Pulley systems and friction (simple or compound)

[gloo]

This is a two part question:

1. With a simple pulley system using one pulley - say 10000 kg on each side - the ability to pull either one up or down to change the position is theoretically just the friction on the system and any extra length of rope on one side?

2. Would it be more work lost on pulling up a large weight (i.e. 1 million Kg) with a 1 pulley system with equal weight on each side OR would it be more work on a multiple compound pulley system?
--- The goal of my question in part 2 is whether one large weight on a single pulley would mean more friction than a lighter counterweight...but it has more pulleys for the rope to run through?

 

[NihalRi]

I do not think that it's either one or the other. It will all depend on the weights, materials and lengths of ropes involved.

 

[Dale]

Would it be more work lost on pulling up a large weight (i.e. 1 million Kg) with a 1 pulley system with equal weight on each side OR would it be more work on a multiple compound pulley system

There are two sources of "loss" in a non ideal pulley. One is friction, and the other is rotational KE.

The friction scales with the tension, so that will be essentially constant (2 pulleys, 1/2 tension).

The rotational KE does not scale, so it will increase with more pulleys. But it is also temporary, meaning that you get this energy back when you stop.

 

[sophiecentaur]

OR would it be more work on a multiple compound pulley system?

The friction force for a pulley will be proportional to the 'normal force' on the bearing. That's based on basic friction theory. The final pulley in a system will be supporting the whole of the weight of the load, whether the effort is supplied directly (as with a single pulley) or via another pulley. Any extra pulleys will be supporting some weight and adding to the friction force that the input pull has to provide. So, as you increase the velocity ratio, you will be increasing the loss and the effective Mechanical Advantage will be less and less pro rata. (The efficiency will go down). If you take any system with a very high velocity ratio (such as a screw or a rack and pinion) the losses can be so high that it may not actually work backwards - if you try to swap load and effort. You pays yer money and takes yer pick, depending how weak the person or motor drive happens to be.

 

[Dale]

The final pulley in a system will be supporting the whole of the weight of the load,

Good point, I think you are correct. I was just thinking of the tension being reduced in the rope.

 

[sophiecentaur]

Good point, I think you are correct. I was just thinking of the tension being reduced in the rope.

We would really need to draw an example pulley system and commit to a particular layout but I am pretty sure that you will end up with a series of additional friction forces, one from each additional pulley, which will always come to more than the force from just one. I must get out my pencil tomorrow morning.

 

[Dale]

We would really need to draw an example pulley system and commit to a particular layout but I am pretty sure that you will end up with a series of additional friction forces,

Yes, me too. I think my original comment was a mistake. It isn't the tension in the rope that determines the force at the bearing, but the load.

 

[anorlunda]

There are two sources of "loss" in a non ideal pulley. One is friction, and the other is rotational KE.

There is a third source that can be very significant. Bending and unending forces on the rope or cable going through the pulleys, I test that regularly on my 6:1 main sheet system. With zero load applied, it takes a lot of force to pull the rope through.

Large diameter pulleys minimize the bending force, but maximize rotational energy.

 

[sophiecentaur]

There is a third source that can be very significant. Bending and unending forces on the rope or cable going through the pulleys, I test that regularly on my 6:1 main sheet system. With zero load applied, it takes a lot of force to pull the rope through.

Large diameter pulleys minimize the bending force, but maximize rotational energy.

Thin line or even wire will be higher efficiency - but tear your hands apart.