Very small objects, such as dust particles, experience a linear drag force, = (bv, direction opposite the

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Very small objects, such as dust particles, experience a linear drag force, 

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= (bv, direction opposite the motion), where b is a constant. That is, the quadratic model of drag of Equation 6.15 fails for very small particles. For a sphere of radius R, the drag constant can be shown to be b = 6phR, where h is the viscosity of the gas.

a. Find an expression for the terminal speed vterm of a spherical particle of radius R and mass m falling through a gas of viscosity h.

b. Suppose a gust of wind has carried a 50-mm-diameter dust particle to a height of 300 m. If the wind suddenly stops, how long will it take the dust particle to settle back to the ground? Dust has a density of 2700 kg/m3, the viscosity of 25­oC air is 2.0 × 10-5 N s/m2, and you can assume that the falling dust particle reaches terminal speed almost instantly.

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