What is an inelastic collision? What is a perfectly inelastic collision?

In an inelastic collision, a portion of the kinetic energy is converted to another kind of energy, such as heat or shape deformation.

In an inelastic collision, kinetic energy is lost because a portion of the initial kinetic energy is converted to another kind of energy.

As a result, in an inelastic collision, the internal kinetic energy is not conserved.

In collision the forces are generated in the form of action-reaction force. So the net external force on the system remains zero.The force is defined as rate of change of momentum.So, when net force is zero , change in momentum will be zero or momentum will remain conserve.

\(\begin{aligned}{F_{net}} = \dfrac{{\Delta P}}{{\Delta t}} &= 0\\\dfrac{{{P_{final}} - {P_{initial}}}}{{\Delta t}} &= 0\\{P_{final}} - {P_{initial}} &= 0\\{P_{final}} &= {P_{initial}}\end{aligned}\)

Hence, in an inelastic collision momentum of the system remains conserved while internal kinetic energy does not conserve.

The value of coefficient of restitution (e) in case of inelastic collision lies between 0 to 1.

\(0 < e < 1\)

In perfectly inelastic collision there is complete loss of internal kinetic energy of the system.In such type of collisions,sometimesthe objects stick together.It reduces internal kinetic energy more than any other type of inelastic collision.

The value of coefficient of restitution (e) in case of inelastic collision is zero. So,the velocity of separation of the bodies is zero because they got stuck together.

In this collision the forces are generated in the form of action-reaction force. So the net external force on the system remains zero.Hence, linear momentum of the system remains conserved.

As there is permanent deformation in the shape of the body and release of energy the form of heat.Hence the total internal kinetic energy of the system does not conserve in perfectly inelastic collision.