Calculating Centrifugation Distance and Acceleration for Blood Plasma Separation

[dragonladies1]

Homework Statement

Human blood contains plasma, platelets, and blood cells. To separate the plasma from other components, centrifugation is used. Effective centrifugation requires subjecting blood to an acceleration of 2000g or more. In this situation, assume that blood is contained in test tubes of length L = 14.3 cm that are full of blood. These tubes ride in the centrifuge tilted at an angle of 45.0° above the horizontal (see figure below)

(a) What is the distance of a sample of blood from the rotation axis of a centrifuge rotating at a frequency f = 3480 rpm, if it has an acceleration of 2000g?
cm

(b) If the blood at the center of the tubes revolves around the rotation axis at the radius calculated in Part (a), calculate the accelerations experienced by the blood at each end of the test tube. Express all accelerations as multiples of g.
minimum acceleration g
maximum acceleration g

Homework Equations

Is this the correct equation for problem a:

a_tan=a_c*r

The Attempt at a Solution

2000g=((2*pi*r)/(1/58))²*r
.015=r³
r=.25 cm

 

[Delphi51]

I think the formula is a = v²/r, where v = 2πrN/T
N is the 3480 turns and T the 60 seconds.
When substituting the v equation into the a one, one of the r's will cancel out - you will not get an r cubed. The 2π will be squared.