Can You Lift Yourself on a Pulley?

[suyver]

To be honest: I don't really understand LURCH's relativity-argument. Sorry...

However, I do have a question regarding Doc Al's reasoning (you haven't convinced me yet!)

Originally posted by Doc Al
Consider the equilibrium case: the tension (T) in the rope equals the weight of the platform + person. The forces on the person are the rope tension and weight (acting down) balanced by the normal force of the platform (acting up). The forces on the platform are its weight and the normal force (N) of the person (acting down) balanced by the tension in both ropes (pulling up).

I think a agree with this, so far...

Originally posted by Doc Al
[...]To exert additional rope tension ΔT, the person would need to push ΔT harder against the platform. But the ropes pull up on the platform with twice ΔT. Thus, there will be a net increase in force on the platform (and on the person).

And here is the part I disagree with!

We are still talking about ONE pully, so I do not see where the doubling of the applied force would come from. If I pull with additional force ΔF, then this force would be devided over the two parts of the rope and not added to the two parts individually. This will cause your ΔT to be exactly equal to the extra ΔF that was applied. So, we are still in equilibrium and nothing will happen. (I think)

 

[Doc Al]

Originally posted by suyver
To be honest: I don't really understand LURCH's relativity-argument. Sorry...

Me neither.

However, I do have a question regarding Doc Al's reasoning (you haven't convinced me yet!)

I had enough trouble convincing myself.

We are still talking about ONE pully, so I do not see where the doubling of the applied force would come from. If I pull with additional force ΔF, then this force would be devided over the two parts of the rope and not added to the two parts individually. This will cause your ΔT to be exactly equal to the extra ΔF that was applied. So, we are still in equilibrium and nothing will happen. (I think)

There is one pulley, true enough. But, just like in any pulley arrangement, the rope pulls on it twice. When you pull with an additional force, that force goes to increasing the tension---it better, how else can you exert a force on the rope? The force is not divided over different parts of the rope: the tension is the same throughout the rope.

Take another look at the equations I gave and it might make more sense. To lift himself, the person must exert slightly more than the total weight of the system.

 

[suyver]

Doc Al,

I am not ignoring your reply, but I am thinking about it. Intuitively, I disagree with you. But I am thinking of a clear formuation that will also prove that you are incorrect. ... Or maybe that I have been wrong all along...

 

[LURCH]

Dang! And here I thought I had stated my position so much more clearly.[b(]

Well, the main gist of it was that it's not a question of how much force you exert against the rope in your hand, or the platform under your feet, or the pulley. It is entirely a question of how hard you are pulling on the ceiling. If that force is greater than your own body weight, you will pull the ceiling down to your self (which is the same as to say you'll pull yourself up to the ceiling).

BTW, this will go to experiment during the holidays, and then we will all have a definitive answer.

 

[Moose352]

Doc, can you please draw a FBD of the system so we can better understand your reasoning?

 

[NateTG]

Ok let's take a look at this a different way. Consider that the mechanical advantage that the pulley provides is proportional to the rates of movement of the rope and the load.

Now if the person pulls a meter of rope through the pulley, the platform must rise by a meter, since the distance from the person to the pulley is fixed. Therefore the mechanical advantage is 1, and the person must pull the full weight of the platform and the person.

For the formally inclined, consider that the amount of work the person does is the force that he needs to move the rope multiplied by the distance that he moves it, and you will find the same result.

Since most people can dead lift more than their body weight, the answer to the original question depends on the weight and geometry of the platform/pulley arrangement.

 

[Doc Al]

Originally posted by Moose352
Doc, can you please draw a FBD of the system so we can better understand your reasoning?

I could, but it's trivial. I described the forces in a previous post. The three equations I presented result from free body diagrams of the: a) entire system (platform+person), b) platform alone, and c) person alone. All forces are vertical.

 

[suyver]

Originally posted by Doc Al
The dynamics are as follows:
ΔT = m_total a (forces on total system)
2ΔT – ΔN = m_platform a (forces on platform)
ΔN – ΔT = m_person a (forces on person)

I think these equations are correct. (i.e. I can't find something wrong with them.) Just to simplify them, I'll rephrase them. Let's assume that m_platform=0 and let's call m_person just m, so then I have:

ΔT = m a (forces on total system)
2ΔT – ΔN = 0 (forces on platform)
ΔN – ΔT = m a (forces on person)

From this I get that 2ΔT = ΔN.
Now I see from the middle and bottom equations that indeed ΔT = m a, which agrees with the top one.

So it seems that you were correct Doc Al!

Has anybody actually done the experiment?

 

[LURCH]

Originally posted by suyver


Has anybody actually done the experiment?

