(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A particle of mass m approaches a stationary particle of mass 3m. They bounce off elastically. Assume 1D. Find the final velocities using the center of mass coordinate system.

2. Relevant equations

(All quantities with r or v are vectors r1 and r2 represent the vectors from the origin to each particle.)

Coordinates of the Center of mass vector.

[tex]R=\frac{m_1v_1+m_2v_2}{m_1+m_2}[/tex]

Coordinates from vector 2 to vector 1

[tex]r=r_1-r_2[/tex]

Inverse transformations

[tex]r_1=R+\frac{m_2}{m_1+m_2}[/tex]

[tex]r_2=R+\frac{m_1}{m_1+m_2}[/tex]

3. The attempt at a solution

Those equations are from my notes/book. I applied them so..

[tex]r^{CM}_1=r_1-R[/tex]

and

[tex]r^{CM}_2=r_2-R[/tex]

I really do not know how to solve for velocities this way. It is late and maybe I am having a brain fart but how am I supposed to use the conservation of momentum relation to find velocity if it always equals zero in this coordinate system? All I have to work with is the conservation of energy. Can anyone help me out? :(??

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# Collisions in Center-of-Mass coordinates

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