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A layer of glycerine 1 mm thick lies between a flat plate of area 100 cm² and a large fixed plate. If glycerine has a viscosity of 1.0 kg/(m*s), what force is needed to slide the upper plate at a speed of 7 cm/s?
- 3.5 N
- 0.7 N
- 1.4 N
- None
Correct answer: 0.7 N
Solution
The viscous (shearing) force is F = eta*A*(velocity gradient) = eta*A*v/d. Substituting eta = 1.0, A = 0.01 m², v = 0.07 m/s, d = 0.001 m gives F = 1.0*0.01*0.07/0.001 = 0.7 N.
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