Creative Thinking

By Alexander Calandra (1911–2006)

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.

--From Wikipedia

According to Snopes.com, more recent (1999 and 1988) versions identify the problem as a question in "a physics degree exam at the University of Copenhagen" and the student as Niels Bohr, and includes the following answers:^[21]

• Tying a piece of string to the barometer, lowering the barometer from the roof to the ground, and measuring the length of the string and barometer.
• Dropping the barometer off the roof, measuring the time it takes to hit the ground, and calculating the building's height assuming constant acceleration under gravity.
• When the sun is shining, standing the barometer up, measuring the height of the barometer and the lengths of the shadows of both barometer and building, and finding the building's height using similar triangles.
• Tying a piece of string to the barometer, and swinging it like a pendulum both on the ground and on the roof, and from the known pendulum length and swing period, calculate the gravitational field for the two cases. Use Newton's law of gravitation to calculate the radial altitude of both the ground and the roof. The difference will be the height of the building.
• Tying a piece of string to the barometer, which is as long as the height of the building, and swinging it like a pendulum, and from the swing period, calculate the pendulum length.
• Marking off the number of barometer lengths vertically along the emergency staircase, and multiplying this with the length of the barometer.
• Trading the barometer for the correct information with the building's janitor or superintendent.
• Measuring the pressure difference between ground and roof and calculating the height difference (the expected answer).

--Note: Someone posted this answer.
I like throwing it of the roof and count the seconds the most, but what the instructors wanted to hear is most likely to apply the barometric formula, which reads p(h)=p0exp(−mghkBT)$p(h)=p_0\exp (\frac{-mgh}{k_{B}T})$, assuming the same temperature hat level p0$p_0$ and p(h)