2. What is elastic collision? Explain with reason what will happen when
a). a heavy body collides with a light body at rest.
b). alight body collides with aheavy body at rest.

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Solution

Let us assume two bodies:
masses : m1 & m2
initial velocity: u1 & u2
final velocity: v1 & v2
Elastic Collision
In collision if the kinetic energy of the collision before collision is equal to kinetic energy after the collision.
or
velocity of approach = velocity of separation
Condition:

No external impulse acting.

No friction acting.

Duration of collision small.

Let us assume two bodies:
masses : m₁ & m₂
initial velocity: u₁& u₂
final velocity: v₁ & v₂
They undergo collision:
Linear momentum balance:
m₁u₁+ m₂u₂ = m₁v₁ + m₂v₂
Kinetic Energy balance
1/2 m₁u₁² +1/2 m₂u₂² = 1/2 m₁v₁² + 1/2 m₂v₂²
If collision is elastic
velocity of approach = velocity of separation
u₁-u₂ = v₂-v₁

So if collision is elastic and you solve the momentum and energy equations you will get v₁ & v₂ as:
$v_{1} = \frac{(m_{1} - m_{2}) u_{1}}{m_{1} + m_{2}} + \frac{2 m_{2} u_{2}}{m_{1} + m_{2}} v_{2} = \frac{2 m_{1} u_{1}}{m_{1} + m_{2}} + \frac{(m_{1} - m_{2}) u_{2}}{m_{1} + m_{2}}$

a). a heavy body collides with a light body at rest.
m₁>>>>m₂
u₂=0
So from the above formula:
v₁ = u₁
v₂ = 2u₁

b). a light body collides with a heavy body at rest.
m₂>>>>>>m₁
u₂=0
v₁ = -m₂/m₂ * u₁ +0 = -u₁
v₂=0

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