To find the number of revolutions per second at which the centrifuge should be operated, we need to use the relationship between the centripetal force acting on the red blood cell and the angular speed of the centrifuge.
1. Start by expressing the centripetal force acting on the red blood cell using the formula for centripetal force: F = m * ω^2 * r, where F is the force, m is the mass, ω is the angular speed, and r is the radius.
2. Rearrange the formula to solve for the angular speed (ω): ω^2 = F / (m * r).
3. Substitute the given values into the formula: F = 4.0 x 10^-11 N, m = 3.0 x 10^-16 kg, and r = 14.0 cm (convert to meters by dividing by 100).
4. Calculate ω^2: ω^2 = (4.0 x 10^-11 N) / ((3.0 x 10^-16 kg) * (0.14 m)).
5. Take the square root of ω^2 to find ω: ω = sqrt((4.0 x 10^-11 N) / ((3.0 x 10^-16 kg) * (0.14 m))).
6. Finally, convert the angular speed from radians per unit of time to revolutions per unit of time by multiplying by (1 / (2Ï€)).
This will give you the number of revolutions per second at which the centrifuge should be operated.