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Measuring height with a barometer
To all who believe there is only one right answer:
A young man was being interviewed for entrance to Cambridge college to study
physics. He was asked among other things, the following question:
How would you measure the height of a skyscraper using a barometer?
The candidate replied as follows: Take a very long piece of string. Tie one
end of it to the barometer. Keeping hold of the other end, dangle the
barometer off the roof of the skyscraper until it reaches the ground. Then
the length of the string plus the length of the barometer equals the height of
the skyscraper. The interviewing tutors did not accept the answer, and the
candidate was rejected. But he appealed to the university authorities on
the grounds that his answer while perhaps unorthodox, was undeniably correct.
It so happened that professor Iza Conman of Michigan was in Cambridge at the
time as visiting professor, and he was asked to arbitrate in the dispute. He
asked the candidate to see him, and gave him five minutes to reply to the same
question in a way that showed knowledge of the basic principles of physics.
The young candidate was silent for three minutes. Conman warned him that the
time was running out. "The problem is," said the candidate, "I've thought of
several possible answers, but I can't decide which is the best."
"One minute," said Conman. "Well," said the candidate, "You could take the
barometer to the roof of the building and drop it, using a stopwatch to measure
the time the barometer took to reach the ground. If this t is time, and the
acceleration due to gravity is g, then the height of the building would be
gt/2. (editor's note: neglecting friction and lift.) But then you've got an
"If the sun is shining, you could measure the length of the barometer, the
length of its shadow, and the length of the skyscraper's shadow. Then it's
just a matter of proportional arithmetic to work out the height of the sky-
"If you want to be highly scientific you could tie a piece of string to the
barometer and make it swing like a pendulum, first on the roof and then on the
ground. Then you could work out the acceleration due to gravity on the roof
and on the ground from the period of the oscillation of the pendulum. From
this difference you can determine the height of the building.
"Or you could walk up the stairs with the barometer and a pencil, marking off
lengths of the barometer as you go. Adding them up at the end."
"If you want to be boring you could measure the air pressure on the roof and
at ground level, convert millibars to meters and get the height of the sky-
scraper from that.
"But in the end the best method would probably be to knock on the janitor's
door and say, `Look; if you tell me how high this building is, I'll give you
this lovely new barometer.'"