Collisions - Elastic and Inelastic Collisions

During a collision, the objects involved push against each other with strong forces. These forces change the motion of each object individually. However, because there is no external force acting on the entire system, the total momentum of all objects together always stays the same. This principle is called conservation of linear momentum. But while momentum is always conserved during collisions, the total kinetic energy of the system may or may not be conserved. This difference between momentum and energy conservation helps us understand two different types of collisions: elastic collisions and inelastic collisions.

A collision where the kinetic energy of the entire system is conserved during the collision (along with the linear momentum).

OR

The collision in which the total kinetic energy before and after the collision remains the same, and both momentum and kinetic energy are conserved, is called Elastic Collision.

A collision where there is a loss in kinetic energy during the collision, but linear momentum is conserved.

OR

The collision in which the total kinetic energy does not remain constant after collision, is called Inelastic Collision.

\[\sum\vec{p}_{initial}\] = \[\sum\vec{p}_{final}\]

Where:

• \[\sum\vec{p}_{initial}\] = total initial momentum of all objects
• \[\sum\vec{p}_{final}\] = total final momentum of all objects

∑KE_initial = ∑KE_final

Where:

• ∑KE_initial = total initial kinetic energy
• ∑KE_final = total final kinetic energy

∑KE_initial > ∑KE_final

Where:

• The lost kinetic energy is due to internal friction or vibrational motion of atoms, causing a heating effect
• Linear momentum is still conserved: \[\sum\vec{p}_{initial}\] = \[\sum\vec{p}_{final}\]

Elastic Collisions:

• Kinetic energy is conserved (does not change)
• Linear momentum is conserved
• Very rare in everyday life
• Common in atomic and molecular collisions (like in the kinetic theory of gases)
• Both objects rebound from each other

Inelastic Collisions:

• Kinetic energy is lost during the collision
• Linear momentum is conserved
• Very common in everyday life
• Energy is lost as heat due to internal friction or vibration of atoms
• Objects may stick together or deform

The collision in which the particles get stuck together after collision and the loss of kinetic energy is maximum, is called Perfectly Inelastic Collision.

The ratio of the relative velocity of separation to the relative velocity of approach between two colliding objects is called the Coefficient of Restitution.