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 6.50 103 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 4.95 cm from the axis of rotation?

Explanation / Answer

for circular motion

acceleration = v2 / r

you are told the acceleration is 6500*9.8 = 63700 m/s2 and

r = 0.0495m

You also know that v = 2r/T so now

   a = (2r/T)2 / r

   a = 42 r / T2

solve for T, the time for one revolution:

   T = sqrt (42r/a) = sqrt (4*2 * 0.0495 / 63700) = 0.005539 seconds

number of revolutions in one minute?

   60 seconds * (one rev / 0.005539 sec) = 10833 revolutions in one minute

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