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Dynamics -Key concepts 4

Direct Central Impact
A collision is an isolated event in which two or more moving bodies (colliding bodies) exert forces on each other for a relatively short time. A high force applied over a short time period when two or more bodies collide is called as Impact.
Types of Impact
1.Elastic Impact
2.Plastic Impact or Inelastic Impact
If the two objects adhere and remain connected after the impact, the impact is said to be perfectly plastic.
Coefficient of Restitution
During the impact, each object can lose energy This loss in energy can be expressed as the difference in velocity after the collision divided by the difference in velocity before the collision, or

The prime velocities, vB' and vA' are velocities after the collision. The coefficient of restitution is a measure of the energy that is lost during a collision. 
For a perfectly elastic collision (e = 1), no energy is lost. The Coefficient of Restitution for small rubber balls is very close to one, which makes them very bouncy and fun to play with.
In a perfectly inelastic collision,The coefficient of restitution (e = 0) the colliding particles stick together. and move with same velocity V
 It is necessary to consider conservation of momentum:
m_a \mathbf u_a + m_b \mathbf u_b = \left( m_a + m_b \right) \mathbf v \,
where v is the final velocity, which is hence given by
\mathbf v=\frac{m_a \mathbf u_a + m_b \mathbf u_b}{m_a + m_b}
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