Sir Ernest Rutherford, President of the Royal Academy, and recipient of the Nobel Prize in Physics, related the following story:
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
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 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 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 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
[gravity] 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 tack, 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 tell him how to think.
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The name of
the student was Niels Bohr. (1885-1962) Danish Physicist; Nobel Prize 1922;
best known for proposing the first 'model' of the atom with protons &
neutrons, and various energy state of the surrounding electrons-the familiar
icon of the small nucleus circled by three elliptical orbits ... but more significantly,
an innovator in Quantum Theory.
A barometer