Human blood contains plasma, platelets, and blood cells. To separate the plasma

Question

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 = 15.6 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 = 3780 rpm, if it has an acceleration of 2000g?

(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 = ?
maximum acceleration= ?

For part A i got 12.5 cm, which is correct, however i can't get part B right at all.

minimum acceleration = ?
maximum acceleration= ?

For part A i got 12.5 cm, which is correct, however i can't get part B right at all.

Explanation / Answer

Indeed part a) is right, so I guess you know how to convert rpm in rps (revolutions per second), and how to calculate the acceleration in terms of the angular velocity.
b) Assuming that the distance calculated before is the distance of the center of the tube to the rotation axis, since the tube is tilted 45º and its total length is 15.6cm = 0.156 m, then the minimum and maximum distances of the extreme points of the tube to the rotation axis are
d1 = 0.125 - 0.156/2*sqrt(2) = 0.01469 m
d2 = 0.125 + 0.156/2*sqrt(2) = 0.2353 m.
Then the minimum and maximum accelerations will be w1 and w2, respectively, where
a1 = d1*w^2 = 0.01469*395.64^2 m/s^2 = 2299.44 m/s^2 = 234.6 g
a2 = d2*w^2 = 0.2353*395.64^2 m/s^2 = 36831m/s^2 = 3758 g.
The results are reasonable, since the distance of the center of the tube to the rotation axis is of the same order of magnitude than the distance of the extreme points of the tube to its own symmetry axis.

Related Questions

Navigate

• Browse (All)
• Browse H
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.