Climbing a Pulley: Conservation of Momentum & Energy?

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Discussion Overview

The discussion revolves around the application of conservation laws in physics, specifically conservation of momentum and energy, in scenarios involving pulleys and swings. Participants explore how these principles apply when a person climbs a pulley, walks on a plank on ice, and swings off a swing seat.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants suggest that when a person climbs a pulley at constant speed, both the person and the mass on the other end will rise at the same speed.
  • Others argue that Newton's laws should be applied to analyze the situation more rigorously.
  • There is a discussion about whether conservation of momentum applies in the case of the man climbing the rope, with some participants questioning how to define the system involved.
  • One participant raises a scenario involving a man walking on a plank on frictionless ice, suggesting that momentum is conserved due to the absence of external forces.
  • Concerns are expressed about the conservation of energy in the context of a person flying off a swing, with one participant questioning where the energy goes if the kinetic energy after the event does not equal the initial energy.
  • Another participant suggests that the swing seat should not propel backward when the person leaves, questioning the nature of the event as a collision.
  • Some participants discuss the implications of significant force vectors and the motion of the swing set if it were not anchored to the ground.
  • There is a repeated inquiry into how to determine the speed of the swing and the person after jumping off, given initial conditions.

Areas of Agreement / Disagreement

Participants express differing views on the application of conservation laws, particularly regarding energy and momentum in various scenarios. No consensus is reached on the correctness of the claims or the application of these principles.

Contextual Notes

Participants highlight the need for clear definitions of systems when discussing conservation laws. There are unresolved questions regarding the conditions under which conservation of energy and momentum apply, particularly in non-collision scenarios.

physics_liker
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On a standard pulley, on one end of the rope hangs a mass equal to a person's weight. That person is climbing up on the other end of the rope at constant speed. My guess is that the man and the mass will rise up at the same speed.

And does the conservation of momentum apply in this case? How does the conservation of momentum work if a case is in a similar situation? For example, a man walking on a plank of wood of his equal weight on frictionless ice. Relative to the ground, the man is moving at half of his walking speed.

Let's say you are swinging on a swing, and suddenly fly off at the lowest point of the swing path tangentially and leave the swing seat. Now in this case, the conservation of momentum applies, but not the conservation of energy. In this "reverse inelastic collision", (as I like to think of it as) where does the energy go?
 
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physics_liker said:
On a standard pulley, on one end of the rope hangs a mass equal to a person's weight. That person is climbing up on the other end of the rope at constant speed. My guess is that the man and the mass will rise up at the same speed.
Why guess? Apply Newton's laws.

And does the conservation of momentum apply in this case? How does the conservation of momentum work if a case is in a similar situation? For example, a man walking on a plank of wood of his equal weight on frictionless ice. Relative to the ground, the man is moving at half of his walking speed.
In the case of the man and plank, there are no external (horizontal) forces on that system, thus momentum is conserved. Is that the case for the man climbing the rope? (First define the system you would like to consider.)

Let's say you are swinging on a swing, and suddenly fly off at the lowest point of the swing path tangentially and leave the swing seat. Now in this case, the conservation of momentum applies, but not the conservation of energy. In this "reverse inelastic collision", (as I like to think of it as) where does the energy go?
What do you mean "conservation of energy" doesn't apply? (Or "conservation of momentum" does, for that matter?)
 
physics_liker said:
Let's say you are swinging on a swing, and suddenly fly off at the lowest point of the swing path tangentially and leave the swing seat. Now in this case, the conservation of momentum applies, but not the conservation of energy. In this "reverse inelastic collision", (as I like to think of it as) where does the energy go?

I wonder if you are thinking that the swing seat should propel backwards as you slide-off forwards? If that's the case, why should it? The scenario is not a collision event.
 
Doc Al said:
Why guess? Apply Newton's laws.

I didn't literally guess. I just wasn't sure of the answer, so I used the word "guess". I think the situation is similar to the one walking on ice. For every inch of rope you pull down its original position, your hand reaches 2 inches up the rope (assuming that he stretches two full arm lengths). But since one inch is descended down, the man only advances one inch upward, as does the mass on the other end of the rope.

In the case of the man and plank, there are no external (horizontal) forces on that system, thus momentum is conserved. Is that the case for the man climbing the rope? (First define the system you would like to consider.)
I'd like to consider both cases, actually. I don't quite understand the concept of conservation of momentum. The only case I have used the concept on is for collisions. I don't know how it applies to the pulley and the plank. I'd like someone to give me an answer for this question.

