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## Question

a rope is supposed to be hung over a wheel fixed to the roof of a building; at one end of the rope a weight is fixed, which exactly counterbalances a monkey which is hanging on the other end. Suppose that the monkey begins to clime the rope, what will be the result?

Imagen the rope is perfectly flexible and the pulley frictionless.

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Both the monkey and the weight move toward the pulley at equal velocity with the monkey always facing the weight, if they start facing one another.

Edited by jagerbombs

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Try to think about the monkey's speed compared to the pulley and compared to the rope.

This all depends on the coefficient of friction of the pulley and the initial acceleration of the Monkey,

High Friction plus slow start equals monkey gets to top without creating enough force to move the weight on the other side.

low friction and fast start means the weght is coming over the top.

the monkey would have to be climbing twice as fast (relative to the rope) than the the weight is moving for them to climb at the same rate relative to the pulley.

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a rope is supposed to be hung over a wheel fixed to the roof of a building; at one end of the rope a weight is fixed, which exactly counterbalances a monkey which is hanging on the other end. Suppose that the monkey begins to clime the rope, what will be the result?

Imagen the rope is perfectly flexible and the pulley frictionless.

According to Newton's third law F12=-F21(all forces occur in pairs, and these two forces are equal in magnitude and opposite in direction).That means if the monky by its motion(force) change the motion oh the weight,the weight also (because of the equality of the mutual pressure) will undergo an equal change, in its own motion, toward the contrary part and they will be counterbalanced again.

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Try to think about the monkey's speed compared to the pulley and compared to the rope.

This all depends on the coefficient of friction of the pulley and the initial acceleration of the Monkey,

High Friction plus slow start equals monkey gets to top without creating enough force to move the weight on the other side.

low friction and fast start means the weght is coming over the top.

the monkey would have to be climbing twice as fast (relative to the rope) than the the weight is moving for them to climb at the same rate relative to the pulley.

To derby_derby

You are wrong.It's given that the weight is fixed at the one end of the rope,which exactly counterbalances a monkey which is hanging on the other end.That means,that the monky and the weight have equal in magnitude force and opposite in direction.No matter with what speed the monky will climb the rope,the forces will becom equal again in magnitude,i.e. the position will be fixed again.The speed with wich the weight will move depence of it's mass.If the mass is less then the monky's,no matter with what speed the monky moves,the weight will move faster and the opposite ih the mass is bigger.

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You are all over thinking this one...it doesn't matter if the rope or weight move or not, because the masses are equal until the monkey reaches the top of the pulley.

When the monkey is opposite the weight on the rope, both exert equal forces on each other. Once the monkey passes the fulcrum of the pulley, his mass will not be pulling down on the rope with an equal force as that of the weight on the other end of the rope. I would predict that the monkey would flip over the top of the pulley and get dragged to the ground by the falling weight.

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In Lewis Carroll's opinion, the 'weight' goes neither up nor down. However, most mathematicians and scientists believe that the weight and monkey would always remain opposite to each other; hence, as the monkey climbs up the rope, the weight also goes up.

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In Lewis Carroll's opinion, the 'weight' goes neither up nor down. However, most mathematicians and scientists believe that the weight and monkey would always remain opposite to each other; hence, as the monkey climbs up the rope, the weight also goes up.

If they are exactly counter balanced and the and no other forces are affecting it the monkey should in theory be able to climb up and down the rope. In practice it can't work that because the monkey would exert a pulling force on the rope which would serve to pull the monkey up and the weight. Faster the monkey climbs the faster the weight goes up. If you add in friction which was removed in the puzzle it is is possible for the monkey to climb the rope w/o upsetting the weight. If you make the the rope long enough enough that it touches the ground the monkey would get to a point and the weight would be able to make no net gain as it would start pulling the monkey up. And, if you add inertia to that enough rope so that it touches the ground and it is high enough such that when the weight started falling down with speed... the monkey would fly off the rope near the pulley and then the wheight would fall so I think in real life both would just end up on the ground at some point after the monkey started climbing...

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