Does the mechanical advantage of a pulley change when lifting yourself

[kasra12321]

So basically, at my work at a science center, we have this exhibit where you lift yourself using different pulleys. I noticed that the pulleys were labeled wrong. They should have been, 1/2, 1/3, and 1/5 but were labeled, 1/3, 1/4, and 1/6. I brought this up with management and received an email from the VP of Education with a document explaining why I am wrong.

http://imgur.com/MlT8cVh

That's what she sent me. But I am still not sure and I have spoken to a few people that have told me that the advantage of the pulley doesn't change whether you are on it and pulling or self or not. So I was wondering what you guys thought. I just want multiple opinions before I tell the VP of Education that she is wrong. Thanks for the help!

 

[russ_watters]

Welcome to PF!

When you are lifting yourself with a single overhead pulley, the length of rope moving through your hands is different from the height you gain above the ground. This difference is the extra mechanical advantage.

Another easy way to see it is there are two strands of rope supporting your weight, so each must only be supporting half.

 

[mickybob]

So basically, at my work at a science center, we have this exhibit where you lift yourself using different pulleys. I noticed that the pulleys were labeled wrong. They should have been, 1/2, 1/3, and 1/5 but were labeled, 1/3, 1/4, and 1/6. I brought this up with management and received an email from the VP of Education with a document explaining why I am wrong.

http://imgur.com/MlT8cVh

That's what she sent me. But I am still not sure and I have spoken to a few people that have told me that the advantage of the pulley doesn't change whether you are on it and pulling or self or not. So I was wondering what you guys thought. I just want multiple opinions before I tell the VP of Education that she is wrong. Thanks for the help!

That document you posted doesn't provide a very good explanation, but they are correct about the ratios.

 

[sophiecentaur]

You just have to be correct. Your VP is getting the wrong answer because she is not approaching the problem formally. She is counting things twice in the 'pulling yourself up' case. Imagine drawing Fig3 upside down, with you lifting a weight equal to your own, fixed to the pulley and you are up on the beam pulling one end of the rope with the other end tied to the beam. This way up would involve exactly the same forces and work done. In both cases, you would have to move two units of rope length for every one unit of height gained. It's the number of vertical runs of rope that govern the MA. There is nothing magical about lifting yourself.

BTW You should strictly be using the term 'Velocity Ratio' in this argument (the ratio of the distance moved by the Effort divided by the distance moved by the Load) because MA is the actual ratio of forces involved and relates to useful work done. The weight of the chair and pulleys (plus friction, of course) all affect the MA whereas VR is just determined by geometry. Unless you actually know the other details, you can only know the VR.
I imagine that the results in your demo are so far from theory, due to friction etc that the disagreement with the correct (or their version of) theory is bad enough for no one to have really scrutinised things. They just notice it gets easier with more strings. lol
Google Velocity ratio and Mechanical Advantage, there should be plenty to read and to hit her with.

 

[mickybob]

You just have to be correct. Your VP is getting the wrong answer because she is not approaching the problem formally. She is counting things twice in the 'pulling yourself up' case. Imagine drawing Fig3 upside down, with you lifting a weight equal to your own, fixed to the pulley and you are up on the beam pulling one end of the rope with the other end tied to the beam. This way up would involve exactly the same forces and work done. In both cases, you would have to move two units of rope length for every one unit of height gained. It's the number of vertical runs of rope that govern the MA. There is nothing magical about lifting yourself.

BTW You should strictly be using the term 'Velocity Ratio' in this argument (the ratio of the distance moved by the Effort divided by the distance moved by the Load) because MA is the actual ratio of forces involved and relates to useful work done. The weight of the chair and pulleys (plus friction, of course) all affect the MA whereas VR is just determined by geometry. Unless you actually know the other details, you can only know the VR.
I imagine that the results in your demo are so far from theory, due to friction etc that the disagreement with the correct (or their version of) theory is bad enough for no one to have really scrutinised things. They just notice it gets easier with more strings. lol
Google Velocity ratio and Mechanical Advantage, there should be plenty to read and to hit her with.

What I say below may be wrong, because for some reason this confuses me(!) but...

First of all, I'm pretending there is no friction. In that case:

If someone else is pulls the rope there is no mechanical advantage. They pull the rope by 1 metre, you move up by 1 metre. No problem.

But when you pull the rope then: from your frame of reference you are moving the rope down 1 metre.

From a 'world' frame of reference, when you pull the rope down by what you consider to be 1 metre - you move up half a metre and the rope moves down half a metre. From your point of view the rope is 1 metre lower than where it was, so you have moved the rope twice as far as you have moved, and the mechanical advantage is apparently 2:1.

 

[sophiecentaur]

You also have to assume the chair weighs nothing, remember - if you want to use MA. (Strictly - but this is PF, doncha know)

I guess the problem here is that ' pulling yourself up' is a bit of a red herring as it's just another version of the same (upside down) pulley arrangement that I was proposing. The 'lift yourself up' alternative not a possible except for loads of a few tens of kg (human mass). It's all down to how many lengths of rope are sharing the weight. I guess the reason for demo-ing it this way is to make it 'child centred' but it doesn't help to understand the mechanics of it imo.
"If someone else pulls the rope" then it's just a different setup so the VR is, not surprisingly, different. The ways it's presented implies that one pulley can't be arranged to give a VR of 2 except when someone lifts themselves - which is not true. The direction of the effort force would just need to be different and this is normally achieved by an extra pulley on the beam.
But it's probably more a matter of 'taste' than I originally thought aamof. And what the arrangement is designed to achieve.

When you are on the chair, you would need to pull in 1m of rope for you to get 1/2m nearer the beam (or the beam to get 1/2m nearer to you) and there will be 1/2m extra rope coiled on the floor. The work done is the same in either frame. Full load times 1/2m or half load times 1m.

 

[kasra12321]

So then she is right because the mechanical advantage does change because as you pull the rope, you are also getting higher?

 

[sophiecentaur]

In that instance she is getting the VR correct. BUT there could be other pulley arrangements where the VR is not better just be virtue of the fact that you are lifting yourself. The conclusion of the experiment implies something that is not true in general.
You have the general principle right so you can work any pulley system out correctly.