The end-of-chapter problem from Serway & Faughn's College Physics
that Ludwik has brought to our attention is a lovely example of an
all-but-useless task set for students.
I wrote "all-but-useless" rather than useless because I guess it could
be argued that it teats the student's ability to plug and chug ("drill
and practice" Ludwik calls it) but that's algebra, not physics. Is
anyone going to argue that the students display their understanding of
physics by plugging in a given number of values (exactly the right
number of values are given in the problem) into a formula?
It might also be argued that the results of the substitutions gives
the students a real-world feel for how fast a centrifuge must go. If
so, can someone explain to me where the value of 4E-11 N for the
magnitude of the force came from. My cynical mind does not accept
that it is an experimentally measured value; I think it came from
Serway or Faugh or one of their problem assistants themselves plugging
numbers into that formula to see what force was associated with an
angular speed of 150 rev/s.
Obviously neither of these arguments for the usefulness of the problem
turn me on.
It's a pity. The example of the centrifuge can be used to promote an
understanding of the physics involved. And understanding is what we
want from our students rather than blind number-plugging.
What is the physics involved?
(1) Why don't the blood corpuscles settle out when the blood is
sitting in test tube? OR What are the forces on any corpuscle
balancing the gravitational force on it?
(2) How are the forces on the corpuscle altered when the tube is
whirling around in a centrifuge?
Here the teacher and student have to be careful, as the explanation is
different in the lab frame of reference and the accelerated centrifuge
frame of reference.
In the lab frame circular motion is involved. Initially the contact
force from its environment is not sufficient to produce a circular
path for the corpuscle. That doesn't happen until, in its outwardly
spiralling path, it reaches a different environment of the end of the
tube and experiences a much greater (radially inward) contact force.
In the accelerated frame of the centrifuge, there is no circular
motion, just a straight line drift, with increasing speed, towards the
end of the tube under the influence of a centrifugal force much
greater than the environmental contact force. At the end of the tube
there is a much increased contact force that first stops the corpuscle
and then allows it to stay at rest in that frame.
Lots of physics, lots of understanding needed, and so much opportunity
for interactive learning. On the other hand, such an opportunity
missed by presenting a plug-in problem.
No wonder Ludwik was so dissatisfied with the situation.