Give two points of difference between elastic and inelastic collisions

Give two points of difference between elastic and inelastic collisions. Two balls A and B with A in motion initially and B at rest. Find their velocities after assume collision is elastic. Each ball is off mass ‘m’.

Answer»

S.No.	Elastic collisions	Inelastic collisions
(i)	K.E. is conserved	K.E. is not conserved.
(ii)	Forces involved must be conservative.	Some or all forces involved may be nonconservative.

Mass of ball A and B = m

Initial velocity of ball A = u₁ = v

Initial velocity of ball B = u₂ = 0

Final velocity of ball A = v₁ and of ball B = v₂

According to conservation of momentum

mv + m₂(0) = mv₁ + mv₂

mv = mv₁ + mv₂ …....(i)

Conservation of K.E.

\(\frac{1}{2}mv^2=\frac{1}{2}mv^2_1+\frac{1}{2}mv^2_2\)

\(mv^2=mv^2_1+mv^2_2\)

\(m(v^2-v^2_1)=mv^2_1\)

From (i) m(v - v₁) = mv₂ ......(ii)

Dividing equation (ii) by (i),

\(\frac{m(v+v_1)(v-v_1)}{m(v-v_1)}=\frac {mv^2_2}{mv_2}\)

or v₂ = v + v₁

Substituting in (i)

mv = mv₁ + m(v + v₁)

or v₁ = 0

Similarly solving v₂ = v

i. e., Ball A stops and ball B starts moving with velocity v, i. e., they exchange their velocities on collision.