Tuesday, 2 September 2008

Thimk Different

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:


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 had not 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 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 H = 1/2 x a x 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 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."

"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 Neil Bohr (known for quantum theory of physics &
mechanics,hydrogen atom etc ) and the arbiter wasRutherford .


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