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

Question

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 6.93 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 3.99 cm from the axis of rotation?

Explanation / Answer

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

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
Radius = 3.93 cm = 0.0393 m

To determine the number of revolutions per minute we need to know the time for 1 revolution.
To determine the time, we need to know the velocity of the end of the centrifuge tube and the circumference of the circle it is moving around!

The problem states that the centripetal acceleration of the sample is 6.93 x 10^3 times as large as the acceleration due to gravity.

Centripetal acceleration = 6.93 * 10^3 * 9.8

6.93 * 10^3 * 9.8 = velocity^2 ÷ 0.0399

velocity^2 = 2709.76

velocity = 60 m/s

Circumference = 2 * * r = 2 * * 0.0399 = 0.2507 m

Distance = velocity * time
0.2507 = 60 * time
time = 0.2507 ÷ 60 = 4.178 * 10^-3 seconds

The centrifuge rotates 1 revolution in 4.178 * 10^-3 seconds.

1 minute = 60 seconds

60 seconds/minute * 1 rev/4.178 * 10^-3 seconds = 14.359 * 10^3 revolutions per minute


The sample is making 14359 revolutions per minute

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