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Potential Function of a Conservative Force

  1. Jan 24, 2013 #1
    1. The problem statement, all variables and given/known data
    Given a conservative force with the Force given as F=y^2(i)+2xy(j), what is the potential function related to it.


    2. Relevant equations

    -dU/dx = F


    3. The attempt at a solution
    I know I have to integrate the components but I don't know how... since the (i) direction was differentiated with respect to x would I just treat the y as constant and say F=xy^2(i)+xy^2(j) + c ?
     
  2. jcsd
  3. Jan 24, 2013 #2

    fzero

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    You're on the right track, but remember that the potential is a scalar function. You've written down a result that is a vector and for some reason called it F. It might help to explicitly write down the components of F in terms of the partial derivatives of U.
     
  4. Jan 24, 2013 #3
    So would it just be U(x,y)=xy^2 + xy^2 = 2xy^2 + c because it's a scalar?
     
  5. Jan 24, 2013 #4

    LCKurtz

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    Close, but no. Remember, you are looking for a scalar function ##U(x,y)## such that ##\nabla U = \vec F##. So you need ##U_x = y^2## and ##U_y = 2xy##. Start by taking the anti-partial derivative of the first one with respect to ##x## by holding ##y## constant, as you asked in your original post. Don't forget when you do that your "constant" of integration will be a function of ##y##. Them make the second equation work.
     
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