Pulley Efficiency Problem (How much rope must be pulled)?

AI Thread Summary
A pulley system with an efficiency of 71.5% requires a force of 641 N to lift a 160 kg desk over a distance of 2.51 meters. To determine how much rope must be pulled, the work done on the desk must be calculated, considering that only 71.5% of the input work contributes to lifting. The relationship between input work, output work, and efficiency is crucial for solving this problem. The discussion emphasizes the need to apply the formulas for mechanical advantage and efficiency to find the required length of rope to pull. Understanding these concepts is essential for tackling similar problems on the test.
glambeth
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Homework Statement


A pulley system has an efficiency of 71.5 percent. How much of the rope must be pulled in if a force of 641 N is needed to lift a 160 kg desk 2.51 meters?


Homework Equations



IMA = De/Dr
MA = Fr/Fe
Efficiency (%) = Wo/Wi
Efficiency (%) = MA/IMA

I have absolutely no idea how to solve this; this is simply a practice problem that I made up and the professor said a similar problem will appear on the test. Could someone show me how to do this?? I would appreciate it greatly.


The Attempt at a Solution

 
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glambeth said:

Homework Statement


A pulley system has an efficiency of 71.5 percent. How much of the rope must be pulled in if a force of 641 N is needed to lift a 160 kg desk 2.51 meters?

Homework Equations



IMA = De/Dr
MA = Fr/Fe
Efficiency (%) = Wo/Wi
Efficiency (%) = MA/IMA

I have absolutely no idea how to solve this; this is simply a practice problem that I made up and the professor said a similar problem will appear on the test. Could someone show me how to do this?? I would appreciate it greatly.

The Attempt at a Solution


How much work is needed to lift the desk?

Only 71.5% of the work done to the rope goes into lifting the desk.

How much work needs to be does to the rope?
 

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