Problem of impact:

Generally, it is noticed that in analyzing the problem of impact there are five unknowns as follows :

 (i) Final velocities V₁′ and V₂′ ,

 (ii) Common velocity Vc at the instant of maximum deformation, and

 (iii) The impulse (I)

(a) during deformation =

(b) during recovery  =    

Though, number of equations involves are only 4 as specified by Eqs. (2) to (5). Newton has mentioned one more experimental - based coefficient called coefficient of restitution (e) which is described as

e is termed as the ratio of impulse during recovery to that during deformation. e values are to be find out experimentally in certain ranges of values of velocity of approach. Table gives the idea of values of e when approach velocity is about 2 to 3 m/sec.

Table: Coefficient of Restitution of Materials