Relativity: Force and a Collision

[Amrator]

Homework Statement

Two identical masses m are initially at rest, a distance x apart. A constant force F accelerates one of them toward the other until they collide and stick together. What is the mass of the resulting particle?

Relevant Equations

$$F = \gamma^3 ma$$
$$F = \frac{dE}{dx}$$
$$E = \gamma mc^2$$
$$P = \gamma mv$$

I don't know if I did this correctly.
$\int Fdx = \int dE$
$F \Delta x = \Delta E$
$Fx = Mc^2 - (mc^2 + mc^2)$
$M = \frac{Fx + 2mc^2}{c^2}$

$M$ is the mass of the resulting particle. $2mc^2$ is the total energy before the collision. The issue is I'm assuming that the resulting particle is also stationary. I don't know this for sure though.

 

[anuttarasammyak]

It seems all right. Two clay balls collide to one big ball and stays still which has high temperature ,i.e. a lot of internal energy.

EDIT: I misunderstood the problem as the force comes from mutual interaction.

 

[PeroK]

The issue is I'm assuming that the resulting particle is also stationary. I don't know this for sure though.

It can't be stationary, as you must have conservation of momentum.