A centrifuge is a device in which a small container of material is rotated at a

Question

A centrifuge is a device in which a small container of material is rotated at a high speed on a circular path. Such a device is used in medical laboratories, for instance, to cause the more dense red blood cells to settle through the less dense blood serum and collect at the bottom of the container. Suppose the centripetal acceleration of the sample is 3.97 x 103 times as large as the acceleration due to gravity. How many revolutions per minute is the sample making, if it is located at a radius of 5.11 cm from the axis of rotation?

Explanation / Answer

Force = mass * acceleration

The acceleration due to gravity is 9.81m/s^2, so the centripetal acceleration is

9.81 * 3.97 * 10^3 = 38.95 * 10^3 m/s^2

Centripetal force = (mass * velocity^2) ÷ radius

You can determine the equation for centripetal acceleration from the 2 equations above.

mass * acceleration = (mass * velocity^2) ÷ radius
Divide both sides by mass

Centripetal acceleration = velocity^2 ÷ radius

a = v^2/r
So

v^2 = a r = 38.95 * 10^3 * 0.0511 =1.99 * 10^3

v = (1.99 * 10^3 ) = 44.60m/s

So in 1 min a point on the circumference will move a distance of

44.60* 60 = 2676 m

So the number of revolutions would be

2676 / (2r) = 2676 / (2 * pi * 0.0511) = 8334.611 rpm.

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