Posted by Eng on Sunday, February 7, 2010 at 5:08pm.
A potential energy function for a twodimensional 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 :)