The coefficient of restitution (COR), often denoted as “e,” is a measure of the elasticity of a collision between two objects. It quantifies how “bouncy” or “springy” a collision is. The coefficient of restitution ranges from 0 to 1, with different values indicating different types of collisions:

1. Perfectly Elastic Collision (e = 1): In a perfectly elastic collision, the two objects rebound from each other with no loss of kinetic energy. This means that the relative speed of separation after the collision is the same as the relative speed of approach before the collision. The COR for perfectly elastic collisions is 1.
2. Inelastic Collision (0 < e < 1): In an inelastic collision, the two objects collide and may stick together or separate with a loss of kinetic energy. The COR for inelastic collisions falls between 0 and 1, indicating that some kinetic energy is lost during the collision. The smaller the COR, the less elastic the collision.
3. Perfectly Inelastic Collision (e = 0): In a perfectly inelastic collision, the two objects collide and stick together, moving as one mass after the collision. There is a complete loss of kinetic energy, and the COR is 0. This represents the least elastic type of collision.

The coefficient of restitution depends on various factors, including:

• Nature of the Materials: The materials and their physical properties involved in the collision play a significant role. Objects made of different materials will have different COR values.
• Surface Conditions: The roughness or smoothness of the surfaces in contact can affect the COR. Rough surfaces tend to result in lower COR values.
• Relative Speeds: The initial speeds and directions of the colliding objects also influence the COR. Higher relative speeds tend to result in a lower COR.
• Angles of Collision: The angle at which the objects collide can affect the COR. Collisions that are head-on (perpendicular) tend to have different COR values compared to collisions at an angle.

To summarize:

• Perfectly Elastic Collision: e=1e=1
• Inelastic Collision: 0<e<10<e<1
• Perfectly Inelastic Collision: e=0e=0

The coefficient of restitution is a useful concept in physics and engineering for analyzing the behavior of objects during collisions, and it helps determine how much kinetic energy is conserved or lost in a collision.