How Does Special Relativity Affect the Mass of Colliding Particles?

[coppersauce]

Homework Statement

Two identical masses m are initially at rest, separated by a distance x. A constant force F
accelerates one particle until it collides and combines with the other. What is the mass of
the resulting particle?

Homework Equations

F = gamma³mv

The Attempt at a Solution

Presumably you must calculate conservation of energy (which is whatever the energy is of the single mass moving must equal that of them combined).

Then I guess you need to calculate conservation of momentum, which should also be easy especially since it's in one direction after all.

Lastly you could just plug it into the equation E² = p²c² + (2m)²c²

The thing I don't understand is what energy/momentum the mass has pre-impact. We've never done a problem with the equation I gave before so I'm not sure if it's needed, but in any case I attempted solving with that equation for F and then multiplying by t to get the momentum and got c³*m*a*t/(c² - (at)²)^3/2 which seemed way too complicated for so early. I would also just do energy of the big mass = gamma*m*c^2+mc^2 and that would give me the part for E^2 and i w ould have all necessary parts... But I don't know if my original thing is right at all :/

 

[vela]

This might help:

http://en.wikipedia.org/wiki/Special_relativity#Kinetic_energy