Re: Centrifuge

[John Denker <jsd@MONMOUTH.COM>]

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.