This is the very definition of elastic collision.
By definition, elastic collision means the collision in which there are no dissipations due to heat, plastic deformation, sound waves, etc.
So, by conservation of energy, we mean that the initial kinetic energy before the collision is equal to the kinetic energy after the collision, because it is not converted to any other type of energy.
If two particles with kinetic energies E1 and E2 and momentum P1 and P2 collide, then their energies and momentum after the collision would follow the
report :-
E1*+E2*=E1+E2 . . . (1)
P1*+P2*=P1+P2 . . . (2)
Equation 1 does not hold if the collision is an inelastic collision while Relation 2 holds whether the collision is an elastic collision or not, but the question is why?
Dr Abbas,
In an inelastic collision some of the kinetic energy of the moving parts is converted into heat - if you expand your first equation to account for that you'll find that the total energy is still conserved.
Because, There can be other forms of energies that are not necessarily kinetic energies, but there can be (at least classically) no other form of momentum in 2-body system where the momentum is not contributed by momenta of the two bodies involved (I do not know whether shockwaves in the particles would have some momenta or not, but if I do not go to the level of phonons, i think such contribution is practically zero)
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