barometers

[Kamlesh Kosare <kamleshk@xxxxxxxxxxxxx>]

Some time ago I received a call from a colleague. He was about to give a
student a zero for his answer to a physics question, while the student
claimed a perfect score. The instructor and the student agreed to an
impartial arbiter, and I was selected. I 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."

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 and to certify competence in physics, but the answer did not confirm
this.

I suggested that the student have another try. 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 hadn't written
anything. I asked if he wished to give up, but he said he had many answers
to this problem; he was just thinking of the best one. I excused self 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
x=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. While 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.

"Well," 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 his 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." "On this same tact, you could
take the barometer to the top of the building, attach a long rope to it,
lower it to just above the street, and then swing it as a pendulum. You
could then calculate the height of the building by the period of the
precession". "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.

The student was Neils Bohr and the arbiter Rutherford.


-- 
If you can't explain something to a six-year old, you really don't
understand it yourself -- Albert Einstein