Elastic and Inelastic Collisions
In all collisions the total linear momentum is conserved; the initial momentum of the system is equal to the final momentum of the system. One can argue this as follows. when two objects collide, the mutual impulsive forces acting over the collision time Δt cause a change in their respective momenta:
Δp1 = F12Δt
Δp2 = F21Δt
where F12 is the force exerted on the first particle by the second particle. F21 is likewise the force exerted on the second particle by the first particle. Now from Newton’s Third Law, F12 = –F21. This implies
Δp1 + Δp2 = 0
The above conclusion is true even though the forces vary in a complex fashion during the collision time Δt. Since the third law is true at every instant, the total impulse on the first object is equal and opposite to that on the second.
On the other hand, the total kinetic kinetic energy of the system is not necessarily conserved. The impact and deformation during collision may generate heat and sound. Part of the initial kinetic energy is not transformed in to other forms of energy. A useful way to visualize the deformation during collision is in terms of a ‘compressed spring’. If the ‘spring’ connecting the two masses regains its original shape without loss in energy, then the initial kinetic energy during the collision time Δt is not constant. Such a collision is called an elastic collision. On the other hand the deformation may not be relieved and the two bodies could move together after the collision. A collision in which the two particles move together after the collision is called a completely inelastic collision. The intermediate case where the deformation is partly relieved and some of the initial kinetic energy is lost is more common and is appropriately called an inelastic collision.