ELASTIC COLLISIONS & INELASTIC COLLISIONS

In collisions and explosions, forces act through distances so kinetic energy is rarely conserved even though the total energy and momentum is. We are concerned with kinetic energy in explosions and collisions. We classify collisions into elastic and inelastic.

"Elastic" means "returns exactly to original shape".

Within limits, glass and metals are elastic and return to their original shape. Imagine an aircraft wing if it was not elastic!

During elastic collisions, no heat is generated through deformation of the materials involved, neither is sound or any other energy "loss" process. It follows that kinetic energy remains fixed before and after the collision. In elastic collisions, both momentum and kinetic energy are conserved, one, a vector statement, the other a scalar statement.

One peculiar case of elastic collisions is when the colliding objects have identical mass such as proton into proton in low energy collisions. Similarly, billiard balls collide approximately elastically.

Exactly head on leads to the first stopping and the other moving off - Newton's Cradle.

Off axis collisions between identical masses separate at 90⁰.

This is shown using the vector momentum triangle and the scalar equation of E_k. We show Pythagoras' Theorem holds.

Let the mass of both solids be m. In a simple situation, let one mass be stationary while the other is moving towards it at a velocity v.

After the collision, let one move off at v₁, the other at v₂.

Then, the above momentum triangle holds and also, as it is elastic;

1/2 mv² = 1/2 mv₁² + 1/2 mv₂², so , cancelling the 1/2 and multiplying everything by m,

we have (mv)² = (mv₁)² + (mv₂)²

This is Pythagoras' Thm so the angle of separation is 90⁰ !

A completely inelastic collision is one like plasticene or putty sticking to a wall after being thrown. Just about all kinetic energy is lost to heat.

Completely inelastic collisions occur when the colliding objects stick together. Maximum E_k is lost.