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 4.35 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 5.32 cm from the axis of rotation?

Answer 1

To find the number of revolutions per minute the sample is making in a centrifuge, use the formula: Centripetal acceleration = (angular velocity)^2 * radius. Rearrange the equation and solve for angular velocity, then convert it to rotations per minute.

Step-by-step explanation:

To find the number of revolutions per minute the sample is making, we can use the formula:

Centripetal acceleration = (angular velocity)^2 * radius

Given that the centripetal acceleration is 4.35 x 10^3 times the acceleration due to gravity, we can set up the equation:

4.35 x 10^3g = (angular velocity)^2 * 5.32 cm

Converting cm to meters and g to m/s^2, we have:

4.35 x 10^3 * 9.8 = (angular velocity)^2 * 0.0532

Rearranging the equation to solve for angular velocity:

(angular velocity)^2 = (4.35 x 10^3 * 9.8) / 0.0532

angular velocity = sqrt((4.35 x 10^3 * 9.8) / 0.0532)

Finally, to find the number of revolutions per minute, we can convert the angular velocity to rotations per minute:

number of revolutions per minute = (angular velocity / (2π)) * 60