Solve Pulley System Problem: Lift 52 kg Desk 2.32 m with 620 N

[kiwikahuna]

Homework Statement

A pulley system has an efficiency of 76.9%. The acceleration of gravity is 9.81 m/s^2. How much of the rope must be pulled in if a force of 620 N is needed to lift a 52 kg desk 2.32 m?

Homework Equations

Force = ma
Work = force * distance

The Attempt at a Solution

Because the efficiency is 76.9%, I divided 620 N by .769 to find the amount of force that the pulley system would actually have to do. (806 N). I then found the amount of work required to lift the desk without the pulley system. 52 kg * 9.81 m/s^2 * 2.32 m = 1182.87 J
To find the distance the rope has to be pulled in, I used the work formula.
1182.87 J = 806 N * (distance)
distance =1.47 m

Pulley problems have never been my forte and I'm not sure if my attempt at this problem was right. Any help would be much appreciated!

 

[anathema]

Your attempt at the solution is correct. You correctly took into account the efficiency of the pulley system and calculated the amount of work required to lift the desk without the pulley system. Your final answer of 1.47 m for the distance the rope must be pulled in is also correct. Good job!

One thing to note is that the efficiency of a pulley system can also be expressed as a percentage, rather than a decimal. So instead of using 0.769, you could use 76.9%. This won't affect your final answer, but it may make the calculation a bit easier.

Keep up the good work!

 

[m2003]

Your approach seems to be correct. To lift the desk using a pulley system, the force exerted by the person pulling the rope must be equal to the weight of the desk plus the weight of the rope itself (since the rope has to support the weight of the desk). Therefore, the actual force needed to lift the desk is 620 N divided by the efficiency of the pulley system (0.769), which gives you 806 N. This is the force that needs to be applied to the rope in order to lift the desk.

Using the equation F=ma, you can find the acceleration of the desk, which is the same as the acceleration of the rope. This is because the rope and the desk are connected and move together. So, 806 N = 52 kg * a, which gives you an acceleration of 15.5 m/s^2.

Next, using the equation Work = force * distance, you can find the work done by the person pulling the rope. This work must be equal to the work required to lift the desk, which is 1182.87 J. So, 1182.87 J = 806 N * distance. Solving for distance gives you 1.47 m, which is the distance the rope must be pulled in order to lift the desk 2.32 m.

Overall, your approach is correct and you have arrived at the correct answer. Keep in mind that pulley problems can be tricky and it's always a good idea to double check your work and make sure the units are consistent throughout your calculations. Great job!