- #1

bobdavis

- 19

- 8

By rearranging terms this seems to be equivalent to $$v_1 = \frac{p}{\bar{m}}-u_1$$$$v_2 = \frac{p}{\bar{m}}-u_2$$ where ##p = m_1u_1+m_2u_2## is total momentum and ##\bar{m} = \frac{m_1+m_2}{2}## is average mass.

The term ##\frac{p}{\bar{m}}## seems to be the same as ##2v_c## where ##v_c## is the velocity of the center of mass of the system. By substituting this into the formula and rearranging it seems the formula is equivalent to $$\bar{v}_1=v_c$$$$\bar{v}_2=v_c$$ where ##\bar{v}_i=\frac{u_i+v_i}{2}## is the average of the initial and final velocities of particle ##i##

Are these alternative formulas correct and if so is there a good way to physically interpret these alternative formulas and the "momentum over average mass" term? If these formulas are correct is there a reason the seemingly more complex standard formula is used instead?