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 5.05 times 103times 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 4.20 cm from the axis of rotation?

Explanation / Answer

centripetal acceleration = v^2/r

given:

v^2/r = 5.05*10^3

=> v^2/(4.2/100) = 5.05*10^3 * 9.8

=> v = sqrt((5.05*10^3)*9.8*(4.2/100)) = 45.5914465662145886 m/sec

thus this is the tangential velocity...

distance in one revolution = perimeter = 2pi*r = 2*3.14*(4.2/100)

time for one revolution(T) = distance/v = 2*3.14*(4.2/100)/ 45.5914465662145886 = 0.0057852957049065996

thus in one sec number of revolutions = 1/T = 1/0.0057852957049065996 = 172.8520115491908891145434

thus in one minute no. of revolutions =172.8520115491908891145434*60 = 10371.120692951453346872604 answer

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