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Kinetic energy with momentum equation

  1. Nov 26, 2007 #1


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    [SOLVED] kinetic energy with momentum equation

    1. The problem statement, all variables and given/known data

    A particle of mass m moves with momentum of magnitude p. Show that the kinetic E of particle is given by [tex] K= p^2/2m [/tex]

    express magnitude of particle's momentum interms of it's Kinetic Energy and mass.

    2. Relevant equations

    Kf + Uf= Ki + Ui

    1/2mvf + mgy = 1/2mvi + mgy

    pf= pi

    mvf= mvi

    3. The attempt at a solution

    not exactly sur how to incorperate the momentum into the kinetic E equation.

    my attempt looks ridiculous.

    not sure if it's Kf= Ki
    because they just say the Kinetic E

    K= 1/2mv^2

    p= mv

    [tex]K= \frac{P*v} {2}[/tex]

    What am I doing incorrectly?

    b) Express magnitude of the particle's momentum in terms of it's kinetic E and mass

    I guess I would just rearrange the equation they gave me

    [tex]K= \frac{p^2} {2m}[/tex]

    [tex] p= \rad{K*2m} [/tex]
  2. jcsd
  3. Nov 26, 2007 #2
    This would be correct if K = p/2m

    But you have to isolate p^2. Dont you miss the [tex] {\sqrt {equation}} [/tex] ?
  4. Nov 26, 2007 #3
    Nothing incorrect, just incomplete. Multiply the expression on the right by m/m.

    That looks good.
  5. Nov 26, 2007 #4

    You lose one stage:[tex]v=\frac{p}{m}[/tex]

    This equation is important.Because in the Hamitonian equation,all the element must be
    expressed by P and q.q is the generalized coordinate .
    Last edited: Nov 26, 2007
  6. Nov 26, 2007 #5


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    Gold Member

    Thank you everyone. I get why I have to multiply it by m/m.
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