Posted by **Eng** on Sunday, February 7, 2010 at 5:08pm.

A potential energy function for a two-dimensional force is of the form U = 3 x^(4)y - 8 x. Find the force that acts at the point (x, y). (Use x and y as appropriate.)

I know its something about partial derivatives but I'm not sure how to go about it. And the answer has to be in vector components (ihat jhat)

- Physics -
**Damon**, Sunday, February 7, 2010 at 5:25pm
Well, if a force is acting on something and energy is conserved and there is no change in kinetic energy then

Delta U = increase in potential energy from point a to point b = integral Fx dx + integral Fy dy where the integrals are from a to b.

That is the work we would do on the system. The force the system exerts is equal and opposite by Newton #3.

So I have a hunch that

Fx = -dU/dx

and

Fy = -dU/dy

and the vector F = Fx i + Fy j

so here

U = 3 x^(4)y - 8 x

-dU/dx = -12 x^3 y +8

-dU/dy = -3 x^4

and

F = (-12 x^3 y +8)i - 3 x^4 j

- Physics -
**Eng**, Sunday, February 7, 2010 at 6:55pm
Yes! Thank You! I was very close but I messed up on my derivative somehow :)

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