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When an object moves through a fluid, the fluid exerts a viscous force on the object that tends to slow it down. For a small sphere of radius R, moving slowly with a speed v, the magnitude of the viscous force is given by Stokes law, F = πηphRv, where η is the viscosity of the fluid.
(a) What is the viscous force on a sphere of radius R = 5.0 × 10-4 m that is falling through water (η = 1.00 × 10-3 Pa ∙ s) when the sphere has a speed of 3.0 m/s?
(b) The speed of the falling sphere increases until the viscous force balances the weight of the sphere. Thereafter, no net force acts on the sphere, and it falls with a constant speed called the "terminal speed." If the sphere has a mass of 1.0 × 10-5 kg, what is its terminal speed? |
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