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Re: Centrifuge

At 02:59 PM 11/2/00 -0500, Ludwik Kowalski wrote:

The word "payload" was not used in our textbook and
I am not sure what it means in this cotext.

The payload is blood in this context. What other meaning could "payload"
possibly have in this context?

Students are not physics majors and ths problem was
chosen to drill them in the use of the formula explained
in the text. Some problems may indeed be "open-ended"
but drill-and-practice problems are also useful sometimes.
I am not addressing the issue of how many problems of
each kind produce the best result.

OK. If it is just a plug-in-the-numbers problem, why not just plug in the
numbers, get the right answer, and move on?

There is nothing in the statement of the problem that requires
consideration of radii other than r=R.

If OTOH you use your physics judgement to complexify the problem, to force
considerations of radii other than r=R, then you must also use your physics
judgement to re-simplify the problem and determine that the other radii are
not significant.

I suppose you could design a perverse centrifuge where the payload was
spread out over a huge range of radii -- but the statement of the problem
does not require or even suggest this.

A SAMPLE OF BLOOD IS PLACED IN A CENTRIFUGE
OF RADIUS 15 CM. THE MASS OF A RED CORPUSCULE
IS 3E-16 KG AND THE MAGNITUDE OF THE FORCE
REQUIRED TO MAKE IT SETTLE OUT OF THE PLASMA
IS 4E-11 N. AT HOW MANY REVOLUTIONS PER
SECOND SHOULD THE CENTRIFUGE BE OPERATED?

!50 rev/sec was calculated with r=R and it seems to me that
this is not sufficient.

I say again, if it is to be considered a plug-in-the-numbers question, why
not take the author at his word and plug in r=R=15cm?

Problem #21 from College Physics of Serway& Faughn
(5th edition, page 211) asks students to calculate v when
m, R and F=(m*v^2)/R are given. The answer one gets
(150 rev/s) is the same as that shown in the book. Note
that R is "the radius of the centrifuge".

The problem defines F as "the force required to make
it [particle of mass m] settle out of the plasma". Most
blood particles are initially at r<R.

What basis is there for asserting that "most" particles are at r<R?

For that matter, why assume that ANY of them are at r<R?

If by mischance r is not exactly R, what reason is there to think this is
significant?

If you have in mind some geometry different from the real-world centrifuge
I documented in my previous email, please be specific. The ball's in your
court.