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Momentum and Kinetic Energy

  1. Oct 9, 2011 #1
    1. The problem statement, all variables and given/known data
    (a) A particle of mass m moves with momentum of magnitude p. Show that the kinetic energy of the particle is given by K=p[itex]^{2}[/itex]/2m. (b) Express the magnitude of the particle's momentum in terms of its kinetic energy and mass.


    2. Relevant equations
    Would the p=mv be needed?


    3. The attempt at a solution
    I don't know how to get it started. I think I can get it if I can get it started.

    Thank you.
     
  2. jcsd
  3. Oct 9, 2011 #2

    robphy

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    What is your [starting] expression for kinetic energy?
    How is the new expression different from the old one? Any variables missing from one vs the other?
     
  4. Oct 9, 2011 #3
    The equation for kinetic energy is k=.5mV^2 and the new equation is K=p^2/2m. Momentum is missing from the first equation and velocity is missing from the second equation.
     
  5. Oct 9, 2011 #4
    If velocity is missing from the final equation, that means it was substituted in the original equation for K.E. From the equation for momentum (which you listed: p = mv), what is velocity equal to?
     
  6. Oct 9, 2011 #5
    K=p^2/2m
    K=.5mV^2
    p=mv
    V=p/m
    K=.5m(p/m)^2
    K=p^2/2m
     
  7. Oct 9, 2011 #6
    Oh, you had it already! Perfect :smile:
     
  8. Oct 9, 2011 #7
    Thank you for the help. :)
     
  9. Oct 9, 2011 #8
    No problem
     
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