Relativistic momentum and conservation of this

[Niles]

Homework Statement

A particle with mass m and speed (4/5)c collides with a particle (with mass m as well, but speed = 0) un-elastically, and continues as one particle.

I have to find the speed and mass for this "joined" particle.

The Attempt at a Solution

Ok, first - conservation of momentum!

1) I use that gamma_1*m*(4/5)c + 0 = gamma_2*M*v

2) I also use gamma_1*m + m = gamma_2*M

Is this correct? In the notes I took in class today, I wrote this for #1: gamma_1*m*(4/5)c + 0 = gamma_2*M - but I guess I wrote this one down wrong?

Thank for you all in advance.

 

[nrqed]

Homework Statement

A particle with mass m and speed (4/5)c collides with a particle (with mass m as well, but speed = 0) un-elastically, and continues as one particle.

I have to find the speed and mass for this "joined" particle.

The Attempt at a Solution

Ok, first - conservation of momentum!

1) I use that gamma_1*m*(4/5)c + 0 = gamma_2*M*v

2) I also use gamma_1*m + m = gamma_2*M

Is this correct? In the notes I took in class today, I wrote this for #1: gamma_1*m*(4/5)c + 0 = gamma_2*M - but I guess I wrote this one down wrong?

Thank for you all in advance.

Your equations 1 and 2 are correct. Note that gamma_1 is known so that leaves two unknowns: M and v.

 

[Niles]

Great, thanks!

 

[Meir Achuz]

M=2m. Then gamma2 cancels out of the equation for v,