Question

A ball of mass m traveling at a speed of $0.80c$ has a perfectly inelastic collision with an identical ball at rest. If Newtonian physics were correct for these speeds, momentum conservation would tell us that a ball of mass $2m$ departs the collision with a speed of $0.40c$. Let’s do a relativistic collision analysis to determine the mass and speed of the ball after the collision.

a. What is${\gamma }_p$, written as a fraction like a/b?

b. What is the initial total momentum? Give your answer as a fraction times $mc$.

c. What is the initial total energy? Give your answer as a fraction times$m{c}^2$. Don’t forget that there are two balls.

d. Because energy can be transformed into mass, and vice versa, you cannot assume that the final mass is$2m$. Instead, let the final state of the system be an unknown mass $M$ traveling at an unknown speed $u_f$. You have two conservation laws. Find $M$ and $u_f$.

Short answer

f

Step-by-step solution

St

f