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Conservative FOrce

  1. Nov 22, 2012 #1
    1. The problem statement, all variables and given/known data

    Find the work done by a force F = ix^2y^3 + jx^3y^2
    Show that this
    is a conservative force and find the potential energy U(x, y).

    2. Relevant equations
    A force F is conservative when :
    dFx/dy = dFy/dx


    3. The attempt at a solution

    dFx/dy = d(x^2y^3)/dy = (2xdx/dy)(y^3) + (x^2)(3y^2)
    dFy/dx = d(x^3/y^2)dx = (3x^2)(y^2) + (x^3)(2ydy/dx)

    They're not equivalent though
     
  2. jcsd
  3. Nov 22, 2012 #2
    Solution : dFx/dy = 3x^2y^2 = dFy/dx

    Can someone explain me the derivative technique? I don't know they get these...
     
  4. Nov 22, 2012 #3

    haruspex

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    Should be partial derivatives: ∂Fx/∂y = ∂Fy/∂x
    They will be when you change to partial derivatives. (∂y/∂x = ∂x/∂y = 0)
     
  5. Nov 24, 2012 #4
    WHat do you mean partial ??

    Can you or anyone show me just a first few steps?
     
  6. Nov 24, 2012 #5
    I'm self studying AP Physics C in high school. Am I expected to know it? Are there any simpler way to solve it? ( My way is to integrate in different paths, but I"m not sure)
     
  7. Nov 24, 2012 #6

    haruspex

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    If you have a number of independent variables (in this case, x and y), and a function f of these, the partial derivative of f wrt x (written ∂f/∂x) means the change in f as x changes slightly but y stays constant. So when performing a partial derivative wrt x, treat y as a constant: ∂y/∂x = 0. Likewise ∂x/∂y = 0.
    Plug those into the equation you got.
     
  8. Nov 24, 2012 #7
    Are those material in Calculus 2??
     
  9. Nov 24, 2012 #8

    haruspex

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    I don't know what education system you're in, let alone what's in what syllabus.
     
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