâre a science-minded fellow. Mostly because the Krieger photo.
Keep in mind, not a super-science fellow, but I always attribute more weight to your posts because âwell, there must be some science behind it! Look at that lab coat!â
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âcanât apply an unbalanced forceâ is not the same as âcanât apply a forceâ. any force that the chimp applies to the rope (or the rope applies to the chimp; same thing) transfers to the weight through the pulley in the opposite direction. for the chimp to move upwards, a force must be applied. this force applies equally to the weight (balanced forces), so it moves upwards at the same rate.
You forget. This is a physics problem, which means that you have to assume a spherical chimpanzee. 
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Chimps are smart. It wouldnât take long for him to figure out that it would be less work to get to the top by simply reaching across and pulling down on the weighted end of the rope.
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Which one extends furthest above its center of gravity, the top of the weight or the reach of the chimp?
Well, at 10kg itâs obviously some kind of genetically engineered micro-chimp, so the suit would be proportionally lighter as well.
Or, more likely, itâs a puzzle written by a physicist: the only profession where practitioners seem to have less real-world knowledge than doctors.
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Because of the lack of friction, any shortening of the rope between the chimp and the weight (i.e. from the chimp climbing it) must be distributed equally on both sides. For every inch of rope the chimp pulls, half an inch will roll through the pulley, so both sides will rise by half an inch. If you assume they started so that the top of the chimpâs reach was level with the top of the weight, theyâll both reach the pulley at the same time. There is nothing the chimp can do to change its height relative to the weight. Only an external interference could unbalance the system and allow one to reach the top first.
If you donât believe it, try taking the pulley out of the problem entirely. Imagine you and your twin (i.e. the same weight as you) are both sitting on scooters on a smooth level floor, holding a rope between you. What happens if you pull on the rope? What happens if your twin pulls on the rope? What happens if you both pull half as hard at the same time? Itâs the same result in all three cases: you both move toward each other at the same speed and meet in the exact center at the same time.
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The monkey could climb half way up the rope, hold it tight, pull up the rope behind him, grab the end of the rope from below, let go of the middle, and apply quite a force to the weight on the other end.
Hmm. How about this: if the monkey jerks on the rope, the monkey and the weight reach the top at about the same time, but if the monkey climbs very slowly, he reaches the top and the weight doesnât move.
My notion is probably not right if the wheel and rope have no friction.
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So if you substitute the monkey with Donald Trump, the weight with the Republican Party, the rope with delegates and the wheel with our inevitable plunge into our dying sun, the solution becomes obvious.
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