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

Question

Very small objects, such as dust particles, experience a linear drag force, D = (bv, direction opposite the motion), where b is a constant. For a sphere of radius R, the drag constant can be shown to be b=6R, where is the viscosity of the gas. Suppose a gust of wind has carried a 44-m-diameter dust particle to a height of 320 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 25C air is 2.0×105Ns/m2, and you can assume that the falling dust particle reaches terminal speed almost instantly.

Explanation / Answer

g = local acceleration due to gravity
At terminal speed m * g = 6 * pi * n * R * v
So :
v = (m * g) / (6 * pi * n * R)
DUST mass = volume * density = 4.24115e-6 kg
Assume local gravity @ 9.8 (m/s) /s
v = (4.24115e-6 * 9.8) / (6 * pi * 2*10^-5 * 44*10^-6)
v = 2506.95 m/s
t = s / v
= 320 / 2506.95
= 0.127 seconds

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