How do you calculate the coefficient of restitution?

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How do you calculate the coefficient of restitution?

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Answer 1 · 2015-04-19T17:26:31

The coefficient of restitution often denoted $e$ $e$ can be found with some notion of Newton's Experimental Law.

This law states that: "in a system of colliding bodies(usually 2 bodies) the relative velocity of separation is directly proportional to the relative velocity of approach".

Mathematically expressed, $V_{A} - V_{B} α U_{A} - U_{B}$ $V_A-V_B alpha U_A-U_B$
$or V_{B} - V_{A} α U_{B} - U_{A}$ $or V_B-V_A alpha U_B-U_A$
For a system of colliding bodies $A$ $"A"$ and $B$ $"B"$

The constant of proportionality is $- e$ $-e$
Thus we have,

$V_{A} - V_{B} = - e (U_{A} - U_{B})$ $V_A-V_B =-e (U_A-U_B)$

$\Rightarrow e = - \frac{V_{A} - V_{B}}{U_{A} - U_{B}}$ $=> e=-(V_A-V_B)/( U_A-U_B )$

Thus, all you need to calculate e are the respective initial and final velocities of the two bodies involved in collision.

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How do you calculate the coefficient of restitution?

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