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The potential energy function of a particle moving in one-dimension is

  1. Nov 30, 2011 #1
    1. The problem statement, all variables and given/known data

    U = k(x^2 + y^2) What is the force exerted on the particle?

    2. Relevant equations

    F = -(¶U/¶x ihat +¶U/¶y jhat +¶U/¶z khat) <--couldnt get the del symbol right
    determining force from potential energy

    3. The attempt at a solution

    F = -¶/¶x[k(x^2+y^2)]ihat - ¶/¶y[k(x^2 +y^2)]jhat
    =-[2kx + Y^2]ihat - [kx^2 + 2ky]jhat

    Im new to calculus, and im pretty sure that im not doing the derivative of this right...any help would be greatly appreciated.
  2. jcsd
  3. Nov 30, 2011 #2


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    Staff: Mentor

    When you're doing partial derivatives of a function of several variables (x,y,z,...) with respect to a given variable, all the other independent variables are treated as constants. So,

    [itex]-\frac{\partial U}{\partial x} = -2 k x ~~~~~~~~~~-\frac{\partial U}{\partial y} = -2 k y[/itex]
  4. Nov 30, 2011 #3

    Andrew Mason

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    Science Advisor
    Homework Helper

    The partial derivative with respect to one variable is taken with the other variable held constant. So [itex]\partial U/\partial x = 2kx\hat x[/itex] and [itex]\partial U/\partial y = 2ky\hat y[/itex].

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