Composite Particle Rest Mass Calculation

[zhillyz]

Homework Statement

A particle of rest mass $m_0$ and kinetic energy $2m_0c^2$ and sticks to a stationary particle with rest mass $2m_0$. Find the rest mass of the composite particle.

Homework Equations

Conservation of momentum and thus energy.

$E_{bef} = E_r + E_k = E_{aft}$ where E_r is energy of rest particle

The Attempt at a Solution

$E = m_{01}c^2 + mv\gamma + m_oc^2 = m_{02}c^2$. The first half of the equation there is a kinetic part and a part at rest, the second half is only at rest.

I am thinking I am supposed to be substituting the questions given data into this equation and cancelling expressions but i am not sure how to proceed.

 

[vela]

Homework Statement

A particle of rest mass $m_0$ and kinetic energy $2m_0c^2$ and sticks to a stationary particle with rest mass $2m_0$. Find the rest mass of the composite particle.

Homework Equations

Conservation of momentum and thus energy.

$E_{bef} = E_r + E_k = E_{aft}$ where E_r is energy of rest particle

The Attempt at a Solution

$E = m_{01}c^2 + mv\gamma + m_oc^2 = m_{02}c^2$. The first half of the equation there is a kinetic part and a part at rest, the second half is only at rest.

I am thinking I am supposed to be substituting the questions given data into this equation and cancelling expressions but i am not sure how to proceed.

What are $m_{01}$, $m_{02}$, $m_o$ (not $m_0$), and $m$ supposed to represent? None of those quantities appear in the problem statement.

Your equation doesn't make sense. You're adding energy to momentum $\gamma mv$. That doesn't work out unit-wise. I take it v is supposed to be the speed of the first particle.

Think about this: After the two particles collide and stick together, is the composite particle at rest or not?

It's best if you stick to working with energy E, momentum p, and mass m rather than writing things in terms of $\gamma$ and speed v. It'll simplify the algebra.