How can I prove an elastic collision?
Using two ways:
If the total energy of a system of particles after collision is equal to the total energy after collision.
This method is called the law of conservation of energy.
Many time i case of simple collision we take the mechanical energy,This would be enough for school level purposes.
But in case ,we take the collision of Neutrons or the collision at the subatomic level,we take into account the nuclear forces and their work,gravitational work. etc.
Hence in simple we can assert that during Any elastic collision in universe ,no Energy is Lost.
In this method we use the Newtons law of Restitution.
Firstly we state it.
It states that during any collision the Ratio of Relative velocity of separation after collision of the system of particles to The relative velocity of approach of system of particles is a constant,called the coefficient of restitution.
In This specific case this coefficient of restitution has a value of one.