Small, slowly moving spherical particles experience a drag force given by Stokes’ law: where r is the radius of the particle, is its speed, and η is the coefficient of viscosity of the fluid medium. (a) Estimate the terminal speed of a spherical pollution particle of radius 1.00 x 10-5 m and density of 2000 kg/m3. (b) Assuming that the air is still and that η is 1.80 x 0-5 N · s/m2, estimate the time it takes for such a particle to fall from a height of 100 m.

You need Stokes' law to do that problem. You did not include it in the question, but I assume you have it or can look it up. (See also below) (a) The terminal speed of the particle is the value for which the Stokes' drag equals the weight minus the buoyancy force. (b) For the time to fall 100 m, divide 100m by the terminal speed.

The equations you need can be found at

http://en.wikipedia.org/wiki/Stokes'_law

To estimate the terminal speed of the spherical pollution particle, we can use Stokes' law. Stokes' law states that the drag force experienced by a small, slowly moving particle in a fluid is directly proportional to its velocity.

(a) Terminal speed can be calculated using the equation:

v_terminal = (2/9) * (r^2) * (g) * (ρ_particle - ρ_medium) / η

where:
- r is the radius of the particle (1.00 x 10^-5 m)
- g is the acceleration due to gravity (9.8 m/s^2)
- ρ_particle is the density of the particle (2000 kg/m^3)
- ρ_medium is the density of the fluid medium (assume air with negligibly small density)
- η is the coefficient of viscosity of the fluid medium (1.80 x 10^-5 N·s/m^2)

Substituting the given values into the equation:

v_terminal = (2/9) * (1.00 x 10^-5 m)^2 * (9.8 m/s^2) * (2000 kg/m^3) / (1.80 x 10^-5 N·s/m^2)

Solving this equation will give us the terminal velocity.

(b) To estimate the time it takes for the particle to fall from a height of 100 m, we can use the kinematic equation:

s = ut + (1/2)gt^2

where:
- s is the distance fallen (100 m)
- u is the initial velocity (0 m/s, as the particle starts from rest)
- g is the acceleration due to gravity (9.8 m/s^2)
- t is the duration of falling time (what we need to find)

Rearranging the equation:

t = sqrt((2s) / g)

Substituting the given value:

t = sqrt((2 * 100 m) / (9.8 m/s^2))

Solving this equation will give us the time it takes for the particle to fall from a height of 100 m.