# A particle of rest mass m_0 and kinetic energy and sticks to a stationary particle wi

1. Aug 12, 2012

### zhillyz

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

Conservation of momentum and thus energy.

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

3. 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.

2. Aug 13, 2012

### vela

Staff Emeritus
Re: A particle of rest mass m_0 and kinetic energy and sticks to a stationary particl

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.

Last edited: Aug 13, 2012