Let’s examine whether or not the law of conservation of momentum is true in all reference frames if we use the Newtonian definition of momentum: p_x = mu_x. Consider an object A of mass 3m at rest in reference frame S. Object A explodes into two pieces: object B, of mass m, that is shot to the left at a speed of c/2 and object C, of mass 2m, that, to conserve momentum, is shot to the right at a speed of c/4. Suppose this explosion is observed in reference frame S' that is moving to the right at half the speed of light.
a. Use the Lorentz velocity transformation to find the velocity and the Newtonian momentum of A in S'.
b. Use the Lorentz velocity transformation to find the velocities and the Newtonian momenta of B and C in S'.
c. What is the total final momentum in S'?
d. Newtonian momentum was conserved in frame S. Is it conserved in frame S'?