Dissolved CO₂ in champagne exerts an equilibrium pressure that rises with temperature (Henry's law). Fitting real bottle measurements gives approximately:
P_bottle(T) ≈ 4.1 + 0.128·T [bar]
so a bottle chilled to 6 °C sits near 4.9 bar while one left at 24 °C nears 7.2 bar — colder really does mean a slower, safer pop. Shaking nucleates bubbles and lets dissolved gas escape solution faster than normal diffusion, producing a transient pressure surge behind the cork (modelled here as a capped multiplier, since it is a kinetic effect, not a change in equilibrium).
The cork is held by neck friction until the net force wins; once released it accelerates over a short effective length ℓ as the seal breaks:
F = (P_bottle·shake_factor - P_atm - P_friction)·A
v₀ = √(2·F·ℓ / m)
This 2D view then tracks the cork as a simple point-mass projectile under gravity alone (no air drag, for a clean side-on parabola) — a deliberately simplified companion to the full 3D model, which adds drag and free 3D rotation.