Not yet. Am working extra hours from now till holidays, and preparing for said holidays in my free time. When the Yuletide actually arrives (with its accompanying vacation time) it is my intention to go to a certain pole-barn currently owned by my familly and conduct experimentation. I do not currently have in my possession either a platform of 0 mass nor a pully with 0 drag, but will attempt to approximate.

 

[Doc Al]

Originally posted by suyver
So it seems that you were correct Doc Al!

Yay! I knew you'd come to your senses, suyver. (Just kidding. )

 

[fotonios]

my opinion

your description was a bit unclear...
but i think it was because the question is a bit tricky...and the whole setup is a bit strange...not really because of your english...mine aint better either!

now...lets imagine the system...the rope comes down from the roof,through the pully..and I am standing right above the pully(which is attached on the plattform),and the rope that goes through the pully gomes up again, from the other side of the pully, in my hands.

now...there is only one end of the rope that goes up to the roof,clearly the tension in this end of the rope is equal to my mass plus the mass of the platform.

now since the rope is massless,and the pully has no (inner friction)even while I am just holding the rope still,the tension of the rope on the other end(the one that goes in my hands)is equal to the tension in the rope that goes up to the roof.

so even at this point i will have to be able to support such a force(my mass plus platform mass) and in an actually very difficult and awkward posture!...not to mention that the whole system would not even ballance like this cause i would not be able to put my centre of mass exactly above the pully(if the pully is at the centre of mass of the platform).

anyway...then in order for this system to move upwards i would have to pull with a force slighty above the total weight of the system...

its not true what other people said that if i pull one foot of rope,the platform will come up half.(they are cofusing it with other things!)

the length of the rope i pull,is the distance the platform moves upwards!...so u see its a very dificult thing to do...pulling the total weight of the system.(at least not for long!)

i think most people would not be able to do it!

 

[Doc Al]

Originally posted by fotonios

so even at this point i will have to be able to support such a force(my mass plus platform mass) and in an actually very difficult and awkward posture!...not to mention that the whole system would not even ballance like this cause i would not be able to put my centre of mass exactly above the pully(if the pully is at the centre of mass of the platform).

Yes, one would have to be very careful in any real implementation of this "physics puzzler". A more realistic model would have the platform constrained to move only in the vertical direction, like an elevator car in a frictionless shaft.

anyway...then in order for this system to move upwards i would have to pull with a force slighty above the total weight of the system...

Yep.

its not true what other people said that if i pull one foot of rope,the platform will come up half.(they are cofusing it with other things!)

Correct. If you read through the entire thread, you will see that much of the confusion was due to a misunderstanding of the original problem.

the length of the rope i pull,is the distance the platform moves upwards!...so u see its a very dificult thing to do...pulling the total weight of the system.(at least not for long!)

i think most people would not be able to do it!

I agree.

 

[fotonios]

a helpfull note...

just to add to my previous reply...don't confude internal forces of a system with exernal!

the forse the person exerts on the platform..is always equal and in balnce with the force the platform exerts on him...its the external force of the (rope's end) that goes up to the roof that is actualy pulling the system upwards.

analysing the internal forces will only confuse you...they are always balanced and cancel out each other!.

learn to visualise the system corectly and ideintify external and internal forces pairs!

 

[LURCH]

Did the experiment yesterday. Did indeed lift myself up off the floor, as did my brother. However, it was extremely difficult; far more than it should have been. I am still trying to figure out why it took so much effort.

I didn't have a scale that I thought could survive the forces involved, but it felt very much like lifting twice my body weight. After the experiment, my brother grabbed me around the waist and lifted me. He did this without much straining. It was far more difficult for him to lift his own weight with the pully. This is odd because I weigh 60lbs more than my brother. Might try again when I can get a tough enough scale, just to see if the force required really is twice the body weight of the person doing the experiment.

 

[willy.d.smart]

"So it makes no difference if this one pulley is attached to the platform or to the ceiling? My system would be identical to its reverse"

Wrong!
One i just feel like being a douche bag right now but anyways

If the pulley were attached to the platform and the rope to the ceiling then it would have no stability and you would fall off. But if the pulley were attached to the ceiling the you would have the stability to pull yourself up. Its just common sense.
There is a exception. A block and tackle, as my dad calls it, has a rope that goes from mounted pulley to secondary pulley to mounted pulley then to the ground. I think that kind of pulley would give you the necessary stability to pull yourself up.

And can some of you people spell pulley right.

I know over use of smilies

 

[willy.d.smart]

You know what! We're arguing over a freakin pulley. I mean Seriously why are we wasting our time with this you know what . . . . bye I am not comin back as a matter of fact what am i still doing here i mean serio... "Offline Forever"

 

[russ_watters]

Ok... Welcome to PF and maybe next time you could have a look at the date on the posts you are replying to...