Μm) in water. Assuming the particles are spherical and have a density of 1.5 g/cm3, calculate:

a) The gravitational force acting on a single starch particle.

b) The buoyant force acting on a single starch particle.

c) The net force acting on a single starch particle.

d) The sedimentation coefficient of the starch particles.

Solution:

a) The gravitational force acting on a single starch particle can be calculated using the formula:

Fg = mg

Where, Fg is the gravitational force, m is the mass of the particle, and g is the acceleration due to gravity.

The mass of the particle can be calculated using the formula:

m = (4/3)πr3ρ

Where, r is the radius of the particle and ρ is the density of the particle.

Substituting the given values, we get:

m = (4/3)π(10-6 m)3(1.5x103 kg/m3) = 1.41x10-13 kg

The acceleration due to gravity is 9.81 m/s2.

Therefore, the gravitational force acting on a single starch particle is:

Fg = mg = (1.41x10-13 kg)(9.81 m/s2) = 1.39x10-12 N

b) The buoyant force acting on a single starch particle can be calculated using the formula:

Fb = Vρf g

Where, V is the volume of the particle, ρf is the density of the fluid, and g is the acceleration due to gravity.

The volume of the particle can be calculated using the formula:

V = (4/3)πr3

Substituting the given values, we get:

V = (4/3)π(10-6 m)3 = 4.19x10-18 m3

The density of water is 1000 kg/m3.

Therefore, the buoyant force acting on a single starch particle is:

Fb = Vρf g = (4.19x10-18 m3)(1000 kg/m3)(9.81 m/s2) = 4.11x10-14 N

c) The net force acting on a single starch particle can be calculated by subtracting the buoyant force from the gravitational force:

Fn = Fg - Fb = 1.39x10-12 N - 4.11x10-14 N = 1.35x10-12 N

d) The sedimentation coefficient of the starch particles can be calculated using the formula:

s = (2r2ω)/kT

Where, r is the radius of the particle, ω is the angular velocity of the centrifuge, k is the Boltzmann constant, and T is the temperature.

The Boltzmann constant is 1.38x10-23 J/K and the temperature is assumed to be 25°C (298 K).

Substituting the given values, we get:

s = (2(10-6 m)2(20000 rpm)(2π/60 s/min))/[(1.38x10-23 J/K)(298 K)] = 1.10x10-11 s-1

Therefore, the sedimentation coefficient of the starch particles is 1.10x10-11 s-1.