# Math Help - [SOLVED] Collision of particles - coefficient of restitution

1. ## [SOLVED] Collision of particles - coefficient of restitution

If there is a particle X of mass 3m which is moving with velocity Ui on a smooth horizontal table and it collides with a particle Y of mass 5m which is at rest (and we are given that the coefficient of restitution between the particles is e, then how can I find the velocities of X and Y immediately after the collision in terms of e and u?

Also is there a way of showing the speed of X immediately after the collision does not exceed 3u/8 for all values of e?

2. Originally Posted by moolimanj
If there is a particle X of mass 3m which is moving with velocity Ui on a smooth horizontal table and it collides with a particle Y of mass 5m which is at rest (and we are given that the coefficient of restitution between the particles is e, then how can I find the velocities of X and Y immediately after the collision in terms of e and u?
$\text{Coefficient Of Restitution (e)} = \frac{\text{Velocity of Seperation}}{\text{Velocity of Approach}}$

You are told that particle Y is at rest hence $U_y = 0$.

$e = \frac{V_x + V_y}{U} \implies V_x+V_y = eU \ \ \ ---(1)$

Also, by Conservation of Linear Momentum; Momentum Before = Momentum After. Therefore:

$(3m)(U) + (5m)(0) = (3m)(V_x) + (5m)(V_y) \implies 3U = 3V_x + 5V_y \ \ \ ---(2)$

Solve The simultaneous equation to get Velocity of $x$ and $y$ in terms of $e$ and $U$.

3. Originally Posted by moolimanj
Also is there a way of showing the speed of X immediately after the collision does not exceed 3u/8 for all values of e?

Depending on your result for $V_x$, you may get a negative answer which will mean that the particle has changed direction. This implies that you can produce an inequality where $V_x \le 0$ and when solved you should get it to show that it does not exceed $\frac{3u}{8}$
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Also, you can see this thread which has a similar question that I posted once and received help on: http://www.mathhelpforum.com/math-he...stitution.html