The Student and The Barometer

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,if the sun is shining you could measure the height of the barometer, then set it on end and measure the length of its shadow. Then you measure the length of the skyscraper's shadow, and thereafter it is a simple matter of proportional arithmetic to work out the height of the skyscraper.

"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 teach him how to think.

The name of the student was Niels Bohr, who later received the Nobel prize for Physics.

A U.S Army Colonel issues a directive
A U.S. ARMY COLONEL ISSUED THE FOLLOWING
DIRECTIVE TO HIS EXECUTIVE OFFICERS:

"Tomorrow evening at approximately 2000 hours Halley's Comet
will be visible in this area, an event which occurs only once every
75 years. Have the men fall out in the battalion area in fatigues,
and I will explain this rare phenomenon to them. In case of rain,
we will not be able to see anything, so assemble the men in the
theater and I will show them films of it."

EXECUTIVE OFFICER TO COMPANY COMMANDER:

"By order of the Colonel, tomorrow at 2000 hours, Halley's comet
will appear above the battalion area. If it rains, fall the men out in
fatigues, then march to the theater where this rare phenomenon
will take place, something which occurs only once every 75 years."

COMPANY COMMANDER TO LIEUTENANT:

"By order of the Colonel in fatigues at 2000 hours tomorrow evening,
the phenomenal Halley's Comet will appear in the theater. In case
of rain, in the battalion area, the Colonel will give another order,
something which occurs once every 75 years."

LIEUTENANT TO SERGEANT:

"Tomorrow at 2000 hours, the Colonel will appear in the theater with
Halley's Comet, something which happens every 75 years if it rains,
the Colonel will order the comet into the battalion area."

SERGEANT TO SQUAD:

"When it rains tomorrow at 2000 hours, the phenomenal 75 year old
General Halley, accompanied by the Colonel, will drive his comet
through the battalion area theater in fatigues."