A flat-bottomed body is driven by a constant horizontal force of 100 N. Its contact area is 10 m² and it moves over a fixed surface with a Newtonian liquid layer of effective thickness 10 m and viscosity 2 Pa·s between them. Assume a linear velocity profile and neglect all other resistance. If its limiting speed is N m/s, find N.
Physics · Properties of solid and fluid · viscosity and terminal velocity
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Question

A flat-bottomed body is driven by a constant horizontal force of 100 N. Its contact area is 10 m² and it moves over a fixed surface with a Newtonian liquid layer of effective thickness 10 m and viscosity 2 Pa·s between them. Assume a linear velocity profile and neglect all other resistance. If its limiting speed is N m/s, find N.

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

G1 Physics · Accepted Answer

Viscous resistance is F(viscous) = ηAv/D. Substitute: η = 2 Pa·s, A = 10 m², D = 10 m. Therefore, F(viscous) = 2×10×v/10 = 2v. At limiting speed, net force is zero: 100 = 2v. Thus, v = 50 m/s. Hence, N = 50.