Why does the rope move with only 5N force applied?

[DocZaius]

Hello,

I am having trouble understanding an example shown on youtube regarding pulleys.

http://www.youtube.com/watch?v=vSsK7Rfa3yA#t=3m0s

In the example in the video above (I linked to the time when the example starts), the narrator uses an example where he pulls a rope with 5 Newtons for 2 meters, making a weight of 10 Newtons raise 1 meter. He is demonstrating mechanical advantage.

http://en.wikipedia.org/wiki/File:Pulley1a.svg

That is the basic setup, with W = 10N

However my understanding is that if 5 Newtons is applied to the end of that rope, the system will be in equilibrium. In the picture above, the implication seems to be that if the end of the rope has W/2 applied to it, there is no movement.

So how can the person in the video be pulling on that rope with a force of 5 Newtons and make the rope move at all?

Thanks.

 

[tiny-tim]

Hello DocZaius!

… my understanding is that if 5 Newtons is applied to the end of that rope, the system will be in equilibrium. In the picture above, the implication seems to be that if the end of the rope has W/2 applied to it, there is no movement.

So how can the person in the video be pulling on that rope with a force of 5 Newtons and make the rope move at all?

You're right, it will take slightly more than 5N to start the rope moving …

but once it is moving, it can be kept moving at constant speed without any net force, so 5N is enough.

 

[DocZaius]

Hello DocZaius! You're right, it will take slightly more than 5N to start the rope moving …

but once it is moving, it can be kept moving at constant speed without any net force, so 5N is enough.

So if I understand you correctly, the author of the video must have been pulling the end of the rope with a force X > 5N. And we must then use that X (which is NOT equal to 5) in the rest of his calculations.

Is that right? If this is correct, I feel it can be confusing and misleading to a student to be given X = 5N when X MUST be greater than 5N.

 

[russ_watters]

So if I understand you correctly, the author of the video must have been pulling the end of the rope with a force X > 5N. And we must then use that X (which is NOT equal to 5) in the rest of his calculations.

Is that right? If this is correct, I feel it can be confusing and misleading to a student to be given X = 5N when X MUST be greater than 5N.

This is much ado about nothing. I see no decimal points there, so quibbling over whether you need 5N or 5.0000000000000000001N isn't useful.

 

[tiny-tim]

… the narrator uses an example where he pulls a rope with 5 Newtons for 2 meters, making a weight of 10 Newtons raise 1 meter. He is demonstrating mechanical advantage.
…
So how can the person in the video be pulling on that rope with a force of 5 Newtons and make the rope move at all?

So if I understand you correctly, the author of the video must have been pulling the end of the rope with a force X > 5N. And we must then use that X (which is NOT equal to 5) in the rest of his calculations.

I haven't watched the video, but you haven't quoted anything from it that contradicts the correct statement that, using this pulley, you can move a weight of 10 N with a force of 5 N.

 

[DocZaius]

I haven't watched the video, but you haven't quoted anything from it that contradicts the correct statement that, using this pulley, you can move a weight of 10 N with a force of 5 N.

I understood from your previous reply than 5N isn't enough. You need slightly more than 5N.

My interpretation of your previous reply is that once you attach a weight of 5N at the end of the rope, all it takes is a force greater than 0 pulling on the end of that rope (in addition, of course, to the 5N weigh you just attached) for the 10N weight to move up.

If this interpretation is incorrect, please tell me where I go wrong. If this interpretation is correct, then it seems to me you can't move that 10N weight up with a force of exactly 5N.

This is much ado about nothing. I see no decimal points there, so quibbling over whether you need 5N or 5.0000000000000000001N isn't useful.

I think the difference between X = 5 and X > 5 is quite important and in this particular case, seems to be the difference between a 10N weight moving up and a 10N weight not moving up.

 

[tiny-tim]

If this interpretation is incorrect, please tell me where I go wrong. If this interpretation is correct, then it seems to me you can't move that 10N weight up with a force of exactly 5N.

You can move it with 5 N. You can't start it moving with 5 N.

 

[DocZaius]

You can move it with 5 N. You can't start it moving with 5 N.

Thank you for that clarification. Seems to me that a student might have said (and been correct) that if all the instructor is doing is applying exactly 5N to the end of that rope, that rope isn't moving. Then as an aside, the instructor maybe would have said that for a split second he pulled very slightly harder than 5 N and then went back to pulling with exactly 5N for the remainder of the distance. He then would say he ignores that very tiny force at the beginning and resumes his calculations. This approach seems not entirely correct (since that initial extra force is ignored) but seems more correct than a constant 5 N scenario.

 

[tiny-tim]

Seems to me that a student might have said (and been correct) that if all the instructor is doing is applying exactly 5N to the end of that rope, that rope isn't moving.

No, if all the instructor is doing is applying exactly 5N to the end of that rope, that rope isn't accelerating. But it certainly can be moving.

Btw, you still haven't quoted what the video actually says, that you disagree with.

 

[DocZaius]

No, if all the instructor is doing is applying exactly 5N to the end of that rope, that rope isn't accelerating. But it certainly can be moving.

I am back to confused again. It can be moving with exactly 5N?

Imagine for the following picture that W=10 N and that a 5 N weight is attached at the end of the rope. No other forces - the weight attached is exactly 5N. This is the initial setup. What happens? Is there any movement?

http://en.wikipedia.org/wiki/File:Pulley1a.svg

I thought there wouldn't be, but your "can be moving" statement puts that into doubt again.

Please note that the above scenario I just proposed is not the scenario in the video (since in the video there is movement). I am only asking about this scenario to see if I understand a more basic situation correctly (one in which the pulley system does not move).

Btw, you still haven't quoted what the video actually says, that you disagree with.

Until I have the behavior of the pulley system down correctly, I will hold off on what I think is incorrect about the video, since my claim would be based on my own mistakes.

 

[tiny-tim]

I am back to confused again. It can be moving with exactly 5N?

Imagine for the following picture that W=10 N and that a 5 N weight is attached at the end of the rope. No other forces - the weight attached is exactly 5N. This is the initial setup. What happens? Is there any movement?

If the initial setup is stationary, it will remain stationary. If the initial setup is moving, it will continue to move with the same speed.

There will be no acceleration.

In your original example, if the instructor is applying exactly 5N to the end of the rope, then the rope isn't accelerating. But it certainly can be moving.

 

[DocZaius]

If the initial setup is stationary, it will remain stationary. If the initial setup is moving, it will continue to move with the same speed.

There will be no acceleration.

In your original example, if the instructor is applying exactly 5N to the end of the rope, then the rope isn't accelerating. But it certainly can be moving.

OK, it is as I thought regarding the 5N weight's effect on the system with an initially stationary setup.

Then back to my problem with the video. I cannot quote something from the video as you request, since my problem lies with what is not said. The instructor never accounts for the reason the rope is initially moving. He never says the initial setup is moving (shouldn't we assume an initial setup is not moving if it is not explicitly stated otherwise?). He never says he initially pulls with a force greater than 5N (to accelerate it), to then go back to exactly 5N (to keep it moving at the same speed).

One is left to wonder, why is the rope initially moving without any accounting for it?

The reason I bring this up is that many students would assume a force of 5N was enough to accelerate it. They will watch the video and think "pulling that rope with 5N accelerated that rope since the instructor stated no other interaction made with the system" when as you say, 5N only keeps it moving at its speed.