Inelastic relativistic collision

[armandowww]

A particle with rest mass $$m_{0}$$ moves at a speed of $$0,8c$$. It's going to collide with a particle with rest mass $$3m_{0}$$. If the latter was standing still before impact and if the collision is completely inelastic, what are the conservation laws valid? What is the final single particle rest mass?

 

[robphy]

What have you tried so far?

 

[armandowww]

In my opinion, the total energy and the quadrimpulse must conserve. We can use a reference frame system centered in the first particle and consider the target particle as coming toward the origin in relative motion...

 

[pervect]

quadrimpulse? What's that? I hope it's a typo...

Meanwhile, write down an expression for the total energy of the system before and after the collision, that should get you one of the two equations you need.

 

[robphy]

Certainly the key to the problem is recognize what is physically being conserved.
Then, if you think geometrically, your math problem can be solved by drawing the appropriate triangle [for this inelastic collision] and realizing that you are essentially using the analogue of the law of cosines.

 

[armandowww]

quadrimpulse? What's that? I hope it's a typo...

I was taught that, in restrict relativity, quadrimpulse is introduced as a four-dimensional vector resulting on the generalization of common momentum vector which, on the contrary, is featured by tri-dimensions.
Its formal expression could be given as: $$\underline{p}\equiv \left(m\vec{v},mc\right)\equiv \left(\vec{p},mc\right)$$. This definition remainds to the famous issue that space (3D) and time (1D) are not to be considered apart any more, because they are interrelated each other and behave as as a whole, the space-time (4D).