# Relativistic Conservation of Momentum Confusion

1. Sep 30, 2014

### Pezz

Hey all,

Simple question yet it creating a lot of confusion in me and I need some clarification. This is an example given in a book I'm reading and I just don't understand one piece of it. In the S frame a completely inelastic collision between two particles traveling at each other at speed u and mass m will result in 2m as per conservation of momentum. The S' frame is moving at speed u along the positive x axis, and thus in that frame one of the particles is still while the other travels at speed 2u according to classical mechanics. However using relativistic velocity addition the speed of the oncoming particle is different and the book concludes that the momentum is not conserved because:

"Before the collision the momentum in the S' frame is p'=mu' ( where u' is the relativistic velocity of the oncoming particle ), whereas after the collision it is simply p'=2mu."

Can someone clarify this for me? Why is the momentum not conserved? Shouldn't u in p'=2mu for final momentum also be u'?

2. Sep 30, 2014

### vela

Staff Emeritus
I think you need to provide more context. What's the book trying to show? Is the book analyzing the situation using Newtonian mechanics or relativistic mechanics?

3. Sep 30, 2014

### Pezz

I finally understood it... I was missing a small detail involving an equation that was right in front of me the whole time... thanks for offering your help, that was frustrating... I guess I should just take more time on understanding things :P