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 3.79 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 5.61 cm from the axis of rotation?

Explanation / Answer

As the centrifuge rotates one time, the sample moves a distance that is equal to the circumference of the circle.

Circumference = 2 * * 0.0561 = 0.35
This is approximately 0.35meters.

Centripetal acceleration = v^2/r = v^2/0.056
Centripetal acceleration = 3.79 * 10^3 * 9.8 = 37142 m/s^2
v^2/0.056 = 37142
v^2 = 2079.9
v = 45.60

The velocity is approximately 45.6m/s. To determine the number of times the centrifuge rotates in one second, divide the velocity by the circumference.

N = 37142 ÷ (.35) = 550.6
To determine the number of times the centrifuge rotates in one minute, multiply by 60.
N =550* 60 = 33038.15
Rpm is approximately 33038

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