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Relativistic Newton's 2nd Law

  1. Apr 19, 2007 #1
    1. The problem statement, all variables and given/known data
    Show that F=dp/dt=gamma^3*m*a for a relativistic system
    assumption: force, motion in same direction

    2. Relevant equations

    p = gamma*m*v(t)
    gamma = 1/sqrt(1-v(t)^2/c^2)

    3. The attempt at a solution

    p= v(t)*m/sqrt(1-v(t)^2/c^2)

    using product rule then chain rule
    dp/dt= (1/sqrt(1-v(t)^2/c^2) + (v(t)/c)^2/(1-v(t)^2/c^2)^3/2)*m*dv/dt

    dv/dt= a

    how do i get m*a*gamma^3 from this??
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Apr 19, 2007 #2


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    Just put the two terms over the common denominator of (1-v(t)^2/c^2)^3/2 and combine them. You are almost there.
  4. Apr 19, 2007 #3
    thanks... i had tried everything except the obvious which you just stated.
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