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 Problem of Problems
A young couple decided to wed.

As the big day approached, they grew apprehensive.

Each had a problem they had never before shared with anyone, not even each other.

The Groom-to-be, overcoming his fear, decided to ask his father for advice.

"Father," he said, "I am deeply concerned about the success of my marriage."

His father replied, "Don't you love this girl?"

"Oh yes, very much," he said, "but you see, I have very smelly feet, and I'm afraid that my fiance will be put off by them."

"No problem," said dad, "all you have to do is wash your feet as often as possible, and always wear socks, even to bed."

Well, to him this seemed a workable solution.

The bride-to-be, overcoming her fear, decided to take her problem up with her mom.

"Mom," she said, "When I wake up in the morning my breath is truly awful."

"Honey," her mother consoled, "everyone has bad breath in the morning."

"No, you don't understand,. My morning breath is so bad, I'm afraid that my fiance will not want to sleep in the same room with me."

Her mother said simply, "Try this. In the morning, get straight out of bed, and head for the kitchen and make breakfast. While the family is busy eating, move on to the bathroom and brush your teeth. The key is, not to say a word until you've brushed your teeth."

"I shouldn't say good morning or anything?" the daughter asked.

"Not a word," her mother affirmed.

"Well, it's certainly worth a try," she thought.

The loving couple were finally married. Not forgetting the advice each had received, he with his perpetual socks and she with her morning silence, they managed quite well.

That is, until about six months later. Shortly before dawn one morning, the husband wakes with a start to find that one of his socks had come off.

Fearful of the consequences, he frantically searches the bed. This, of course, wakes his bride and without thinking, she asks, "What on earth are you doing?"

"Oh, my," he replies, "you've swallowed my sock!"