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 parent's night before Christmas
'Twas the night before Christmas when all through the house
I searched for the tools to hand to my spouse.
Instructions were studied and we were inspired,
In hopes we could manage "Some Assembly Required."
The children were quiet (not asleep) in their beds,
While Dad and I faced the evening with dread:
A kitchen, two bikes, Barbie's town house to boot!
And, thanks to Grandpa, a train with a toot!


We opened the boxes, my heart skipped a beat....
Let no parts be missing or parts incomplete!
Too late for last-minute returns or replacement;
If we can't get it right, it goes in the basement!

When what to my worrying eyes should appear,
But 50 sheets of directions, concise, but not clear,
With each part numbered and every slot named,
So if we failed, only we could be blamed.

More rapid than eagles the parts then fell out,
All over the carpet they were scattered about.
"Now bolt it! Now twist it! Attach it right there!
Slide on the seats, and staple the stair!
Hammer the shelves, and nail to the stand."
"Honey," said hubby, "you just glued my hand."

And then in a twinkling, I knew for a fact
That all the toy dealers had indeed made a pact
To keep parents busy all Christmas Eve night
With "assembly required" till morning's first light.

We spoke not a word, but kept bent at our work,
Till our eyes, they went bleary; our fingers all hurt.
The coffee went cold and the night, it wore thin
Before we attached the last rod and last pin.

Then laying the tools away in the chest,
We fell into bed for a well-deserved rest.
But I said to my husband just before I passed out,
"This will be the best Christmas, without any doubt.

Tomorrow we'll cheer, let the holiday ring,
And not have to run to the store for a thing!
We did it! We did it! The toys are all set
For the perfect, most perfect, Christmas, I bet!"

Then off to dreamland and sweet repose I gratefully went,
Though I suppose there's something to say for those self-deluded...
I'd forgotten that batteries are never included!