- #1
Xyius
- 508
- 4
Homework Statement
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.
Homework 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]
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? :(??