# Question on collisions

1. May 27, 2005

### allistair

There's something in my theoretical mechanics handbook that i don't quite understand. Say you have an observer in a labratory watching 2 particles, one of wich is in a state of rest (m_2) and the other one (m1) is moving towards it.

the placevector of the center of mass of the system is
$$R = \frac{m_{1}.R_{10}+m_{2}.R_{20}}{m_{1}+m_{2}}$$
wich moves with a speed
$$V = \frac{m_{1}.v_{10}}{m_{1}+m_{2}} = \frac{p_{10}}{m_{1}+m_{2}}$$
v_10 and R_10 and R_20 seen by the labratory observer, say you have an observer at the centre of mass of the system, he observes the particles with speeds v_1 and v_2

for the observer at the centre of mass before the particles collide the impules p_1 and p_2 are the same but in oppsing directions. Now my handbook states that
$$p_{1}=p{2} = m_{2}.V = \frac{m_{2}.p_{10}}{m{1}+m{2}}$$
wich i don't fully understand

Last edited: May 27, 2005
2. May 27, 2005

### arildno

1.Compute the velocities of the particles relative to C.M.
2. Then figure out their momenta.

3. May 27, 2005

### allistair

i worked it out like you said and i was able to get the answer, thx alot, intuitivly the answer just felt a bit wrong.

4. May 27, 2005

### arildno

$$0=p_{1}+p_{2}$$ since the systems total momentum (i.e, 0) must equal the sum of the constituent particles' momenta.