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

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    Force Lift Piano
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Homework Help Overview

The discussion revolves around the mechanics of lifting a 51 kg piano using a pulley system, specifically examining how multiple pulleys can reduce the force required to lift the object. Participants are exploring the relationship between the distance the rope is pulled and the height the piano is raised.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants are attempting to understand the force required to lift the piano with a single pulley compared to a system with multiple pulleys. Questions are raised about how the mechanical advantage of the pulley system affects the required force and the distance the piano rises relative to the rope pulled.

Discussion Status

The discussion is ongoing, with participants providing hints and exploring different scenarios involving single and multiple pulleys. Some guidance has been offered regarding the mechanics of pulleys, but there is no explicit consensus on the calculations or methods to find the required force.

Contextual Notes

Participants are working under the assumption that the mass of the piano is 51 kg and are considering the implications of mechanical advantage in their calculations. There is also a reference to a review sheet that provides a specific answer, which may influence the discussion.

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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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.
 
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
 

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