A sphere has terminal speed 10 m/s and Stokes time constant 2 s. Starting from rest, it travels a distance x = N ln2 − 10 metres before reaching half its terminal speed. Find N.
Physics · Properties of solid and fluid · viscosity and terminal velocity
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Question

A sphere has terminal speed 10 m/s and Stokes time constant 2 s. Starting from rest, it travels a distance x = N ln2 − 10 metres before reaching half its terminal speed. Find N.

G1 Physics · Accepted Answer

Distance travelled before reaching half terminal speed is x = vₜτ(ln2−1/2). Substitute: vₜ = 10 m/s, τ = 2 s. Then, x = 10×2(ln2−1/2) = 20ln2−10. Comparing with x = Nln2−10, we get N = 20.