First slide

Coefficient of restitution

Question

A ball A moving with a certain velocity collides with another ball B of the same mass at rest. If the coefficient of restitution is e, the ratio of the velocities of A and B just after the collision is

Moderate

A

1 + e / 1 - e
B

1 + e / 2
C

(1 - e )/ 2
D

1 - e / 1+ e

Solution

$\large {v_1} = \left( {\frac{{{m_1} - e{m_2}}}{{{m_1} + {m_2}}}} \right)u\;;{v_2} = \frac{{\left( {1 + e} \right){m_1}{u_1}}}{{{m_1} + {m_2}}}$
$\large \frac{{{v_1}}}{{{v_2}}} = \frac{{1 - e}}{{1 + e}}\$
Alternative Method :
Conserving Momentum
mV₁ + mV₂ = mu₁ + m X 0
⇒ V₁ + V₂ = u₁ ........................ (1)
Also V₂ - V₁ / u₁ = e ⇒ V₂ - V₁ = e u₁ ................. (2)
Sloving , V₂ = (1+e) u₁ / 2 ; (1+e) u₁ / 2

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