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 :)

## Answer this Question

## Related Questions

- physics - A potential energy function for a two-dimensional force is of the form...
- Physics 3 - A potential energy function for a two-dimensional force is of the ...
- PHYSICS - A potential energy function for a two-dimensional force is of the form...
- Physics Please help !! - A single conservative force = (6.0x - 12) N where x is ...
- physics - A block is moving down an incline a distance of 5 m form point A to ...
- physics - What does it mean to say the Coulomb Force is a conservative force? ...
- physics - A force is given by Fx=Ax^-3, where A=8.0 N*m^3.(a) For positive ...
- physics - A single conservative force F = (7.0x - 11)i N, where x is in meters, ...
- physics - A single conservative force F = (6.0x - 11)i N, where x is in meters, ...
- Physics - I came here earlier with this question: "A force of 20 N acts toward ...