Suppose we have a frictionless surface and a small particle of mass $m$ which collides with velocity of $V$ with stationary particle of $2m$ elastically. I know how to deal with this simple problem here but I have got a confusion regarding coefficient of resistitution equation . Firstly I wrote equation of linear momentum conservation
$$mV=2mV_1 + mV_2$$
Now I can conserve kinetic energy but I want to write other equation using resistitution coefficient(after all I can avoid squares )
$$e=\frac{v_{separation}}{v_{approach}}$$
Now here $e=1$(elastic collision )
So what will be second equation ?
$$V=V_2-V_1$$
Or
$$V=V_1-V_2$$
This is confusing me too much
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The coefficient of restitution $e$ is defined in a way that $$-ev_{app}=v_{sep}$$ where $v_{app}$, $v_{sep}$ are relative velocities of approach and seperation respectively.
From this, you get, $-eV=V_2-V_1$ and consequently, (since $e=1$ for elastic collisions), $V=V_1-V_2$.
answered Feb 16, 2015 at 14:11