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Potential Energy and Force

  1. Jun 19, 2007 #1
    1. The problem statement, all variables and given/known data
    A potential energy funtion for a two dimensional force is of the form
    U = ax^3y + bx
    where a =10.51 J/m^4 and b = -8 J/m.
    Find the magnitude of the force that acts at the point (x,y) for x =93, y =68

    2. Relevant equations
    F(x) = dU/dx

    3. The attempt at a solution
    Given the PE function, I know that I have to take the derivative to find Force but I am confused as to how to do this with it being in 2-d. There are two variables, x and y. Help please.
  2. jcsd
  3. Jun 20, 2007 #2


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    U = ax^3y + bx

    then you want to differentiate this with respect to x and then y, you just when you differentiate with respect to x treat ALL the others as constants. And the same way with the y.

    [tex] \dfrac{dU}{dx} = 3ayx^{3y-1} + b [/tex]

    now you try
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