Centripetal acceleration blood plasma problem

[nlsherrill]

Homework Statement

From Tipler's Physics for Scientists and Engineers(the latest edition)

71.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 that are 15 cm long and are full of blood. These tubes ride in the centrifuge tilted at an angle of 45.0° above the horizontal. (a) What is the distance of a sample of blood from the rotation axis of a centrifuge rotating at 3500 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.

Homework Equations

a=v^2/r
v=(2*pi*r)/T

The Attempt at a Solution

First of all the answers are

a)15 cm
b)1300g to 2700g

I honestly don't know how they got part A other than just taking the length of the tube itself, which is 15 cm. Each part of the tube is a different distance from the axis of rotation, so I guess they made a generalization or something.

I do think i know how to get the max an min accelerations though. And also, my webassign is using 16.5 cm as the length of the tube, and I entered that and it counted it wrong, so there must be a different way to find "r"?

any help appreciated.

 

[Doc Al]

I honestly don't know how they got part A other than just taking the length of the tube itself, which is 15 cm. Each part of the tube is a different distance from the axis of rotation, so I guess they made a generalization or something.

No generalization--you have all the information needed to calculate the distance from the axis. Hint: Expression the centripetal acceleration formula in terms of angular speed. The length of the tube is not needed for this part.

 

[nlsherrill]

I think I am catching on a little bit. 2000g in the problem refers to centripetal acceleration, not tangential correct? Should I be integrating to get velocity or anything?

Please forgive my ignorance, my professor has not even gone over this chapter and the homework for it is due tonight...

 

[Doc Al]

2000g in the problem refers to centripetal acceleration, not tangential correct?

Correct.

Hint: a_c = v²/r = ω²r

Figure out ω from the given RPMs. (ω is the angular speed in radians per second.)

You can also stick to the first form of the centripetal acceleration formula (in terms of v), but then you'll have to express the tangential speed v in terms of the RPMs and the radius.

Either way, you'll be able to solve for the radius.

 

[nlsherrill]

Correct.

Hint: a_c = v²/r = ω²r

Figure out ω from the given RPMs. (ω is the angular speed in radians per second.)

You can also stick to the first form of the centripetal acceleration formula (in terms of v), but then you'll have to express the tangential speed v in terms of the RPMs and the radius.

Either way, you'll be able to solve for the radius.

Thanks for your help, I got them!

When I first looked at this problem in the book, and the answer for the first part was exactly that as the length, I was wondering if they just used that. Then I looked on webassign and they had an example with 15.3 as the length and that was also their answer for the radius from the center! How deceiving.

 

[dch1runs]

I can follow this problem through part (a), but I keep getting lost in part (b). Would someone mind clearing it up for me a little?

 

[Doc Al]

I can follow this problem through part (a), but I keep getting lost in part (b). Would someone mind clearing it up for me a little?

Part (a) gives you the radius of the center of the tube. Use the angle of the tube and some trig to find the radii of the ends of the tube.