Barometers and Analog Design...

The Loony Bin ( loonies@bloodaxe.demon.co.uk )
Fri, 27 Sep 1996 16:35:14 +0100


Hiya People...

Here's a physics novelty for you...

Wishes & Dreams...

- ANDREA
        xx

*************<andrea@bloodaxe.demon.co.uk>*************
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  ------- Forwarded foolishness follows -------


By Alexander Calandra


Some time ago I received a call from a colleague, who asked if I would
be the referee on the grading of an examination question.  He was about
to give a student a zero for his answer to a physics question, while the
student claimed he should receive a perfect score and would if the
system were not set up against the student.  The instructor and the
student agreed to an impartial arbiter, and I was selected.  I went to
my colleague's office and read the examination question:

"Show how it is possible to determine the height of a tall building with
the aid of a barometer."

The student had answered: "Take the barometer to the top of the
building, attach a long rope to it, lower it to the street, and then
bring it up, measuring the length of the rope. The length of the rope is
the height of the building."

I pointed out that the student really had a strong case for full credit
since he had really answered the question completely and correctly.  On
the other hand, if full credit were given, it could well contribute to a
high grade in his physics course.  A high grade is supposed to certify
competence in physics, but the answer did not confirm this.  I suggested
that the student have another try at answering the question.  I was not
surprised that my colleague agreed, but I was surprised when the student
did.  I gave the student six minutes to answer the question with the
warning that the answer should show some knowledge of physics.  

At the end of five minutes, he had not written anything.  I asked if he
wished to give up, but he said no. He had many answers to this problem;
he was just thinking of the best one.  I excused myself for interrupting
him and asked him to please go on.  In the next minute, he dashed off
his answer which read:

"Take the barometer to the top of the building and lean over the edge of
the roof.Drop the barometer, timing its fall with a stopwatch. Then,
using the formula S=0.5*a*t^2, calculate the height of the building."

At this point, I asked my colleague if he would give up.  He conceded,
and gave the student almost full credit.  In leaving my colleague's
office, I recalled that the student had said that he had other answers
to the problem, so I asked him what they were.  

"Oh, yes," said the student."There are many ways of getting the height
of a tall building with the aid of a barometer.For example, you could
take the barometer out on a sunny day and measure the height of the
barometer, the length of its shadow, and the length of the shadow of the
building, and by the use of simple proportion, determine the height of
the building."

"Fine," I said, "and others?"

"Yes," said the student."There is a very basic measurement method you
will like.In this method, you take the barometer and begin to walk up
the stairs.  As you climb the stairs, you mark off the length of the
barometer along the wall.  You then count the number of marks, and this
will give you the height of the building in barometer units.

"A very direct method."

"Of course, if you want a more sophisticated method, you can tie the
barometer to the end of a string, swing it as a pendulum, and determine
the value of g at the street level and at the top of the building. From
the difference between the two values of g, the height of the building,
in principle, can be calculated."

"Finally," he concluded, "there are many other ways of solving the
problem. Probably the best," he said, "is to take the barometer to the
basement and knock on the superintendent's door.  When the
superintendent answers, you speak to him as follows:  'Mr.
Superintendent, here is a fine barometer.  If you will tell me the
height of the building, I will give you this barometer.'"

At this point, I asked the student if he really did not know the
conventional answer to this question.  He admitted that he did, but said
that he was fed up with high school and college instructors trying to
teach him how to think, to use the 'scientific method', and to explore
the deep inner logic of the subject in a pedantic way, as is often done
in the new mathematics, rather than teaching him the structure of the
subject.  With this in mind, he decided to revive scholasticism as an
academic lark to challenge the Sputnik-panicked classrooms of America.