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Differentiating force to find potential energy

  1. Jan 27, 2013 #1
    A particle of mass m is moving along the x-axis and experiences a force F(x), also along the x-axis, given by F(x) = -kx. Deduce an expression for the potiential energy of the particle.



    I tried intergrating both side (just to see if it gave me anything helpful). I got ∫F(x)dx=mv for the left hand side and -(1/2)kx^2 on the right hand side but i still don't have the answers. Any help would be much appreciated :)
     
  2. jcsd
  3. Jan 27, 2013 #2
    The potential energy at some position ##x## of an object subjected to a conservative force (in one dimension) is ##V = -\int_{x_0}^{x} F(x') dx'##. ##x_0## is arbitrary, since you can set the zero potential anywhere you like. You didn't need to integrate the left hand side explicitly.

    Edit: Also, don't erase the homework help template. It's there for a reason, as this example demonstrates.
     
  4. Jan 28, 2013 #3
    Ok, i've found the answer and i understand how to do it. Thanks for your help :)
     
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