Introduction to Classical Mechanics · Problem 12.6

Relativity (Dynamics) — Morin

Physics — Mechanics · relativistic-collisions

Problem

A ball of mass

M

and energy

E

collides head-on elastically with a stationary ball of mass

m

. Show that the final energy of mass

M

E' = \frac{2mM^2 + E(m^2 + M^2)}{2Em + m^2 + M^2}.

Hint: This problem is a little messy, but you can save yourself a lot of trouble by noting that

E' = E

must be a root of the equation you get for

E'

. (Why?) As a reward for trudging through the mess, there are lots of interesting limits you can take.