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On the basis of conservation of kinetic energy

Perfectly elastic collision If in a collision, kinetic energy after collision is equal to kinetic energy before collision, the collision is said to be perfectly elastic.
Coefficient of restitution, e = 1
(KE)final = (KE)initial
  • Collision between atomic particles.
  • Bouncing of ball with same velocity after the collision with Earth.
Inelastic collision If in a collision kinetic energy after collision is not equal to kinetic energy before collision, the collision is said to inelastic.
Coefficient of restitution, 0 < e < 1
Here kinetic energy appears in other forms. In some cases, (KE)final < (KE)initial such as when initial KE is converted into the internal energy of the product (as heat, elastic or excitation) while in other cases (KE)final > (KE)initial such as when internal energy stored in the colliding particles is released.
  • Collision between two billiard balls.
  • Collision between two automobile on a road.
In fact all majority of collision belong to this category.
Perfectly inelastic collision If in a collision two bodies stick together or move with same velocity after the collision, the collision is said to be perfectly inelastic.
Coefficient of restitution, e = 0
The term “perfectly inelastic” does not necessarily mean that all the initial kinetic energy is lost, it implies that the loss in kinetic energy is as large as it can be. (Consistent with momentum conservation).

Collision between a bullet and a block of wood into which it is fired, when the bullet remains embedded in the block.


On the basis of the direction of colliding bodies

Head-on or one-dimensional collision In a collision if the motion of colliding particles before and after the collision is along the same line, the collision is said to be head-on or one-dimensional.
Impact parameter b is zero for this type of collision (Fig. 2).
Fig. 2

Collision of two gliders on an air track.


Oblique collision If the collision of two particles glancing, such that their directions of motion after collision are not along the initial line of motion, the collision is called oblique.
If in oblique collision the particles before and after collision are in same plane, the collision is called two-dimensional otherwise three-dimensional.
Impact parameter b lies between 0 and (r1 + r2), i.e., 0 < b < (r1 + r2), where r1 and r2 are radii of colliding bodies.
Fig. 3

Collision of billiard balls.


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