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Question
A ball of mass m, moving with a speed 2v0, collides inelastically (e > 0) with an identical ball at rest. Show that for head-on collision, both the balls move forward.
Solution
Let v1 and v2 be the velocities of the two balls after a collision.
Now, by the principle of conservation of linear momentum,
2mv0 = mv1 + mv2
or 2v0 = v1 + v2
And e = `(v_2 - v_1)/(2v_0)`
⇒ v2 = v1 + 2v0e
∴ 2v1 = 2v0 – 2ev0
∴ v1 = v0 (1 – e)
Since, e < 1 ⇒ v1 has the same sign as v0, therefore, the ball moves on after collision.
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Answer carefully, with reason:
Is the total linear momentum conserved during the short time of an inelastic collision of two balls ?
