Collision of Two Bodies:
Consider the impact between two bodies that move with different velocities along the same straight line. It is assumed that the point of the impact lies on the line joining the centers of gravity of the two bodies. The behavior of these colliding bodies during the complete period of impact will depend upon the properties of the materials of which they are made. The material of the two bodies may be perfectly elastic or perfectly inelastic.
In either case, the first effect of an impact is approximately the same. The parts of each body adjacent to the point of impact are deformed and the deformation will continue until the center of gravity of the two bodies is moving with the same velocity. Assuming that there are no external forces acting on the system, the total momentum must remain constant.
Collision of Elastic Bodies:
When two inelastic bodies A and B as shown in fig (1):
moving with different velocities, collide with each other as shown in fig(2). The two bodies will remain together after impact and will move together with a common velocity.
m1 = Mass of first body A.
m2 = Mass of second body B.
u1 and u2 = velocities of bodies A and B respectively before impact
v = common velocity of bodies A and B after impact.
Collision of Inelastic Bodies:
When two elastic bodies as shown in fig(1), collide with each other, they suffer a change of form. When the bodies first touch, the pressure between them is zero. For a short time thereafter, the bodies continue to approach each other and the pressure exerted by one body over the other body increases. Thus the two bodies are compressed and deformed at the surface of contact due to their mutual pressures.
If one of the bodies is fixed then the other will momentarily come to rest and then rebound. However, if both bodies are free to move, then each body will momentarily come to rest relative to the other. At this instant, the pressure between the two bodies is maximum and the deformation is also maximum.