Coefficient of Restitution

Definition

The coefficient of restitution is a measure of the elasticity of a collision between two objects. It quantifies the ratio of the relative velocity of the objects after the collision to the relative velocity before the collision, and is used to determine the energy lost during the impact.

5 Must Know Facts For Your Next Test

1. The coefficient of restitution, denoted as 'e', ranges from 0 to 1, with 0 representing a perfectly inelastic collision and 1 representing a perfectly elastic collision.
2. In an elastic collision, the coefficient of restitution is 1, meaning the relative velocity of the objects after the collision is equal to the relative velocity before the collision.
3. The coefficient of restitution is used to determine the energy lost during an inelastic collision, as the kinetic energy lost is proportional to (1 - e^2).
4. The coefficient of restitution is an important factor in the analysis of collisions, as it affects the final velocities of the objects involved and the energy dissipated during the impact.
5. The coefficient of restitution can be measured experimentally by observing the relative velocities of the objects before and after a collision.

Review Questions

• Explain how the coefficient of restitution is used to determine the energy lost in an inelastic collision.
  • The coefficient of restitution, denoted as 'e', is a measure of the elasticity of a collision. In an inelastic collision, where kinetic energy is not conserved, the amount of energy lost is proportional to (1 - e^2). The closer the coefficient of restitution is to 0, the more energy is lost during the collision, as the objects will deform or stick together. Conversely, the closer the coefficient of restitution is to 1, the more elastic the collision, and the less energy is lost.
• Describe the relationship between the coefficient of restitution and the conservation of momentum in a collision.
  • In a collision, the total momentum of the system is conserved, regardless of the coefficient of restitution. However, the coefficient of restitution does affect the final velocities of the objects involved. In an elastic collision, where e = 1, the relative velocity of the objects after the collision is equal to the relative velocity before the collision. In an inelastic collision, where e < 1, the relative velocity after the collision is less than the relative velocity before the collision, indicating a loss of kinetic energy.
• Analyze how the coefficient of restitution influences the behavior of collisions in one-dimensional and two-dimensional scenarios.
  • The coefficient of restitution plays a crucial role in the analysis of collisions in both one-dimensional and two-dimensional scenarios. In one-dimensional elastic collisions, the coefficient of restitution determines the final velocities of the objects, with the relative velocity after the collision being equal to the relative velocity before the collision. In one-dimensional inelastic collisions, the coefficient of restitution affects the amount of kinetic energy lost and the final velocities of the objects. In two-dimensional collisions, the coefficient of restitution, along with the collision geometry, determines the final velocities and trajectories of the objects involved, which is essential for understanding the dynamics of collisions in more complex scenarios.

Related terms

Elastic Collision: A collision in which there is no net loss of kinetic energy, and the total momentum is conserved.

Inelastic Collision: A collision in which kinetic energy is not conserved, and the colliding objects stick together or deform permanently.

Momentum: The product of an object's mass and velocity, which is conserved in an isolated system.