How Does Relativistic Motion Affect Newton's Second Law?

[limiss]

Homework Statement

Show that F=dp/dt=gamma^3*m*a for a relativistic system
assumption: force, motion in same direction

Homework Equations

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

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??

 

[Dick]

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.

 

[limiss]

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.

thanks... i had tried everything except the obvious which you just stated.