Solve Relativistic Momentum PROBLEM - Extra Factor of u Explained

[meriadoc]

PROBLEM SOLVED - the worked example I was referring too was wrong :/
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Hello, I've been stuck on a question in one of my SR problem sets for some time now, and managed to find a worked solution to a similar problem online. I've attached an image of the problem (the missing text just says that two particles of equal mass are accelerated to a speed u).

It begins by showing that in frame S, both particles have the same energy, which is

E = \gamma m u

It then uses the 4-momentum transformations for the second particle (the one that is moving in both frames), noting that

(p^0)' = \gamma (p^0 - \frac{v}{c} (p^1)')

But then it goes on to define p^1 as

p^1 = \gamma m u (-u)

This is where I made the mistake in my working, I used

p^1 = \gamma m (-u)

I don't understand why the proper momentum of the second particle has an additional factor of u associated with it. Any explanation would be greatly appreciated.

Cheers.

 

[Simon Bridge]

It begins by showing that in frame S, both particles have the same energy, which is
E=γmu

$\gamma mu$ is not energy.
http://www.lecture-notes.co.uk/susskind/special-relativity/lecture-5/proper-velocity-and-momentum/