1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
    [tex]T=\frac{1}{2}m\dot{x}^2[/tex]

    [tex]U=constant[/tex]

    [tex]F=m\ddot{x}[/tex]

    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

    ehild

    User Avatar
    Homework Helper
    Gold Member

    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

    ehild

    User Avatar
    Homework Helper
    Gold Member

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Particle subject to position dependent force
  1. Position of a particle (Replies: 2)

Loading...