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Elastic Collisions

A perfectly elastic collision is sometimes defined as a collision in which the kinetic energy of the system remains conserved. Let us express the kinetic energy as the sum of kinetic energy k_t due to tangential components of the velocity and k_n due to normal components of velocity. That is, initially, we have

= k_n + k_in

Now, we find that,

= k_it

Let us look at the normal components; in elastic collision, e = 1, and hence

Now, we have

Substituting for v_1n and v_2n from above, we find

= k_fn

Thus, we have, k_f = k_ft + k_fn = k_f

i.e. the total final kinetic energy of the colliding particles remains equal to their initial kinetic energy in a perfectly collision (e = 1).