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 viscosityof the gas.

1. Suppose a gust of wind has carried a 60-

m-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 25C air is 2.0×105Ns/m2, and you can assume that the falling dust particle reaches terminal speed almost instantly.

Explanation / Answer

Formula to be used:
v = m*g / (6R)

R = 60*10^-6 m
= 6*10^-5 m

volume = (4/3)*pi*R^3
= (4/3) *pI* (6*10^-5)^3
= 9.05*10^-13 m^3

m = density * volume
= 2700* 9.05*10^-13
=2.44*10^-9 Kg

v = m*g / (6R)
= (2.44*10^-9 )*9.8 / (6*3.14*2*10^-5*6*10^-5)
= 1.06 m/s

Now distance to be travelled = 300 m
time taken = distance / terminal velocity
= 300 / 1.06
= 283 s
= 4.7 minutes

Answer: 4.7 minutes

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