OK. I missed that. If the rope has zero weight, then they arrive at the same time. If the rope has any weight at all, the weight arrives first.
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Ladies and gentlemen, this marks the first time these words have ever been typed on the Internet.
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Iâm just amazed that Shutterstock had this graphic ready to go.
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Iâm going with the weight because of Newtonâs third law. If thereâs no friction on the rope at the wheel, then the rope should pull freely as the chimp starts to climb. The monkey is exerting muscle force against the rope and there is no opposing force to counter the effect of gravity. The chimp would then remain at the same height as the weight is pulled towards the top.
But yeah, I was a history major in college so thereâs thatâŚ
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Youâre right that Death SAID IT FIRST, but Terry later rephrased it to illustrate his thoughts on religion.
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âŚa duck?
Except she canât climb upward without using the rope. Newtonâs 3rd law tells you the upward force this puts on her is exactly the same as the downward force on the rope. The pulley turns that into an upward force on the weight. So taking the friction and weight of the rope as zero, both have to move upward at the same rate.
Iâm going to guess this means the chimp still gets to the top first, since in my experience most weights are considerably more dense and so donât have the same reach. However, the illustration clearly shows a monkey, so it is possible Iâm missing some subtlety.
Thatâs exactly what the third law says doesnât happen. The monkey â if thatâs what weâre going with, I guess it fits a weight of 10 kg better anyway â putting a force on the rope is the same as the rope putting an equal and opposite force on the monkey.
If you imagine the monkey and weight on a rope in zero gravity, you can see that the center of mass will stay constant and pulling will only bring both in toward it. If things are perfectly balanced thatâs the same thing that happens here, only folded over the pulley by gravity.
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This is an interesting one. If the monkey really canât exert a force on the rope that isnât counterbalanced by the weight then ⌠I like the idea that monkey just climbs up the rope while the weight stays in place. Technically, if the wheel is frictionless and the rope has zero weight, the monkeyâs weight will decrease as it climbs away from the center of gravity so the weight will also drop
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I think youâre right that both would move upward since the force of the chimp climbing would cause the weight to rise, though there might be a kicker in that the chimpâs rate of climbing isnât likely to be consistent. Maybe as the chimp jerks on the rope in its climb, since it wouldnât have a constant acceleration the chimp and weight will both wobble up and down as they reach a kind of equilibrium, and which happens to reaches the top would vary? We really need to get a chimp, rope, pulley, and weight to test this.
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No they donât - the weight is attached to the rope, it has a speed of 0 with respect to the rope.
I pictured the chimp as a rope-pulling machine, rather like a chainhoist. Since the rope travels perfectly freely, thereâs no upward force on the chimp, and the weight travels up till it hits the pulley.
I believe this is the correct answer. As long as there is no friction at the pulley and the rope weighs nothing, it would go something like: Chimp moves up 1m, then the weight moves up 0.5m while the chimp moves down 0.5m
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Simple answer: they both arrive at the same time. âNegligible weightâ for the rope means we can ignore rope lengths on either side. âSlide perfectly freelyâ - frictionless pulley. For the monkey to move upwards, it must exert a downwards force on the rope (for every action force,there is an equal and opposite reaction force), this gets transmitted as an equal upwards force on the weight. Same force applied to objects of equal mass, both accelerate upwards at the same rate (F=ma). Same acceleration, same distance, they arrive at the same time.
More complicated answer: the monkey gets there very slightly earlier. When the monkey pulls down on the rope, it starts accelerating immediately, but it takes some time for the force to travel up the rope, over the pulley, and back down to the weight. How long depends on the speed of a compression/expansion wave along the rope. But this time means the monkey will arrive slightly before the weight.
Now, if they had specified a âperfectâ rope that can not lengthen or contract⌠weâd be back to the simple answer. Of course, weâd also have violated relativity as information (force) would have been tranmited instantly along the rope. But, why not â weâve already got two impossible things (weightless rope, frictionless pulley).
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That sort of jerkiness could happen if there were friction, meaning for instance you have to overcome the inertia of the pulley wheel. Without it, though, thereâs no reason to imagine those two things as separated in time; the pull and movement of the rope happen together.
So we can divide your meter into millimeters, and say that for every 1 mm the chimp climbs, the rope should already slide enough to bring it back down 0.5 mm. And for every micrometer, and so ad infinitum. Take it to the limit, so the action and reaction are simultaneous, and you get that the chimp and weight will always move up at the exact same rate no matter how it varies moment to moment.
of course it is, because even if someone on the internet MEANT that, theyâd have typed it as,
âI think your right and I was wrongâ
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Oh, so now the chimpâs a jerk?!?
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In the absence of friction or rope weight, this is entirely a question about acceleration.
Imagine no pulley, a 10 lb space monkey at the at one end of a linear rope and a 10lb weight at the end (perfectly at rest, no spinning). Monkey gives a tug, both accelerate towards each other and meet in the middle. In space you only need one tug to do it, since their is no need to fight deceleration due to gravity. With the original situation each tug on the rope is brought to a halt by gravitational deceleration, but it acts the same on the monkey and weight, so you can ignore it, except for the fact that you need multiple tugs.
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The difference is that when the chimpanzee reaches up to haul down more rope, its center of gravity only shifts slightly, as the arm is significantly lighter than its head/abdomen, whereas the weightâs center of gravity always remains the same.
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Wouldnât it take more force for the chimp to ascend than the weight, due to the increased air resistance from its irregular shape? That would imply that the weight reaches the top first.
Unless youâre assuming this is happening in a vacuum, in which case, neither reaches the top because the chimp suffocates.
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Maybe itâs a perfectly spherical chimp?
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