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 8.93×10 3 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 3.33cm from the axis of rotation?

Explanation / Answer

The centripetal acceleration is equal to 8.93x10^3 times acceleration due to gravity. Fc = Fg x 8.93x10^3 Fc = mv^2/r Fg = mg mv^2/r = 8.93x10^3mg cancel mass from both sides v^2/r = 8.93x10^3g multiply r on both sides v^2 = 8.93x10^3gr square root both sides v = sqrt(8.93x10^3gr) = sqrt(8.93x10^3 x 9.8 x 0.0333) = 53.98 m/s Circumference of rotation is 2(pi)r C = 2(pi)(0.0333) = 0.209 m v/C calculates number of rotations per second v/C = 258 rotations per second convert to per minute by multiplying 60 258 x 60 = 15480 rotations per minute Hope it helps :D

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