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

  1. #1
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    [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?
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  2. #2
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    Quote Originally Posted by moolimanj View Post
    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.
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  3. #3
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    Quote Originally Posted by moolimanj View Post
    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
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