Elastic and Inelastic Collision in one and two Dimension

In an elastic collision, both kinetic energy and momentum are conserved. The total energy before and after the collision remains constant while in inelastic collisions  momentum is conserved, but kinetic energy is not. Some kinetic energy is converted into other forms of energy such as heat or sound. Understanding these collision types helps in analyzing various physical situations and solving problems in physics.

1.0Definition of Collision

• When two particles approach each other and share common space then their momentum gets redistributed and this phenomenon is called collision.
• Particles approach each other just before collision, means they have velocity of approach
• Particles get separated after collision means they have velocity of separation. 

2.0Line of motion and line of impact

1. Line of motion(LOM): The line along which particles are moving just before collision.

Ex.- 1 Objects moving along same line

Ex. - 2 Objects moving in same plane but along different line

2. Line of impact(LOI):Line along which Transfer  of momentum takes place  it is line along common normal as normal forces are responsible for redistribution of momentum

3.0Type of collision

1. Head-on collision or 1-D collision

• If line of motion and line of impact are same then it is head on collision
• In head on collision particles move along same line before and after collision
• In head on collision initial velocities of colliding objects lie along common normal

2. Oblique collision or 2-D collision

• If line of motion and line of impact are not same then it is Oblique  collision
• In Oblique  collision particles move along different line before and after collision

4.0Process of Collision and Coefficient of Restitution

• To understand the mechanism of a collision, let us consider two balls A and B of masses m_A and m_B moving with velocities u_A and u_B in the same direction as shown. Velocity u_A is larger than u_B so that ball A hits the ball B.
• During the impact, both the bodies push each other and first they get deformed till the deformation reaches a maximum value and then they try to regain their original shapes due to elastic behaviour of the materials the balls formed of.

No external forces Principle of Conservation of Momentum is applicable

• During collision

5.0Deformation period

• The time interval during which deformation takes place.
• During the period of deformation, due to push applied by the balls on each other, speed of ball A decreases and that of ball B increases.
• At the end of the deformation period, when the deformation is maximum both the balls move with the same velocity say it is u. Thereafter, the balls will either move together with this velocity or follow the period of restitution.