A ball of mass m, moving with a speed 2v₀, collides inelastically (e > 0) with an identical ball at rest. Show that
(a) For head-on collision, both the balls move forward.

(b) For a general collision, the angle between the two velocities of scattered balls is less than 90°.

Question

Philoid · Accepted Answer

a) In this problem if we prove that both the velocities after collision is positive will be enough to prove part a)

Conserving momentum,

---(1)

Where are the velocity of both the ball

Putting equation 1 in above equation we get,

from this we get,

∵

For first inequality, ------(2)

From second inequality, -------(3)

Combining (2) and (3),

We get,

∵ after collision both the velocities are positive

∴ both the balls move in same forward direction.

b)

Let p_o be initial momentum and p₁and p₂be the momentum of ball 1 and 2 respectively after collision. (here bold text means vector)

In inelastic collision,

Conserving momentum,

By vector addition of momentums, we get,

-----(1)

But ∵ there is a loss in kinetic energy

∴

----- (2)

From equation (1) we can write equation (2) as,

-------- (3)

∴ the angle between the two velocities of scattered balls is less than 90°.

A ball of mass m, moving with a speed 2v0, collides inelastically (e > 0) with an identical ball at rest. Show that(a) For head-on collision, both the balls move forward.(b) For a general collision, the angle between the two velocities of scattered balls is less than 90°.