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 4.47 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 4.83 cm from the axis of rotation?

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 4.47 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 4.83 cm from the axis of rotation?

Answer 1

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 5.27 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 2.50 cm from the axis of rotation?

Answer 2

To find the number of revolutions per minute (rpm) the sample is making, we need to first determine the centripetal acceleration of the sample and then use that to calculate the angular velocity (ω) of the rotation. Finally, we can convert the angular velocity to rpm.

The centripetal acceleration of the sample is given as 4.47 x 10^3 times the acceleration due to gravity (g). The acceleration due to gravity is approximately 9.8 m/s^2.

So, the centripetal acceleration (ac) can be calculated using the equation:

ac = 4.47 x 10^3 * g

Next, we need to convert the given radius of 4.83 cm to meters. There are 100 cm in 1 meter, so the radius (r) in meters becomes:

r = 4.83 cm / 100 = 0.0483 m

Now, we can use the centripetal acceleration (ac) and radius (r) to calculate the angular velocity (ω). The formula for centripetal acceleration is:

ac = ω^2 * r

Rearranging the equation, we get:

ω^2 = ac / r

Substituting the values, we have:

ω^2 = (4.47 x 10^3 * 9.8) / 0.0483

Now, we can solve for ω by taking the square root of both sides:

ω = √[(4.47 x 10^3 * 9.8) / 0.0483]

Finally, to get the number of revolutions per minute (rpm), we need to convert ω to rpm. The angular velocity in rpm is given by:

rpm = ω * (60 / 2π)

Substituting the calculated ω, we have:

rpm = √[(4.47 x 10^3 * 9.8) / 0.0483] * (60 / 2π)

Now, we can use a calculator to simplify the expression and find the value of rpm.