Question

What are collisions ? Explain the possible types of collisions? Develop the theory of one dimensional elastic collision?

Answer 1

Collision: event in which 2 or more bodies exert forces on each other in a relatively short time
OR
Incidents in which 2 or more objects collide with greater force



Elastic collision : encounter between 2 bodies in which total kinetic energy of the 2 bodies remain the same
Inelastic collision : in which a part of kinetic energy is changed to some other form of energy in collision

Answer 2

Explanation:

Collisions : A strong interactions between bodies that occurs for a very short interval during which redistribution of momenta occur ignoring the effect of other forces are called collisions. Collisions are of two types : i) Elastic collision : The collision in which both momentum and kinetic energy is constant is called elastic collision. ii) Inelastic collision: The collision in which momentum remains constant but not kinetic energy is called Inelastic collision. Elastic collision in one dimension : Consider two smooth, nonrotating spheres of masses m1 and m2 moving along a straight line which coincides with the line joining their centres of mass. They are moving in the same direction with initial velocities u1 and u2 and after collision the two bodies move with final velocities v1 and v2 respectively in the same direction. Let the colli sion be elastic in nature. Hence both momentum and kinetic energy are conserved. According to law of conservation of linear momentum. m1u1 + m2u2 = m1v1 + m2v2, m1 (u1 – v1) = m2 (v2 + u2) ––– (1) According to law of conservation of kinetic energy ...(2) u1 + v1 = v2 + u2, u1 – u2 = v2 – v1 ––– (3) In one dimensional elastic collision, the relative velocity before collision is equal to the relative velocity of separation after collision. From equation (3) u1 – u2 = – v1 + v2, v2 = u1 – u2 + v1 ––– (4) Sub equation (4) in equation (1) we get m1 (u1 – v1) = m2(u1 – u2 + v1 – u2), m1u1 – m1v1 = m2 u1 – 2m2 u2 + m2 v1 m1 u1 – m2 u1 + 2m2 u2 = m1 v1 + m2 v1, (m1 – m2) u1 + 2m2 u2 = (m1+m2) v1 v1 = ...(5) From the equation (4), v1 = v2 – u1 + u2 Sub. this value in equation (1)