Very small objects, such as dust particles, experience a linear drag force, D(vector) = (bv, direction opposite the motion), where b is a constant. That is, the quadratic model of drag of Equation 6.16 fails for very small particles. For a sphere of radius R, the drag constant can be shown to be b = 6πμR, where h is the viscosity of the gas.

a. Find an expression for the terminal speed v_term 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–μm–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 25°C air is 2.0 × 10^-5 N s/m², and you can assume that the falling dust particle reaches terminal speed almost instantly.