Elastic Collision Calculator

Calculate Parameters for Elastic Collisions

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Final Velocities Calculator

Calculate final velocities in an elastic collision

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Energy Conservation Verifier

Verify energy conservation in an elastic collision

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One-Dimensional Collision Calculator

Calculate parameters for head-on elastic collisions

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Understanding Elastic Collisions

What is an Elastic Collision?

An elastic collision is one in which both momentum and kinetic energy are conserved. No energy is converted to other forms like heat or sound.

Conservation Laws

In elastic collisions:

  • Momentum is conserved: m₁v₁ᵢ + m₂v₂ᵢ = m₁v₁f + m₂v₂f
  • Kinetic energy is conserved: ½m₁v₁ᵢ² + ½m₂v₂ᵢ² = ½m₁v₁f² + ½m₂v₂f²

Special Cases

Notable elastic collision scenarios:

  • Equal masses: Objects exchange velocities
  • Stationary target: Simple formulas apply
  • Much larger mass: Acts like reflection

Applications

Elastic collisions are important in:

  • Atomic and molecular collisions
  • Billiards and snooker
  • Gas molecule interactions
  • Particle physics

Real-World Considerations

Perfect elasticity is rare because:

  • Some energy always converts to heat
  • Deformation usually occurs
  • Sound energy is produced
  • Air resistance affects motion

Essential Elastic Collision Formulas

Final Velocities (General)

v₁f = ((m₁-m₂)v₁ᵢ + 2m₂v₂ᵢ)/(m₁+m₂)

v₂f = (2m₁v₁ᵢ + (m₂-m₁)v₂ᵢ)/(m₁+m₂)

Equal Masses

v₁f = v₂ᵢ

v₂f = v₁ᵢ

Stationary Target

v₁f = ((m₁-m₂)v₁ᵢ)/(m₁+m₂)

v₂f = (2m₁v₁ᵢ)/(m₁+m₂)