Re: Centrifuge

[Ludwik Kowalski <KowalskiL@MAIL.MONTCLAIR.EDU>]

John's reply (see below) was clear but not very useful. It
is true that the author "doesn't quite say that lesser forces
ensure no settling". But this is the implied assumption.

The word "payload" was not used in our textbook and
I am not sure what it means in this cotext. How can the
process of "settling" be explained at this level?

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.

So let us accept the idea that a centrifuge problem in which
things are "spelled out in all necessary detail" is desired. In
my opinion the problem is not well formulated. Since not
everybody has the text let me quote the problem, as printed.

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. Here is my original message again:

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.
.
Since v=w*r one has F=m*r*w^2. At a constant w
F increases when r increases. Does this mean that
particles at r<R will not settle at 150 rev/sec?

What is a better way to formulate the centrifuge
problem in a non-calculus physics course?
Ludwik Kowalski
---------------------------------------------------
John Denker wrote:

> At 12:49 PM 11/2/00 -0500, Ludwik Kowalski wrote:
>
> > Since v=w*r one has F=m*r*w^2. At a constant w
> > F increases when r increases. Does this mean that
> > particles at r<R will not settle at 150 rev/sec?
>
> Well, the problem as quoted doesn't quite say that.
> It says F is sufficient to ensure settling.
> It doesn't quite say that lesser forces ensure no settling.
>
> And why does anybody care, anyway?  Reasons for not caring are:
> 1) One assumes the centrifuge is designed so that there is
> no payload at locations r < R.
> 2) One also assumes that for this application, a little extra force
> is harmless, so points where r > R need not cause concern.
>
> > What is a better way to formulate the centrifuge
> > problem in a non-calculus physics course?
>
> What's wrong with the problem as stated?
> Perhaps a statement supporting assumption (2) would help.
> Perhaps a picture supporting assumption (1) would help. I suppose
>    some students don't know what a real centrifuge looks like....
>    http://progen.com.au/showcase_apr99_labnet_centrufuge.htm
>
> On the other hand, suppose a real-world boss assigned this problem to a
> real-world employee.  The boss would like to specify the problem in general
> terms (find a suitable rotation speed) and get an answer.  The employee is
> expected to make reasonable assumptions!  The boss does _not_ want to spell
> out every possible detail!  Therefore I think that it is good to train
> students to handle problems where some details are left unspecified.