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The 'e' Equation

Sphere of mas...

Question

Sphere of mass $m_{1} = 3 k g$ impinges with a velocity of $7 m / s$ directly on another sphere of mass $m_{2} = 5 k g$ at rest. The velocities after impact are in the ratio $2 : 3$ . Find the coefficient of restitution and loss of energy.

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Solution

By applying conservation of linear momentum
$m_{1} V_{1} + m_{2} V_{2} = m_{1} V_{1}^{1} + m_{2} V_{2}^{2}$
$\Rightarrow 3 \times 7 = 3 (2 x) + 5 (3 x)$
$\Rightarrow 21 = 21 x$
$\Rightarrow x = 1$ As final velocity $2 m / s$ and $3 m / s$
$e = \frac{v_{1} - v_{2}}{v_{2}^{1} - v_{1}^{2}}$
$= \frac{7 - 0}{3 - 2}$
$= 7$ .

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