🎱 Collisions (Elastic & Inelastic)

📖 The Physics

When two things crash, one quantity is always conserved: the total momentum. The "before" and "after" totals above always match, no matter what kind of collision it is.

Whether the kinetic energy survives is a different question, decided by the coefficient of restitution e. e = 1 is perfectly elastic (no KE lost, like ideal snooker balls); e = 0 is perfectly inelastic (the bodies stick together and lose the most KE).

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂ (momentum, always) v₂ − v₁ = −e(u₂ − u₁) (restitution)

Set e = 1 and watch the KE stay constant; drop e toward 0 and see the "KE lost" climb as the bodies end up moving together. Try equal masses with e = 1 — they simply swap velocities, a classic result.

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