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Re: centrifuge exercises



At 12:01 AM 11/5/00 -0500, Ludwik Kowalski wrote:

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


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.)

*) 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.