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Q: A person ties one end of a rope around his waist and then runs the other end up to a single pulley, which is anchored to the ceiling, and then back down to his hands. He then pulls on the rope to hoist himself up. What is the mechanical advantage of this system? Could you show me the formula used to calculate it and describe the different forces at work, how they work, and why? What would you call this type of pulley system?
I have found many examples and explanations of simple pulley systems but none that describe and explain this particular scenario. I have tried it myself and found it very easy to pull myself up but I didn't have an in-line scale to measure the force needed to lift myself.
My guess would be 2:1 because my weight is split between the two halves of the rope and because you need to pull the entire length of rope (twice the length from the floor to the ceiling) to reach the pulley at the top. Iím having a very hard time convincing my friends of this. They all say itís 1:1 because the pulley is fixed and therefor a class 1 pulley which has a 1:1 advantage.
Thank you. Your help would be greatly appreciated.
- John Bretz (age 43)
Rochester, NY USA
Your friends are right; it is a class 1 pulley. And if your friends standing on the ground were to pull on the other end of the rope they would have to use a force equal to your weight.
On the other hand if it is you, the suspended one, hanging on to the other side of the rope you would have to pull down with half your weight in order to maintain equlibrium. The reason is that if you pull down with half your weight then your effective weight on your side of the pulley is one-half. So you are right, one half plus one half equals one. Try to get an in-line scale and show your friends.
(published on 04/28/08)
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