(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Given:

A 306 kg crate hangs from the end of a 10.3 m long rope. You pull horizontally with a varying force to move it a distance d = 5.7 m to the right. The magnitude of the applied force, F, when the crate is at rest in its final position is 1992.4 N.

Question:

What is the work you do on the crate?

Associated Diagram:

http://img217.imageshack.us/img217/103/prob03axb9.th.gif [Broken]http://g.imageshack.us/thpix.php [Broken]

2. Relevant equations

Work = Force x Displacement x Cos (angle between force and displacement)

Pythagorean Theorem = a^2 + b^2 = c^2

3. The attempt at a solution

To attempt to solve this problem, I assumed 1992.4 N is the force I will be using. I then assumed the displacement would be a right-angled triangle with 5.7 m as the width and the difference between initial height (length of the rope 10.3 m) and final height (which I calculated using Pythagorean theorem to be 8.58m). This right-angled triangle’s hypotenuse, 5.954 m, would be used as my displacement. I then calculated the angle between displacement and force and found that to be 16.8 degrees. Since the motion was pulling and given the displacement, the work done will be a positive value, which I found to be 11356 J or 1.14E+04 J, but this is incorrect. I cannot seem to find a flaw in my reasoning, can you spot anything I’ve forgotten?

I then tried a different approach, calculated the work done by gravitational potential energy to get the work done by the crate. I took this work and assumed it must be equal to the work done by the tension in the y-axis of the string. I used the angle I found with my length dimensions to calculate work done by tension in the x-axis of the string. I assumed it must be equal to the work done by the person. With this I got 3428.3 J, but it was incorrect.

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# Work: Pulling a crate attached to a rope

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