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

## 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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## 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?