Surely fault about relativistic momentum

[BarbaraDav]

Dear Friends

Two identical particles are running, in opposite directions, along the x-axis of a reference frame having the origin coinciding with their barycentre; they hits frontally and glue together.

Their speeds are ("b" for before collision, "a" for after) :

V1b = u
V2b = -u
Va = 0

Let's watch the event from a reference frame moving toward right at speed u.

Relativistic speed composition gives:

V1b' = 0
V2b' = - 2u / ( 1 + u^2/c^2)
Va' = -u

This way the relativistic momentum is not conserved:

m ( 0 )+ m ( - 2u / ( 1 + u^2/c^2) ) != 2m ( -u )

Obviously, I'm wrong but really can't see what is going the bad way.
Please, can you give any hints ?

Best regards!

Barbara Da Vinci
Rome

 

[JesseM]

Relativistic momentum is not equal to mv, it's equal to $$mv\gamma$$, i.e. $$\frac{mv}{\sqrt{1 - v^2/c^2}}$$