A body of mass 100 kg is driven by a constant horizontal force while the viscous resistance is F(viscous) = 2v in SI units. Starting from rest, the time required to reach half its limiting speed is N ln2 seconds. Find N.
Physics · Properties of solid and fluid · viscosity and terminal velocity
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Question

A body of mass 100 kg is driven by a constant horizontal force while the viscous resistance is F(viscous) = 2v in SI units. Starting from rest, the time required to reach half its limiting speed is N ln2 seconds. Find N.

Physics · Properties of solid and fluid · viscosity and terminal velocity

G1 Physics · Accepted Answer

The equation of motion has the form m dv/dt = F₀−kv, where k = 2 N·s/m. The time constant is τ = m/k = 100/2 = 50 s. For linear viscous drag, half the limiting speed is reached at t = τ ln2. Therefore, t = 50 ln2 s. Hence, N = 50.