I admit, I’ve had at least two margaritas and a couple of glasses of wine, and my mind isn’t functioning on all cylinders at the moment. :o
Assume a 100 kg weight suspended from a pulley that is fixed to the overhead. The line goes down and around a free-floating second pulley, and then around a second pulley that is fixed to the overhead. How much force is required on the free end to lift the 100 kg weight?
(No, this is not homework. Sometimes I just think funny things.)
What is a free floating pulley?
What do you mean by “free-floating second pulley”? It sounds like the weight is still suspended by a single line like with a regular fixed pulley. Or are you describing something like a gun tackle (where the “free-floating pulley” supports the weight)?
Use Straight Dope v3.7.3 to see code; not Sultan. Pulleys represented by (O).
A B C D
(O) (O)
| \ / \
| \ / \
| (O) \
| \
| ?
[100 kg]
The fixed pulleys are at A and C. The free floating pulley is at B. How much force must be applied to ? at D to lift the 100 kg weight?
I may not be thinking clearly. Maybe the ‘free floating’ pulley should be attached to the floor. Sorry. Maybe I should go to bed. In any case, perhaps someone could point me to a page that shows how pulleys impart a mechanical advantage?
I don’t see how that arrangement helps at all. Nothing is holding that free floating pulley in place, The first thing that will happen even before you start pulling is it will rise to the level of the higher pulleys. You’ll be lifting 100kg with a bit of added friction.
The simple idea is The rope between the A pulley and the weight obviously must have 100 kg of force on it (yeah yeah I know kg is not a force So it’s 9800 newtons I think). So must each of the other ropes.
The way you use multiple pulleys to help you raise a heavy object is like this:
Unless the floating pulley were attached to the load you’re simply changing the direction of force. For instance redirecting around a corner.
There is no force multiplication in that configuration. You would have the full 100kg of weight on your end of the rope.
Plus a bit more (when it’s pulled) due to pulley friction.
On the other hand, if that “free-floating pulley” were attached to the load, you’d get a mechanical advantage of 3 (assuming that the attachment points are close enough together that the ropes are basically vertical).
It needs to be attached to the weight to be of any benefit.
Wouldn’t it be a factor of two if the load were attached to the movable pulley? I seem to remember that from science class.
Thanks for that. I’m three minutes into it, and it looks like it’s answering my question.
As for the ‘free floating’ pulley, I blame my state last night for misinterpreting a drawing I saw. :smack:
Count the number of rope sections going up from things attached to the load. That’s your mechanical advantage.
If we had the end attached to the ceiling, then down to a pulley on the load and then back up, that’d be two ropes, and hence an advantage of 2. But we have the end attached to the load, up to the ceiling, back down to the load, and then back up, so that’s three ropes, and hence an advantage of 3.