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?
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 :/