Physical Principles & Mathematical Derivation
In a perfectly elastic collision (restitution e = 1.0), zero mechanical energy is lost to permanent deformation or heat. Try setting m₁ = m₂ with m₂ stationary (v₂ = 0) to witness Newtons Cradle 100% velocity transfer!
Questions & Concepts
What physical equation governs 1D Elastic Collision & Momentum Conservation Air-Track Lab?
m₁v₁ + m₂v₂ = m₁v₁′ + m₂v₂′, ½m₁v₁² + ½m₂v₂² = Constant — In a perfectly elastic collision (restitution e = 1.0), zero mechanical energy is lost to permanent deformation or heat. Try setting m₁ = m₂ with m₂ stationary (v₂ = 0) to witness Newtons Cradle 100% velocity transfer!
How are the equations of motion integrated in this simulation?
Nonlinear differential equations are integrated at 240–300 Hz substeps using classical 4th-order Runge-Kutta (RK4) to maintain strict Hamiltonian energy accuracy.