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 tourist wanders into a back-alley antique shop...
A tourist wanders into a back-alley antique shop in San Francisco's Chinatown. Picking through the objects on display he discovers a detailed bronze sculpture of a rat. The sculpture is so interesting and unique that he picks it up and asks the shop owner the price. "Twelve dollars for the rat, sir," says the shop owner, "and an extra thousand for the story behind it." "At that price, you can keep the story, old man," he replies, "but I'll take the bronze rat." The transaction complete, the tourist leaves the store with the bronze rat under his arm. As he crosses the street in front of the store, two live rats emerge from a sewer drain and fall into step behind him. Nervously looking over his shoulder, he begins to walk faster, but every time he passes another sewer, more rats come out and follow him. By the time he's walked two blocks, at least a hundred rats are at his heels, and people begin to point and shout. He walks even faster, and soon breaks into a trot as multitudes of rats swarm from sewers, basements, vacant lots, and abandoned cars... following him. Rats by the thousands are at his heels, and as he sees the waterfront at the bottom of the hill he panics and starts to run full tilt. No matter how fast he runs, the rats keep up, squealing hideously now not just thousands but millions, so that by the time he comes racing to the water's edge a trail of rats twelve blocks long is behind him. Making a mighty leap, he jumps up onto a lamp post, grasping it with one arm, while he hurls the bronze rat into San Francisco Bay as far as he can throw it. Pulling his legs up and clinging to the post, he watches in amazement as the seething tide of rats surges over the breakwater into the sea, where they drown. Shaken and mumbling, he makes his way back to the antique shop. "Ah sir, you've come back for the story," says the owner. "No," says the tourist, "I was just hoping you had a bronze sculpture of a lawyer "