Elastic Collision (1D)

Elastic collision: BOTH momentum AND kinetic energy are conserved.

1D two-body: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂ (momentum) AND ½m₁u₁² + ½m₂u₂² = ½m₁v₁² + ½m₂v₂² (KE).

Solving these gives final velocities in terms of initial — exact formulas exist (see Formulas section).

Equal masses (m₁ = m₂): velocities are EXCHANGED — incoming particle stops, target moves with original speed.

Massive target (m₂ ≫ m₁): incoming particle bounces back with nearly same speed; target barely moves.

Light target (m₂ ≪ m₁): incoming particle continues nearly unchanged; target shoots off at 2u₁.

Real-world approximations: hard steel balls, atomic collisions (in some regimes), Newton's cradle.

Macroscopically, perfectly elastic collisions don't exist — some energy always lost to heat, sound, deformation.