What do you mean "conservation of energy" doesn't apply? (Or "conservation of momentum" does, for that matter?)
I meant that if the conservation of energy applies. The kinetic energy of the person and the swing seat at the bottom point would be equal to the sum of the kinetic energy of the seat and the person after he flies off the swing seat. The latter energy does not add up to the initial energy. So I ask, where does the energy go?
 
pallidin said:
I wonder if you are thinking that the swing seat should propel backwards as you slide-off forwards? If that's the case, why should it? The scenario is not a collision event.

I do not think the swing seat would be propelled backwards. The person on the swing has acquired his speed due to the drop of his own potential energy. But I have another question: how do we know what speed will the person leave off the swing? And I think that if man leaves off the swing with the same speed as that when he is on the swing. Then there is no change in momentum for him, and therefore no reason for the swing to be propelled backwards.
 
Bear in mind that other, significant force vectors are involved here. As you are arcing downwards prior to "sliding-off", a force is being applied on the swing-set frame itself. You may not notice it because the swing-set is anchored in the ground.

A good example might be if the swing set was not anchored to the ground, but instead on wheels. Assuming the ground is flat and friction is minimal, what happens?
The swing set moves back and forth as you swing back and forth(in opposite directions), maintaining a constant center of mass.
Now, when you eject yourself, what happens to the motion of the entire swing-set on wheels?
 
physics_liker said:
I meant that if the conservation of energy applies. The kinetic energy of the person and the swing seat at the bottom point would be equal to the sum of the kinetic energy of the seat and the person after he flies off the swing seat. The latter energy does not add up to the initial energy. So I ask, where does the energy go?
I still am not seeing why you think conservation of mechanical energy does not apply.
 
Doc Al said:
Why guess? Apply Newton's laws.
I didn't literally guess. I just wasn't sure of the answer, so I used the word "guess". I think the situation is similar to the one walking on ice. For every inch of rope you pull down its original position, your hand reaches 2 inches up the rope (assuming that he stretches two full arm lengths). But since one inch is descended down, the man only advances one inch upward, as does the mass on the other end of the rope.


Doc Al said:
In the case of the man and plank, there are no external (horizontal) forces on that system, thus momentum is conserved. Is that the case for the man climbing the rope? (First define the system you would like to consider.)
I didn't literally guess. I just wasn't sure of the answer, so I used the word "guess". I think the situation is similar to the one walking on ice. For every inch of rope you pull down its original position, your hand reaches 2 inches up the rope (assuming that he stretches two full arm lengths). But since one inch is descended down, the man only advances one inch upward, as does the mass on the other end of the rope.


Doc Al said:
What do you mean "conservation of energy" doesn't apply? (Or "conservation of momentum" does, for that matter?)

You can try an example for yourself. Let's the swing is 2 meters above its bottom point. At the bottom point, all potential energy is converted into kinetic energy of the person and the swing. Now I am saying that KE of the swing-person system does not equal to the combined KE's of the two separate systems, namely the swing and the person after he flies off. I had seen a problem like this, so it's not made up. The original question asked for the speed of the swing after the person jumps off. To find that, conservation of momentum can be applied to solve the problem, but not the conservation of energy. (The two speeds from these two different methods differ.)

Now I have another question in addition to the previous ones, how would you find out the speed of the swing and the person afer they jump off, given only the initial potential energy and the weight of the swing and the person. (This time the speed of the person is not given.) Is this problem possible to solve? Since the conservation of energy does not seem to apply in this case. With the conservation of momentum, I can only obtain one equation with two variable speeds. (I am probably not making a clear explanation, nor asking a clear question. But if anyone can understand, please answer my questions. Thank you.
 
physics_liker said:
You can try an example for yourself. Let's the swing is 2 meters above its bottom point. At the bottom point, all potential energy is converted into kinetic energy of the person and the swing. Now I am saying that KE of the swing-person system does not equal to the combined KE's of the two separate systems, namely the swing and the person after he flies off. I had seen a problem like this, so it's not made up. The original question asked for the speed of the swing after the person jumps off. To find that, conservation of momentum can be applied to solve the problem, but not the conservation of energy. (The two speeds from these two different methods differ.)
If the person just let's go and flies off, then mechanical energy is conserved. (The person leaves with the same speed as the swing.) But if the person pushes off from the swing as he flies off, then he's adding energy.
 

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