The combustion of fossil fuels produces micron sized particles of soul, one of t
ID: 1523462 • Letter: T
Question
The combustion of fossil fuels produces micron sized particles of soul, one of the major components of air pollution. The terminal speeds of these particles are extremely small, so they remain, suspended in air for very long periods of time. Futher more, very small particles almost always acquire small amounts of charge from cosmic rays and various atmospheric effects, so their motion is influenced not only by gravity but also by the earth's weak electric field. Consider a small spherical particle of radius r, density rho, and charge q. A small sphere moving with speed upsilon experiences a drag force F_dray = 6 pi r/r upsilon, where eta is the viscosity of the air. (This differs from the drag force you learned in Chapter 6 because there we considered macroscopic rather than microscopic objects.) Soot is primarily carbon, and carbon in the farm of graphite has a density of 2200 kg/m^3. In the absence of an electric field, what is the terminal speed in mm/s of a 3.0 mu m diameter graphite particle? The viscosity of air at 20 degree C is 1.8 times 10^-5 kg/ms. The earth's electric field is typically (150 N/C downward) in this field, what is the terminal speed in mm/s of a 3.0 mu m diameter grpahite particle that has acquired 250 extra electrons?Explanation / Answer
We know that
F = mg
m = density x volume = 2200 x (4/3 x 3.14 x (1.5 x 10^-6)^3)
F = 3.11 x 10^-14 x 9.8 = 3.05 x 10^-13 N = F(drag)
F(drag) = 6 pi eta r v => v = F(drag)/ 6 pi eta r
v = 3.05 x 10^-13 N/ [6 x 3.14 x 1.8 x 10^-5 x 1.5 x 10^-6 x ]
v = 5.99 x 10^-4 m/s = 0.599 mm/s
Hence, v = 0.599 mm/s
b)F(drag) = Fe = q E
F(drag) = 250 x 1.6 x 10^-19 = 4 x 10^-17 N
v = F(drag)/ 6 pi eta r
v = 4 x 10^-17 N/[6 x 3.14 x 1.8 x 10^-5 x 1.5 x 10^-6 x ]
v = 7.86 x 10^-8 m/s = 7.86 x 10^-5 mm/s