Lee's Funnies

Sir Ernest Rutherford, President of the Royal Academy, and recipient of the 
Nobel Prize in Physics, related the following story:

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, 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 
[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.

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The name of the student was Niels Bohr. (1885-1962) Danish Physicist; Nobel 
Prize 1922; best known for proposing the first 'model' of the atom with protons 
& neutrons, and various energy state of the surrounding electrons -- the 
familiar icon of the small nucleus circled by three elliptical orbits ... but 
more significantly, an innovator in Quantum Theory.


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