Finding Force given a mass attached to a rope

[TJDF]

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.

 

[JoAuSc]

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.

 

[baba89]

To solve this problem, you will need to use the equation F=ma, where F is the force applied, m is the mass of the crate, and a is the acceleration of the crate. In this case, the crate is at rest, so the acceleration is 0. Therefore, the equation becomes F=0, which means that the applied force is equal to 0. This may seem counterintuitive, but it makes sense when you think about it. If the crate is at rest, that means that all the forces acting on it are balanced. The force of gravity pulling the crate down is balanced by the force of the rope pulling the crate up. When you pull horizontally on the crate, the force you are applying is also balanced by an equal and opposite force from the rope. Therefore, the net force on the crate is 0 and it remains at rest in its final position.