Does the Efficiency of Pulley Systems Increase with More Pulleys?

[dekoi]

It was my logic that efficiency should decrease as the amount of pulleys introduced into a pulley arrangement increased. This is since the amount of places where frictional resistance can occur is greater. Therefore, as TMA increases, i would expect Efficiency (AMA/TMA) to decrease.


However, my data shows the total opposite . How could this be? Could this be a big experimental error? Somehow i doubt that possibility.

 

[vaishakh]

The typical behavior of a string - tension - makes it comfortable in using pulleys.
e.g. If we lift an object straight up by tieing it to a string we find it difficult. But if we attach the string to a pulley and then try to lift, the tension helps a bit more and we can lift the body easily. However there is need of extra force due to friction at the axle, but it is anyway negligible.

 

[Chi Meson]

The frictional force always depends on the normal force, right? When you increase the TMA, you increase the number of strings holding the load, thereby decreasing the tension in the string and thus the "normal force" on each pulley is decreased. So each pulley now will have less frictional force even though there are more moving pulleys in the system. Usually, this causes the effects to cancel, but if the additional pulleys have less friction than the initial pulleys, then your efficiency would increase.

Also, how many arrangements are you comparing? Two? Three? Five?

If you were to use ship rigging, you would find that the efficiency does decrease as TMA increases, since a significant mass of rope will be added to the system with each extra loop. In the Physics lab, that string we use is very light, and those pulleys are very low friction, so you don't notice this aspect.