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Velocity of COM

Two spheres o...

Question

Two spheres of masses 1 kg and 2 kg are moving with velocities of 10 m/s and 5 m/s respectively in the same direction. After the collision the velocity of the lighter sphere decreases by 4 m/s. Find the velocity of the heavier sphere after collision and calculate the coefficient of restitution.

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Solution

$m_{1} u_{1} - m_{2} u_{2} = m_{1} v_{1} - m_{2} v_{2}$ $m_{1} = 1 k g u_{1} = 10 m l$
$1 \times 10 - 2 \times 5 = 1 \times 4 - 2 \times v_{2}$ $m_{2} = 2 k g u_{2} = 5 m l$
$0 = 4 - 2 v_{2}$ $v_{1} = 4 m / s v_{2} = ?$
$2 v_{2} = u v_{2} = 2$
$∴$ The velocity of heavier sphere is $2 m / s$

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