A typical red blood cell has a mass of 3.0 10-16 kg. A blood sample placed in a centrifuge is subjected to a force of 4.6 10-11 N when the centrifuge is operated at 138 rev/s. What is the diameter of the centrifuge?

Answer 1

To determine the diameter of the centrifuge, we first need to determine its radius. Let the radius be r. To do this, we'll make use of the centripetal force formula, which is given by:

Fc = m*a

where Fc is the centripetal force acting on the red blood cell (4.6 * 10^-11 N), m is the mass of the red blood cell (3.0 * 10^-16 kg), and a is the centripetal acceleration.

The centripetal acceleration of an object rotating in a circle is given by the formula:

a = r*w^2

where r is the radius of the circle, and w is the angular velocity of the object (in radians per second).

First, we need to convert the given revolutions per second (138 rev/s) to radians per second:

Angular velocity (w) = (138 rev/s) * (2 * pi radians/rev) = 866.04 radians/s

Now, we can substitute the centripetal acceleration formula into the centripetal force formula:

Fc = m * r * w^2

We want to solve for r (radius), so let's rearrange the equation:

r = Fc / (m * w^2)

Now, plug in the values:

r = (4.6 * 10^-11 N) / ((3.0 * 10^-16 kg) * (866.04 radians/s)^2)

After calculating, we get:

r ≈ 0.029 m

Now double that value to get the diameter:

Diameter = 2 * r ≈ 2 * 0.029 m ≈ 0.058 m

So, the diameter of the centrifuge is approximately 0.058 meters or 58 mm.