How can multiple pulleys decrease the force needed to lift a piano?

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fattydq
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In raising a 51 kg piano with a pulley system, workers note that for every 2m of rope pulled down, the piano rises only 0.2m . Ideally, how much force is required to lift the piano?

I know the answer is 50 N because it's on my review sheet for a test, but I don't know how it was found. Could someone get me started here?
 
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PhanthomJay said:
If the piano was being raised by a rope around a single pulley, how much force would be required to lift it, and if you pulled the rope down 2 m, how far up would the piano rise? In this particular problem, you have more than 1 pulley involved.

I'm sorry but I don't see how you can use those facts to find the answer, you just restated the question in different words?
 
fattydq said:
I'm sorry but I don't see how you can use those facts to find the answer, you just restated the question in different words?
Iwas just trying to give a hint, not the answer, so I presented you with a different problem, one with a single rope attached to the piano, and wrapped around a pulley fixed to the ceiling, with the free end of the rope hanging down from the other side of the pulley. Now in this new problem I stated, if the piano has a mass of 51Kg, how much minimum force would you have to apply to the free end of the rope in order to lift it off the ground, and if you pulled the rope down 2 m with that force, how high off the ground would the piano be? Think about it.

Now in your problem statement, you lower the rope 2 m and the piano rises just 0.2m, so multiple pulleys are involved, and the force necessary to lift it is smaller, due to the mechanical advantage gained by the use of more pulleys. You might want to check out this site: http://www.technologystudent.com/gears1/pulley7.htm