Chapter 44, Problem 44.56CP

Consider a collision in which a stationary particle with mass M is bombarded by a particle with mass m, speed Ư0, and total energy (including rest energy) E_m. (a) Use the Lorentz transformation to write the velocities v_m and v_M of particles m and M in terms of the speed v_cm of the center of momentum. (b) Use the fact that the total momentum in the center-of-momentum frame is zero to obtain an expression for v_cm in terms of m, M, and v₀. (c) Combine the results of parts (a) and (b) to obtain Eq. (44.9) for the total energy in the center-of-momentum frame.