9.9:
Elastic Collisions: Introduction
Elastic collision of a system necessitates the conservation of momentum and the kinetic energy of the system.
Consider a one-dimensional collision between two marbles A and B. Marble A rolls along the positive x-axis and collides with marble B moving in the same line. The final velocities of the marbles change due to the collision, but they lie in the same line.
Since momentum is conserved, the sum of the momenta of the marbles A and B will be equal before and after the collision.
As the kinetic energy of the system is also conserved, the sum of the kinetic energies of the marbles will be equal before and after the collision.
Based on the equations obtained, if the mass of the marbles and the initial velocities are known, the final velocities can be obtained by solving the equations.
9.9:
Elastic Collisions: Introduction
An elastic collision is one that conserves both internal kinetic energy and momentum. Internal kinetic energy is the sum of the kinetic energies of the objects in a system. Truly elastic collisions can only be achieved with subatomic particles, such as electrons striking nuclei. Macroscopic collisions can be very nearly, but not quite, elastic, as some kinetic energy is always converted into other forms of energy such as heat transfer due to friction and sound. An example of a nearly macroscopic collision is that of two steel blocks on ice. Another nearly elastic collision is between two carts with spring bumpers on an air track. Icy surfaces and air tracks are nearly frictionless, more readily allowing nearly elastic collisions on them.
To solve problems involving one-dimensional elastic collisions between two objects, we can use the equations for conservation of momentum and conservation of internal kinetic energy. Firstly, the equation for conservation of momentum for two objects in a one-dimensional collision implies that the momentum of the system before and after the collision is equal. Secondly, an elastic collision conserves internal kinetic energy, and so the sum of kinetic energies before the collision equals the sum after the collision.
This text is adapted from Openstax, University Physics Volume 1, Section 9.4: Types of Collisions.