# The work-energy theorem

A particle moving in the x direction is being acted on by a net force F(x)= Cx^2, for some constant C. The particle moves from x_initial= L to x_final= 3L. What is deltaK, the change in kinetic energy of the particle during that time?

Express your answer in terms of C and L.

I got 16CL^3 but it keeps saying I'm off by a multiplicative factor. Anyone know where I', going wrong?

## Answers and Replies

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The work done on your particle as it moves in the positive $$x$$-direction is:

$$W = \int_{x=L}^{3L} F(x) dx$$

Interestingly, this is independent of how fast the particle is travelling.

In your case, you have an explicit form for the force: $$F = Cx^2$$, so:

$$W = \int_{x=L}^{3L} Cx^2 dx$$

<< rest of complete solution edited out by berkeman >>

Is this better?

Last edited by a moderator:
thanks!!

hi pterid ... how do u write formulas ??

best regards
rayo

berkeman
Mentor
The work done on your particle as it moves in the positive $$x$$-direction is:

$$W = \int_{x=L}^{3L} F(x) dx$$

Interestingly, this is independent of how fast the particle is travelling.

In your case, you have an explicit form for the force: $$F = Cx^2$$, so:

$$W = \int_{x=L}^{3L} Cx^2 dx$$

<< rest of complete solution edited out by berkeman >>

Is this better?
pterid, Please do not post complete solutions to homework/coursework questions. Even though this thread was originally (incorrectly) posted in the general technical forums, it is easy to recognize it as a homework/coursework question, and should be treated as such, even before a Mentor notices it and moves it to the Homework Help forums.