Alright. Ever since I was a first grader and saw a particular episode of Mr. Wizard’s world on nickelodeon, I have wondered just how in the hell pulley’s work. I understand that if you use one pulley it cuts the work the force you have to exert to lift an object down considerably, and with each added pulley the work load goes down more and more. Using a system of multiple pulleys has an astonishing effect however. When you pull three feet of cord on the work end of the rope, the end holding the object moves substantially less, maybe even as little as a foot or six inches, depending on the number of pulleys. How does this happen? If I am pulling on one end of a rope that’s taught, shouldn’t the other end always move along with it?

Now is the time for all good men to come the the aid of their gazorninplatt.

No. What if the other end is anchored to the roof, and what is moving is the point at which the rope bends through a pulley? You aren’t pulling the end of the rope, you are pulling an ever-changing point on the rope.

Let me see if I can explain it sufficiently…

If you pull on a rope in a tug of war, the other end moves exactly the same as the end you pull on. So, you don’t get any help from the rope.

If you put a pulley on the ceiling and run a rope up to the pulley and then down to a weight, you still have to pull the rope just as far as the weight moves, so again, no help.

Now, if you put a pulley on the top of the weight, and run a rope down from the ceiling through the pulley and up to you on a balcony, you have to pull the rope twice as far as the weight moves. Since you are doing the same amount of work in twice the distance (twice the rope) you only need half the force. Voila, mechanical advantage.

Why do you have to pull twice as much rope? Examine the system. You have a rope going from the ceiling all the way down to the floor, through the pulley, and all the way back to the ceiling. When the weigt is at the top, there will be zero rope left (or a small amount) as the pulley, the anchor, and you are all at the ceiling. So, the entire length of the rope is used to lift the weight up.

With the pulley on the ceiling, you start with the rope going from the weight, to the ceiling, and back down to you on the ground. When you are done and the weight is on the ceiling, you still have the rope coming from the ceiling down to you, so you have only pulled half the rope. Since you have done the same work (pushing the weight to the ceiling) in half the distance (half as much rope) you used twice the force.

Another way of looking at it is ‘How many ropes are sharing the work?’ With the pulley on the ceiling, only one rope attaches to the weight. With the pulley on the weight, TWO ropes are attached to the weight - the one coming down from the anchor, and the one going up to you. The two portions of rope share the work.

If you build a complex system of pulleys such that 10 rope segments are lifting the weight, then with each 10 feet you pull the rope, the weight will only rise 1 foot, because you have had to pull 1 foot out of EACH of the rope segments in order to get 10 feet out of the end of the rope.

It’s just like turning a screw six inches just to get it an inch deep (innuendo intended). Rope pulleys flex, and shorten the distance between themselves. Less work for you.

All right, I admit it. I have no idea what I’m talking about, but I know exactly what I want to say. I just can’t stand an unanswered post.

And apparently, it took ten minutes to say it. I’m going to bed now. Where’s the Alka-Seltzer?

Just try this:

Get two pencils and a piece of string. Tie the string to one of the pencils. Now, hold both pencils in one hand so that they are parallel and about an inch apart, i.e. one at the base of the fingers and one at the tips. Now wrap the piece of string around both pencils a couple of times very loosely. Now, pull on the end of the string. If you pull the string by one inch, the two pencils don’t come 1 inch closer, they come, say, 1/4 inch closer if you looped the string 4 times. However, the force on the pencils will be 4 times stronger than the force it takes to pull the string.

It’s all a matter of Statics. That is, sum of all forces = 0 (at least just before motion occurs). I’ll try to find a picture to explain what the hell I’m talking about, but try cracking open a Statics book in the meantime if you can get your hand on one.

If I’d been paying attention, I would have seen that douglips provided a good explanation. I was going to provide an alternate explanation if I could find a good figure to refer to. The difference between what would’ve been my approach and douglips’ is summation of forces vs. conservation of energy. Both are different, yet valid methods.

You have a lot of good explanations to choose from but they can seem a little abstract. I won’t start going into things that will make your eyes glaze over such as force vectors but the basics of physics is understanding the relationship between force, energy, power and work.

On a simpler level just keep in mind that any simple machine that gives “mechanical advantage” such as pulleys, levers, gears and screws are really trading displacement (distance moved) for force (weight lifted or pull on the rope) while doing the same amount of work.

Here’s the link you’re looking for:
http://howstuffworks.com/pulley.htm

c-man

Here’s another way to look at it:

Lets say you need to lift a 200 pound bed (it has a solid brass frame). You can tie a rope around all for corners, then tie the four ropes together in the balanced center of the bed and lift straight up there. Well, you’re trying to lift 200 pounds on that one combined rope. Too heavy.

So, you get three friends and you each grab a rope (they’re not tied together any more) and you all lift up. You are all now lifting 50 pounds at each corner – doable.

Now you have an idea to do it without your friends: Tie four separate ropes at each corner. Put four pulleys on the ceiling over each corner. Bring each rope up through a pulley and down to you. Now you pull on all four ropes at the same time. However, even though each rope is carrying 50 pounds, you’re trying to pull on all four ropes at the same time – that’s 200 pounds. You can’t do it.

If only there was a way you can be at four places at once to pull 50 pounds on each rope separately…

Ahh, but now you have a better idea. You put pulleys at each of the four corners and pulleys on the ceiling above each corner. Then you snake one rope through all the pulleys. By pulling on this one rope four inches, you make each pulley pull 50 pounds over one inch. You are now in four places at once by way of the pulleys!

Peace.