As an illustration of the principle of relativity in classical mechanics, consider the f...

As an illustration of the principle of relativity in classical mechanics, consider the following generic collision: In inertial frame S, particle A (mass m_A, velocity u_A) hits particle B (mass m_B, velocity u_B). In the course of the collision some mass rubs off A and onto B, and we are left with particles C (mass m_C , velocity u_C) and D (mass m_D, velocity u_D). Assume that momentum (p ≡mu) is conserved in S.

(a) Prove that momentum is also conserved in inertial frame , 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