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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 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 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
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.
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