Very small objects, such as dust particles, experience a linear drag force, D⃗ 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=6πηR, where η is the viscosity of the gas. |
Suppose a gust of wind has carried a 52-μm-diameter dust particle to a height of 260 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/m^3, the viscosity of 25.C air is 2.0×10−5N⋅s/m^2, and you can assume that the falling dust particle reaches terminal speed almost instantly. Answer in minutes |
at terminal speed, drag force is equal to weight.
so,
6nRv = mg
so,
v = mg / 6nR
Now, we need to find mass of particle
mass = density * volume ( treat the particle as sphere)
mass = 2700 * 4/3 * * 26e-6^{3}
mass = 1.9877e-10 Kg
so,
v = 1.9877e-10 * 9.8 / 6 * 2e-5 * 26e-6
v = 0.198744 m/s
so,
t = d / v
t = 260 / 0.198744
t = 1308.2 seconds
or
t = 21.8 minutes
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