Electrodynamics and Relativity — David J. Griffiths
Physics · special-relativity-inertial-frames
Problem
As an illustration of the principle of relativity in classical mechanics, consider the following generic collision: In inertial frame S, particle A (mass mA, velocity uA) hits particle B (mass mB, velocity uB). In the course of the collision some mass rubs off A and onto B, and we are left with particles C (mass mC, velocity uC) and D (mass mD, velocity uD). Assume that momentum (p≡mu) is conserved in S.
(a) Prove that momentum is also conserved in inertial frame Sˉ, which moves with velocity v relative to S. [Use Galileo's velocity addition rule—this is an entirely classical calculation. What must you assume about mass?]
(b) Suppose the collision is elastic in S; show that it is also elastic in Sˉ.