paulp (06/02/82)
The Barometer Story
by Alexander Calandra
(An article from _C_u_r_r_e_n_t _S_c_i_e_n_c_e, _T_e_a_c_h_e_r_s _E_d_i_t_i_o_n, 1964)
Some time ago, I received a call from a colleague who
asked if I would be the referee on the grading of an exami-
nation question. It seemed that he was about to give a stu-
dent a zero for his answer to a physics question, while the
student claimed he should receive a perfect score and would
do so if the system were not set up against the student.
The instructor and the student agreed to submit this to an
impartial arbiter, and I was selected.
The Barometer Problem
I went to my colleagues office and read the examination
question, which was, ``Show how it is possible to determine
the height of a tall building with the aid of a barometer.''
The student's answer was, ``Take the barometer to the top
of the building, attach a long rope to it, lower the barome-
ter 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.''
Now, this is a very interesting answer, but should the
student get credit for it? I pointed out that the student
really had a strong case for full credit, since he had
answered the question completely and correctly. On the
other hand, if full credit were given, it could well contri-
bute to a high grade for the student in his physics course.
A high grade is supposed to certify that the student
possesses a thorough understanding of the course material.
The answer to the question did not confirm this. With this
in mind, I suggested that the student have another try at
answering the question. I was not surprised that my col-
league agreed to this, but I was surprised that the student
did.
Acting in terms of the agreement, I gave the student five
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, since I had another class to take care
of, but he said no, he was not giving up. 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 was:
``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=1/2at829,
calculate the height of the building.''
At this point, I asked my colleague if he would give up.
He conceded and I gave the student almost full credit. In
June 2, 1982
- 2 -
leaving my colleagues office, I recalled that the student
had said 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 barome-
ter, the length of its shadow, and the length of the shadow
of the building, and by the use of simple proportion, deter-
mine the height of the building.
``Fine,'' I said, ``And the others?''
``Yes,'' said the student. ``There is a very basic meas-
urement method that 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 can, in
principle, be calculated.
Finally he concluded, ``If you don't limit me to physics
solutions to this problem, there are many answers, such as
taking the barometer to the basement and knocking on the
superintendents door. When the superintendent answers, you
speak to him as follows: `Dear Mr. Superintendent, here I
have a very fine barometer. If you will tell me the height
of this building, I will give you this barometer.'
At this point, I asked the student if really didn't know
the answer to the problem. He admitted that he did, but
that he was so fed up with college instructors trying to
teach him how to think and to use critical thinking, instead
of showing him the structure of the subject matter, that he
decided to take off on what he regarded mostly as a sham.
June 2, 1982dmmartindale (06/03/82)
I would think that many of the unorthodox methods proposed for measuring the height of the building are potentially much more accurate than measuring air pressure differences with a barometer. Air density (and thus pressure change with altitude) varies quite a bit with temperature; wouldn't you need to have a complete knowledge of the air temperature between ground level and the top of the building in order to get an accurate answer?