Ball in a liquid: choose the liquid, the ball and its radius, then press ▶ Drop. The stopwatch times the
ball between the two bands A and B (20 cm apart), like Station 5. Press ● Record after each drop.
Set the values with the sliders, or type a value in the box next to a slider and press Enter. A value outside the allowed range is set to the nearest allowed value.
Slow runs take a while — use ×5 or ×20. The times shown are always real times.
The Data & analysis tab plots the terminal speed against r².
Skydiver: press ▶ Jump, then ☂ Open parachute whenever you like.
The physics
Stokes' law (small sphere, slow smooth flow): Fd = 6πηrv.
Buoyancy: Fb = ρfluidVg with V = 4/3 πr³. Weight W = ρballVg.
Terminal speed when W = Fb + Fd: vt = 2r²(ρball − ρfluid)g / (9η), so vt ∝ r².
Stokes' law only works when the Reynolds number Re = ρfluidv(2r)/η is small (Re < 1). Fast balls in water and
skydivers are far outside it: there the drag grows roughly with v².
Model: the drag on the ball is 6πηrv × (1 + 0.15 Re^0.687) (a standard correction that is ≈ 1 when Re is small).
Skydiver: drag = ½ρCdAv² with ρ = 1.2 kg m⁻³; area × Cd = 0.70 m² body, 37.5 m² with the parachute — qualitative only.