Newton's Cradle

Lift 1–4 balls and release them with Run. Step advances 0.02 seconds multiplied by the selected time scale. First impact integrates a fresh release until a contact force exceeds 1 N, pauses, and selects 0.001× slow motion. Use Step or Run to follow the force wave through the touching balls.

Model: five identical 0.11 kg spheres of radius 0.015 m on 0.25 m rigid, massless pendulum rods. Adjacent spheres exert a frictionless Hertz force F = Kδ³ᐟ² when compressed; contact energy is 2Kδ⁵ᐟ²/5. Reference parameters E = 200 GPa, ν = 0.3 are steel-like, not a calibrated apparatus. Gravity is 9.81 m/s². The drag rate γ gives angular acceleration −γω, independent of frame rate.

Mechanical energy includes motion, height and contact deformation. Drag loss integrates the energy removed by damping; their sum should remain close to release energy. Each ball is assigned half of each neighboring contact’s energy. Velocity is signed along the pendulum arc. Horizontal momentum is not conserved throughout a swing because the suspension exerts external forces. The familiar N-in/N-out behavior is an approximate outcome, not a programmed rule. Surface losses, plastic deformation, friction and three-dimensional motion are omitted. The view preserves physical proportions; tiny compression is not enlarged.

Inputs update the paused release immediately. Reset keeps the inputs and returns to time zero. Enter does not start playback. Only exact angle/drag drafts, lifted count and time factor are saved, including invalid or incomplete text. Reload or returning to the tool starts a fresh release; motion, contact history, results and expanded details are not restored. Valid version2 numeric settings migrate.

Hinch and Saint-Jean (1999) discuss elastic contact waves and why the usual incoming/outgoing rule is not exact. Their long straight line differs from this five-pendulum model; its numerical results are not used as a calibration. Hinch & Saint-Jean · The fragmentation of a line of balls by an impact