- #1

coppersauce

- 12

- 0

## 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 = gamma

^{3}mv

## 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 E

^{2}= p

^{2}c

^{2}+ (2m)

^{2}c

^{2}

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 c

^{3}*m*a*t/(c

^{2}- (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 :/