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

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SUMMARY

The pulley system in question operates at an efficiency of 71.5%. To lift a 160 kg desk, a force of 641 N is required to move it 2.51 meters. The relationship between the work input and output can be analyzed using the equations for Mechanical Advantage (MA) and Ideal Mechanical Advantage (IMA). The problem requires calculating the amount of rope that must be pulled to achieve the desired lift, factoring in the system's efficiency.

PREREQUISITES
  • Understanding of pulley systems and their efficiencies
  • Familiarity with the concepts of Mechanical Advantage (MA) and Ideal Mechanical Advantage (IMA)
  • Knowledge of work, force, and energy principles in physics
  • Ability to manipulate equations involving efficiency calculations
NEXT STEPS
  • Calculate the work done to lift the desk using the formula Wo = Fr * d
  • Determine the input work (Wi) required based on the system's efficiency
  • Explore the relationship between MA and IMA to find the required rope length
  • Review similar pulley efficiency problems for practice and mastery
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and pulley systems, as well as educators preparing for assessments related to work and energy principles.

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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