The Barometer Story

(There are many versions of this story...)

A student refused to parrot back what he had been taught in class. When the student protested, I was asked to act as arbiter between the student and his professor.

I went to my colleague’s office and 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 the barometer 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.”

A high grade is supposed to certify competence in physics, but the answer did not confirm this. I suggested that the student have another try at answering the question. I gave the student six minutes, with the warning that his answer should show some knowledge of physics. 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 S = ½at2, 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 leaving my colleague’s office, I recalled that the student had said he had other answers to the problem, so I asked him what they were.

“Oh, yes. 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 a simple proportion, determine the height of the building.”

Fine, I said. And the others?

“Yes. 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.”

“Finally, there are many other ways of solving the problem. Probably not the best 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 I have a fine barometer. If you will tell me the height of this building, I will give you this barometer.’”

Other solutions off the ’net:

Walk away from the building with the barometer at arm’s length. Once the apparent height of the barometer is the same as the building’s, measure the distance from the building and the height of the barometer and use a little trig.

Tie the barometer to the end of a long string such that the end just touches the ground when you hold it from the roof. Raise it (say) one foot. Swing the barometer-pendulum and time its period, then calculate the length of the pendulum from the pendulum equation T = 1/(gL)½ — don’t forget to add back that foot.

Walk back a measured distance from the building. using any convenient means, throw the barometer at the top of the building. (Use trial and error until you get the aim right) Measure the angle from the ground and the initial velocity, account for wind and air resistance, use several formulae, and be prepared to account for why you just smashed the shit out of the professor’s new barometer.

Give the barometer to a cab driver in exchange for him taking you over to City Hall so you can look up the height of the building in their records.