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Physics

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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 -

    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 -

    Yes! Thank You! I was very close but I messed up on my derivative somehow :)

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