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Re: centrifuge exercises



Responding to:

... if you formulated a good centrifuge problem ...

John Denker wrote:

Try these. They deal with centrifugation of macroscopic objects, so
they are suitable for S&F chapter 7 or thereabouts. (To do a good job
on the centrifugation of things like blood particles would require ideas
of buoyancy and viscosity that don't show up until chapter 9.)

1) That is OK, suppose that everything up to chapter 10 has
already been learned. Use mud in water (instead of blood) and
assume that all particles, big a small, are spherical. A uniform
initial distribution of radii, from 0.0001 to 0.01 cm is probably
acceptable for a simple typical centrifuge problem. To simplify
we can also assume that all particles are made from aluminum
and are initially at 1 mm below the surface (to avoid surface
tension complications). For example, 20 grams of water and
0.02 grams of Al in a 25 cm tube. First stationary (vertical),
then in very fast horizontal (horizontal).

2) The problems you described are good and worth discussing
in the context of what we teach. Are you saying that this is not
true for the centrifuge (because objects are microscopic)?

3) Unfortunately, I already spent more time on this thread
than I should. I must turn to other priorities. The same is
probably true for you. But you already invested a lot of
time and made a lot of progress. So once again, I would
like to ask you to formulate a centrifuge problem, if you
think it is worth doing, in the context of the first TEN
chapters, as listed yesterday.

Ludwik Kowalski (trying to be honest and modest).

The rest of John's message:

*) You are flying a small airplane in a steady turn. The true airspeed is
100 knots throughout. At t=0 you proceeding northbound. Thirty seconds
later you are proceeding southbound. How many Gees do you experience?
How big is your turning radius?

*) You are flying an airliner in a steady turn. The true airspeed is 500
knots throughout. You do not wish to subject your passengers to more than
1.4 Gees. How quickly can you turn from northbound to southbound? How
big is your turning radius?

*) You are flying a jet fighter in a steady turn. The true airspeed is
1500 knots throughout. You dare not subject yourself to more than 9
Gees. How quickly can you turn from northbound to southbound? How
big is your turning radius?

*) On a typical playground swingset, the largest amplitude you can
conveniently achieve is a 180-degree arc (90 degrees each side of
center); otherwise you have problems with the chains going slack. Suppose
you have set up such a pattern, and suppose there are no further energy
inputs or outputs; neglect friction. How many Gees do you experience at
point A (the top of the arc, 90 degrees from the bottom)? How many Gees
do you experience at point C (the bottom)?

A| |
\___/
C

*) You are flying an airplane. A side view of the flight path is shown
here, labelled in alphabetical order:

____A___B___G____H___I___
/ C \
F| |D
\___/
E

At points A and B this is ordinary upright flight. At point C you roll
inverted and begin a perfectly circular loop-de-loop. At the completion of
the loop (point G) you roll back to upright and fly away normally. You
arrange the radius of the loop so that at in inverted flight at point C you
_just barely_ don't float out of your seat (zero Gee). Assume thrust is
just enough to compensate for drag, so that you have constant mechanical
energy (KE+PE) to a decent approximation throughout. How many Gees
do you experience at point E (the bottom of the loop)?

Note the relationship of this problem to the previous one.