Answer to Question #149526 in Mechanics | Relativity for Mikkos Joshua Garcia

Question

Relate the concept of restitution to the colliding star in the universe?

Answer 1

In physics, a collision takes place when particles, aggregates of particles, or solid bodies move toward each other and come near enough to interact and exert a mutual influence

A stellar collision is the coming together of two stars caused by stellar dynamics within a star cluster, or by the orbital decay of a binary star due to stellar mass loss or gravitational radiation, or by other mechanisms not yet well understood.

When the only forces on the colliding bodies are those exerted by the bodies themselves, the principle of conservation of momentum states that the total momentum of the system is unchanged in the collision process.

Based on whether mechanical energy (and thus, kinetic energy) is conserved or not conserved, collisions are classified as elastic or inelastic, respectively.

The coefficient of restitution indicates how elastic or inelastic the collision is. A coefficient of restitution equal to zero indicates a perfectly inelastic collision, in which the colliding bodies stick together after the collision

In classical mechanics, collision problems are concerned with the relation of the magnitudes and direction of the velocities of colliding bodies after collision to the velocity vectors of the bodies before collision. When the only forces on the colliding bodies are those exerted by the bodies themselves, the principle of conservation of momentum states that the total momentum of the system is unchanged in the collision process. This result is particularly useful when the forces between the colliding bodies act only during the instant of collision. The velocities can then change only during the collision process, which takes place in a short time interval. Under these conditions the forces can be treated as impulsive forces, the effects of which can be expressed in terms of an experimental parameter known as the coefficient of restitution, which is discussed later

Consider a one-dimensional collision of two particles in which the particles have masses m₁ and m₂ and initial velocities u₁ and u₂. If they interact only during the collision, an application of the principle of conservation of momentum fields Eq

$m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2$

where ν₁ and ν₂ are the velocities of m₁ and m₂, respectively, after collision.

It has been found experimentally that in collision processes, the following Eq holds:

$e = \frac{v_1-v_2}{u_1-u_2}$ here In the equation, e is a constant known as the coefficient of restitution, the value of which depends on the properties of the colliding bodies