Calculate Relativistic Mass of Combined Particle

[kwuk]

Hi all, would be very grateful if someone could give me some pointers on this.

If you have two particles of equal rest mass traveling in the same direction, particle A traveling at say 0.5c and particle B behind it traveling at 0.6c and they eventually collide inelastically, how do you calculate the mass of the 'combined particle', as seen by a stationary observer?

Thanks.

 

[vela]

Are you trying to calculate the rest mass of the combined particle? I'm guessing you are otherwise the problem is kind of boring.

In any case, start by writing down the four-momentum of each particle. Using those, you can calculate the four-momentum of the combined particle. Once you have that, it's straightforward to calculate the rest mass or relativistic mass of the combined particle.

One suggestion would be to write the components of the four-momenta in terms of the rapidity $$\theta$$ where $$\beta=\tanh \theta$$.