# Work and Energy Problem

#### kye6338

Hi,
I also need help on this problem:

1. A 384-kg crate hangs from the end of a 11.2 m long rope. You pull horizontally with a varying force to move it a distance d = 5.4 m to the right. a.) What is the magnitude of the applied force F when the crate is at rest in its final position? b.) What is the work done by the weight of the crate?
c.) What is the work you do on the crate?

I'm stuck on part a. This is what I did: I found the angle at the top of the rope to by 28.8 deg from sin theta = 5.4/11.2. From there i used the equation 1/2mv^2=g(11.2-11.2cos28.8). I got the acceleration to be 5.07 m/s^2. Then, I plugged this into the equation F=ma, getting 200.4 N. But, this is not correct. Am I approaching this problem wrong, should I be using a different equation? Please let me know, as I am completely stuck! Thanks!

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#### Astronuc

Staff Emeritus
1/2mv^2=g(11.2-11.2cos28.8). This is not correct for part a.

In part a, "the crate is at rest in its final position", so this is a statics problem.

Resolve the tension, T, of the rope into two components, vertical and horizontal. In statics (at rest), the net force is zero.

Try T sin $\theta$ = F and T cos $\theta$ = mg.

Remember, work is the integral of the applied force over the distance.

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