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Potential Energy - Potential function problem.

  1. Nov 3, 2006 #1
    I'm having trouble starting a certain problem.

    A potential function is given by U(x) = 12 x^2. What will be the acceleration (in meters/second ^2) of a 2 kg mass, when it is at the position x = 0.2 m?

    Any help will be highly appreciated. :smile:
    Last edited: Nov 3, 2006
  2. jcsd
  3. Nov 3, 2006 #2


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    How is the potential energy function related to the force? And in turn, how is force related to acceleration?
  4. Nov 4, 2006 #3
    Hmmm... Well, here is what I can think of from what I've learned in class:

    1. The potential energy function is tied in to a conservative force for x. Maybe I can go with the formula of: F cons. x = - ∂U/∂x
    2. Force is related to acceleration by: F net = (mass) x (acceleration) Thus: *acceleration = (mass) / (F net)
    Am I on the right track?

    *EDIT: acceleration = (F net) / (mass)
    Last edited: Nov 4, 2006
  5. Nov 4, 2006 #4
    yes. now, put all the equations together and solve for acceleration.
  6. Nov 4, 2006 #5
    Alrighty, so by taking the derivative of 12x^2 I get 24x. To get the Force would I multiply 0.2 meters by 24 ?

    B.T.W.: (Thank you for all the replies.)
  7. Nov 4, 2006 #6


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    That's right.
  8. Nov 4, 2006 #7
    not quite, but almost. you forgot the negative when calculating the force.
  9. Nov 4, 2006 #8
    because acceleration does not equal mass/force (you still forgot the negative)
  10. Nov 4, 2006 #9
    Oh my goodness! (brain fart) I see my mistake now. a = Fnet / mass
    Thus being: (-4.8)/(2 kg) = -2.4 m/s^2


    Thank you folks for all your help!
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