Please help: A box on a frictionless plane, find the power based on work and

[nickclarson]

[SOLVED] Please help: A box on a frictionless plane, find the power based on work and

Homework Statement

A box of mass M = 7.68 kg is at rest at the bottom of a frictionless inclined plane.


The box is attached to a string that pulls with a constant tension T = 113 N. Write the general equation that gives the work done by the tension when the box has moved a distance x along the plane. Now, find the speed of the box as a function of x and the angle of the plane. Finally, for a distance of x = 6.38 m and an angle of 30.5°, determine the power delivered by the tension in the string as a function of x.

Homework Equations

$$K=\frac{1}{2}mv^{2}$$
$$P=FV$$

The Attempt at a Solution

I know I am supposed to multiply the net force by velocity for the last part, but I need to find the velocity.

I figured I could use kinetic energy to find the velocity using the ke work theorem. So...

$$KE_{f}-KE_{i}=W$$

And since the initial energy is 0

$$KE_{f}=W$$

Am I on the right track?

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Edit: Solved

Here's the final equation I derived:

$$P=T\sqrt{\frac{2x(T-mgsin\theta)}{m}}$$

 

[member 553083]

For x = 6.38 m and an angle of 30.5°, the power delivered by the tension in the string is P = 544.2 W.