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Homework Help: Force and energy proofs

  1. Sep 6, 2006 #1
    Show that for a single particle with constant mass the equation of motion implies the following differential equation for the kinetic energy:
    [tex]{dT\over dt} = \vec F \cdot \vec v[/tex]

    while if the mass varies with time the corresponding equation is
    [tex]{d(mT)\over dt} = \vec F \cdot \vec p[/tex]

    Proof:

    I was able to prove the first part:
    [tex]T = {1\over 2}mv^2[/tex]
    [tex]{dT\over dt} = {1\over 2} {d(mv^2)\over dt} = \vec v \cdot m{d\vec v \over dt} = \vec F \cdot \vec v[/tex]

    But I am unable to prove the second part. Please help.
     
  2. jcsd
  3. Sep 6, 2006 #2
    what does mT equal in terms of m and v? in terms of p?
    mv=p
    F=dp/dt

    try to play with the equation a little and substitute p in.
     
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