Finding Force given a mass attached to a rope

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SUMMARY

The discussion centers on calculating the applied force, F, on a 306 kg crate suspended by a 10.3 m rope, which is pulled horizontally to move it 5.7 m. The forces acting on the crate include the applied force, gravitational force, and tension in the rope. At the final position, the sum of these forces equals zero, indicating equilibrium. A free body diagram is essential for visualizing and labeling the force vectors involved in this scenario.

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Homework Statement


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. What is the magnitude of the applied force, F, when the crate is at rest in its final position?
Associated Diagram:
http://img217.imageshack.us/img217/103/prob03axb9.th.gif http://g.imageshack.us/thpix.php

Homework Equations



I don't even know how to start this.
 
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There are three forces being applied to the crate: the applied force of you pulling on it, the force of the crate's gravity downward, and the force of the tension of the rope. At the final position, as shown in the diagram, the force vectors should all add to zero. The first step should be to draw a free body diagram and label the appropriate force vectors. Let us know if you need more help.
 

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