Sunday, December 18, 2011

The Barometer

"Joy to the world, the lord has come, joy to the world...",  The Professor was singing and humming in an obviously joyous voice as he lit up his pipe and began the preparations of calling this an year.  "Almost there", he thought, "a few more test papers to grade and off I go, let the Christmas start". He wished for a white Christmas in the beautiful city of Copenhagen but chances seemed slim. 


The test paper was an easy one, he didn't feel like getting anybody in trouble (as he'd done it for the past years, but somehow the buzz was gone :) ). "Given a barometer, how could one measure the height of a skyscraper?". It's trivial for anybody trying to pursue a career, however petty, in physics. The answers were good as well, all indicating the best known method: measure the pressure at the ground level, then at the top, convert the millibars in metres and that's it, we have the precise height. 



If we tie the barometer to a rope and lower it from the top of the skyscraper to the ground, then the height of the skyscraper will be the length of the rope plus the height of the barometer. 

"I cannot believe my eyes", he muttered to himself, "it's always one, one to play the foolish jester, one who not only shows that he doesn't have anything in common with science, but mocks it. Such defiance and impudence will not be overlooked."


Next day, he called upon the "impudent" and began the scolding:


"Smaaaaart", he said in great anticipation of a terrible movie from the 80's, 75 years later, "I like. Smart ass - I don't!! Not only that you showed no knowledge of physics, but you're defying me and your colleagues altogether and you leave me with no option but to fail you". 


"With all due respect, Mr Professor, Sir, but my answer is undoubtedly correct. I will kindly ask a third opinion in the matter". 


Although without any pleasure, the benefit of the doubt was granted and some colleagues of the Professor came along and they gave "the impudent" five minutes to show any respectable knowledge of physics. 


For four minutes he did nothing, wrote nothing on the piece of paper in front of him. 


"I'd like to tell you that the time is almost up, do you have any answers?", inquired the Professor with a self-satisfied smirk on his face.


"Well, Mr Professor,Sir, I have a few answers indeed. One solution would be to go on the skyscraper roof and let the barometer fall. Then time the time it needs to reach the ground and the height could be worked out from the formula H = 1/2 *g*t^2, where g is the gravitational acceleration. Pity though for the barometer.


We could be very scientific about this and tie up a short string to the barometer and swing it like a pendulum both on the roof and at the ground level. The height is worked out by the difference in the gravitational restoring force T = 2 pi sqrroot (l / g).


If the sun is shining we could make use of the shadows of the barometer and the skyscraper. We measure both of them and the we work it out easily using simple maths proportions by using the known length of the barometer.


Or, if there's an outside emergency staircase (and most of the skyscrapers have it!) we could climb it and mark the wall off in barometer's lengths and then just add them up. Quite an arduous job though.


Or, ..."


"Stoooop, please stop! For crying out loud, why can't you give me the simplest answer to this, like anyone else? It's a straighforward answer, for the love of God!"


"The simplest answer would be to knock on the caretaker's door and ask ``I'll give you this brand new barometer if you tell me the height of the skyscraper! Merry Christmas!``"


Legend has it that the student was Niels Bohr, the first Dane to win the Nobel prize for Physics and father to another Nobel laureate



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