PX155 - I1 - momentum

two particles having the same mass, $m$ , have a totally inelastic head on collision, and coalesce to form a new particle of mass, $M$
let $v_{1}^{'} = u$ , so, $v_{2}^{'} = - u$
in $S$ before collision: $$v_{1} = \frac{v_{1}'+u}{1+ \frac{uv_{1}'}{c^{2}}} = \frac{2u}{1+ \frac{u^{2}}{c^{2}}}$$

a n d, v_{2} = \frac{v_{2}^{'} + u}{1 + \frac{u v_{2}^{'}}{c^{2}}} = 0

p_{i} = m v = \frac{2 m u}{1 + \frac{u^{2}}{c^{2}}}

- after:

p_{f} = M u = 2 m u

- we see that $p_{i} \neq p_{f}$