Physics
Collisions and momentum
Conservation laws in impacts: elastic, inelastic, Newton's cradle.
What happens
Compare collisions on a table with Newton's cradle. The table uses momentum and restitution; the pendulum balls follow curved paths, so their supports can supply external impulses. Pull one or two balls, vary the masses and restitution, and compare the motion and kinetic energy. The cradle uses rigid contacts and strings; elastic contact duration, sound and spin are omitted.
Try this
The target is NOT at rest: v₀′ = ((m₀ − e·m₁)·0.8 − (1+e)·m₁·0.4)/(m₀+m₁), zero at m₀ = 2·m₁ for e = 1 - not at equal masses, the cradle's answer.
Equations used in the module
Equations p = Σ m_i v_i e = −(v₂′ − v₁′)/(v₂ − v₁) v₁′ = ((m₁ − e m₂)v₁ + (1+e)m₂v₂)/(m₁+m₂) ΔE = ½ μ(1−e²)(v₁−v₂)²; μ = m₁m₂/(m₁+m₂) θ″ = −(g/L) sin θ; E = ½mL²θ′² + mgL(1−cos θ)
