A question regarding efficiency of pulleys

[Nikola Tesla]

Does a pulley have more efficiency if it has just one of those cirgular thingies


http://upload.wikimedia.org/wikipedia/en/8/8f/Pulley_class2.PNG

or more

http://www.kirkwood.k12.mo.us/parent_student/khs/BartinJ/four_pulley.gif

An explanation would be helpful as well.

 

[Doc Al]

Do you mean efficiency or mechanical advantage? The efficiency of a simple machine is the ratio of useful work to input work; real machines always have an efficiency less than one due to friction. You always lose some energy. (I would imagine that the more pulleys involved, the more friction and thus the lower the efficiency.)

Mechanical advantage is something different. It's the ratio of output force to input force. The entire point of using a pulley (in addition to changing the direction of the force) is to multiply the force. In your first example, the single pulley has a mechanical advantage of 2: If you pull with a force of 10N, the pulley exerts a force of 20N on the attached load. In your second example, the mechanical advantage is 4.

 

[Nikola Tesla]

Do you mean efficiency or mechanical advantage? The efficiency of a simple machine is the ratio of useful work to input work; real machines always have an efficiency less than one due to friction. You always lose some energy. (I would imagine that the more pulleys involved, the more friction and thus the lower the efficiency.)

Mechanical advantage is something different. It's the ratio of output force to input force. The entire point of using a pulley (in addition to changing the direction of the force) is to multiply the force. In your first example, the single pulley has a mechanical advantage of 2: If you pull with a force of 10N, the pulley exerts a force of 20N on the attached load. In your second example, the mechanical advantage is 4.

I am talking about percent efficency of output work over input work. So, are you sure that the less pulleys involved, the better efficiency? Also, let's exclude friction.

I'm not talking about Mechanical advantage, though. However, is there a way of knowing how to calculate the mechanical advantage by looking at the pulley system? I'm sort of able to do it by figuring out how many ropes the object is using, but I do not think it's a proper way of doing it. Thanks for the help.

 

[Doc Al]

I am talking about percent efficency of output work over input work. So, are you sure that the less pulleys involved, the better efficiency? Also, let's exclude friction.

You can't exclude friction, which is the cause of the less than perfect efficiency. Without friction, the efficiency will equal 1.

I'm not talking about Mechanical advantage, though. However, is there a way of knowing how to calculate the mechanical advantage by looking at the pulley system? I'm sort of able to do it by figuring out how many ropes the object is using, but I do not think it's a proper way of doing it. Thanks for the help.

That's how I do it, just count the ropes. Ignoring friction (and the mass of the rope), the tension is the same throughout the rope.

 

[Nikola Tesla]

You can't exclude friction, which is the cause of the less than perfect efficiency. Without friction, the efficiency will equal 1.

Hmm, I see. Thanks for taking the time to answer.

 

[jdavel]

Doc Al,

"...Without friction, the efficiency will equal 1."

Don't forget deformation of the rope. With good bearings, it could be the major cause for less than perfect efficiency.

 

[Doc Al]

Don't forget deformation of the rope. With good bearings, it could be the major cause for less than perfect efficiency.

Interesting. I'll have to think about that. It's not obvious to me how rope deformation affects things.

 

[jdavel]

Doc Al,

Well, don't think too long!

After rethinking, I'm not sure it would make much difference. If the rope has a low k, then some work would go into pulling it tight before anything starts to move. But once the the tension in the rope becomes sufficient to lift the load, no more energy would be lost to stretching of the rope. It would still have to bend as it goes over the pulleys, but that probably doesn't amount to much.

Come to think of it, a system of pulleys with good bearings is probably pretty darn efficient!

 

[Doc Al]

My thoughts exactly.