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Particle subject to position dependent force

  1. Oct 15, 2009 #1
    1. The problem statement, all variables and given/known data
    A particle with total energy E and mass m is subject to a force [tex]F(x)=\xi x^4[/tex]. Find the velocity v of the particle as a function of the position x, and sketch a phase diagram for the motion.

    2. Relevant equations



    3. The attempt at a solution
    [tex]x=\sqrt[4]{\xi m \ddot{x}}[/tex]

    Not sure where to go from here, or what the phase diagram axes should be. Do I just take the time derivative of x and that's my velocity?
  2. jcsd
  3. Oct 15, 2009 #2


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    Homework Helper

    Use the work-energy theorem.
  4. Oct 16, 2009 #3
    "The net work done by all the forces acting on a body equals the change in its kinetic energy."
    Not seeing it...
  5. Oct 16, 2009 #4


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    Homework Helper

    Assume one-dimensional motion along x. You need the velocity of the particle as function of the position: v(x). At t=0 let x=0 and the kinetic energy=E. During some time period t, the displacement of the particle is x(t) and the change of KE is:

    [tex]\Delta E = 1/2 mv(x)^2-E [/tex]

    The particle is subjected to a force of form

    [tex]F(x) = \xi x^4 [/tex].

    The work done by this force while the particle moves from position x=0 to some x(t) is

    [tex]W=\int_0^{x(t)}{F(x)dx}=\int_0^{x(t)}{\xi x^4dx}[/tex]

    Calculate the integral, make it equal to the change of KE, express v(x), sketch v(x) as function of x.
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