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Elastic Collision

An elastic collision is a collision in which the total Kinetic Energy of the system remains constant before and after the interaction. In such collisions, both Momentum and kinetic energy are conserved. This contrasts with Inelastic Collision, where some kinetic energy is transformed into other forms, such as heat or deformation.

Key Characteristics

• Conservation Laws:
  • Total momentum: ${\vec{p}}_{initial}={\vec{p}}_{final}$
  • Total kinetic energy: $K_{initial}=K_{final}$
• Coefficient of Restitution ($e$): For perfectly elastic collisions, $e=1$. The relative speed of separation equals the relative speed of approach.
• Idealization: True elastic collisions are rare in macroscopic systems due to inevitable energy dissipation via sound, heat, or internal friction. They are best approximated by interactions between subatomic particles or rigid bodies with negligible deformation.

Common Examples & Applications

• Billiard balls (approximate elasticity)
• Atomic and molecular scattering
• Newton’s Cradle demonstrations

Complexities and Paradoxes

While ideal elastic collisions follow straightforward conservation laws, real-world scenarios involving multiple elastic objects can exhibit counterintuitive behaviors due to energy transfer dynamics and material properties.

• The Paradox of Zero Bounce: Combining two highly elastic objects does not guarantee an optimal rebound. Specific configurations can result in minimal or zero bounce despite high individual elasticity.
  • See: The Paradox of Zero Bounce from Similarly Elastic Objects
  • Source: The Paradox of Zero Bounce from Similarly Elastic Objects (Steve Mould, “2 Bouncy Things. Zero Bounce.“)

Related Concepts

• Conservation of Momentum
• Kinetic Energy
• Coefficient of Restitution
• Inelastic Collision