Short theory

THE IMPACT is interaction of two or more bodies that takes place during a very short time. A magnitude of internal forces appearing in bodies system during the impact is relatively big, so the external forces acting on the bodies at this moment of time can be neglected. This enables to apply the law of conservation of momentum (law of conservation of impulse) for studying the phenomena of the body’s collision because a system of interacting bodies is isolated

PERFECTLY ELASTIC IMPACT is interaction of two bodies acting with elastic forces at each other, no mechanical energy of the system being transformed into thermal energy (heat). In this case we can apply both the law of conservation of momentum and mechanical energy.

PERFECTLY INELASTIC IMPACT is interaction of two bodies resulting in partial transformation of the mechanical energy into heat. The bodies move after collision as whole body. In this case we can not apply the law of conservation of mechanical energy, but we can apply the law of conservation of momentum and total energy of system. Hence we may write:

a) for perfectly elastic impact

,

,

where m₁ and m₂ are the masses of interacting bodies; V₁ and V₂ are the velocities of the bodies before the impact; and are the velocities of the same bodies after the impact.

b) for perfectly inelastic impact

,

,

where U is the velocity of the bodies system after the impact; Q = E₁ – E₂ is the mechanical energy turned into heat (E₂ and E₁ are the mechanical energy of the system before and after the impact.