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.

Real Estate Ads Translated
Real Estate Ads Translated ============================  Enormous potential: Enormous amount of work to do.Low maintenance lot – No yard; the kids will have to play in the streetClose to school: close to vandals.Outstanding: Sticks out like a sore thumb.One-Of-A-Kind: Ugly as sin.Above ground pool: Piece of leaky plastic filled with water.Unique City Home: Used to be a warehouse.Mint: Someone spilled mouthwash on carpet.1 car garage – You can drive your car into the garage but there is no room to open the doorPicturesque setting: Abandoned cars and waist-high weeds in neighboring lots.Seasonal creek – Muddy ditch across the propertyAbsolute water frontage: Gets flooded out every ten years.Bedroom in basement – Basement has a 1′ by 2′ window.Desirable neighborhood – This little house is extravagantly overpriced because the neighborhood has a snobbish reputationWide-open floor plan: Previous owner removed supporting walls.Ready to move in – the interior has been painted with one coat of cheap paint.Motivated sellers – Bank is about to foreclose.Close to public transportation: Beneath railway line.Territorial view – Good view of your neighbor’s bedroom windowDelightful cottage: Garden is overgrown.Executive style living: Has a spa.Country in the city – A grotesquely overpriced large lot with a 2 bedroom house built before World War I.Prime location: Next to a factory.Newly remodeled kitchen – 50-year old cabinetry and faucets have been replaced with cheap modern equivalents.Stunning house – The house is not ugly.Leafy aspects: Trees block your view.Investment Opportunity: Needs a lot of money spent to fix it up.Lower-level family room: Ping-pong table over sewer opening.Move-in condition: Front door missing.Short walk to shops: 5 minute walk to shops. Minutes to shops: 10 minute walk to shops. Handy to shops: Nowhere near shops.Usable land – All the trees are gone.Must see inside – the outside is ugly.Old World Charm: Has some woodwork. Needs cleaning.Situated in rapidly progressing area: In the sticks.Contemporary Feeling: Has no woodwork. Needs cleaning.Three season sunroom – A small addition the owner did not have enough money to insulate.Tudor – Two bedrooms are in the attic which is not insulated; very hot in summer and very cold in winter.Easy walking distance too ____: Two miles from ____.Developers take note: The house is falling down.Near transportation – Amtrak train goes through the backyard, every 15 minutes, day and night.Wildlife nearby – Children and pets get ticks and fleas.Ready to remodel – the house is about to collapse; you will have to invest twice the asking price in remodel before you can move in.Brand new: 1 year old. New: 3 years old. As new: 6 years old. Modern: 10 years old. Solid: 15 yeas old. Cottage: 25 years old. Full of character: 50 years old.Easy to heat – See “cozy”.Nothing to spend: After buying you'll have nothing left to spend.Upper Bracket: If you have to ask...Includes all the things that make a house a home: Has an indoor toilet.Easy freeway access – Noisy arterial street close to freewayWill not last at this price: Will not sell at this price.Light, open spaces: Many holes in walls.Sophisticated City Living: Next to noisy bar.Neighborhood watch – Your next door neighbor has binoculars trained on your houseClose to lakes: Impossible to park on the street from April to October.Updated kitchen: Sink no longer overflows.Partially renovated: Owner gave up on a hopeless case.Security system: Neighbor has dogHandyman's delight: The roof is about to collapse.Doll-house – Tiny place filled with ugly knick-knacks.Beautifully presented: The lawn has been mowed.Land suitable for a pole home: On a cliff.Cape Cod – Styled after Third World slum dwellings.Brilliant Concept: Do you really need a two-story live oak in your 30-foot sky dome? See "Makes Dramatic Statement."Tasteful: Carpeted.Sunny corner lot – Noisy intersection of two busy streetsConvenient: Located on freeway entrance ramp.Suit young kids: You can allow kids to run wild, nothing worth protecting from damage.Not much mowing: No land.Sophisticated: Black walls and no windows. See "Architect's Delight."Close to all amenities – The backyard is a shopping mall parking lot.Potential is immeasurable: Present value is minimal.Retirement special: A good home to die in.Pet friendly neighborhood – Organic matter constantly deposited in the front lawnA rare find: Rare to find a house built like this still standing.Magnificent aspects: On a hill.Cozy – Not a single room could fit a full size bed.Loads of character: Bizarre.Charming: Tiny. Snow White might fit, but five of the dwarfs would have to find their own place. See "Cute," "Enchanting," and "Good Starter Home."Needs TLC - Major structural damage.You'll Love It: No, you won't.Recreation room with wet bar – Basement has been painted and has a faucet.Prestige surrounds: All the other houses in the street are nicer.Executive home: Overpriced.Storybook – The house is old and the roof is not flatMeticulously maintained in the original condition – The appliances are 50 years oldLots of storage space – Basement too small to be called a family room.Inner city living at its best: Close to muggers.Build sweat equity – The house is not inhabitableGenerous built-ins: Has cupboards.Country living – Too far from anywhere to drive to work.Old charmer – An old and ugly house.Efficiently designed kitchen – The kitchen is too small to fit two people at the same timeSought after location: Frequently broken into.Large family room – Large basement.Just available – Previous owner just died on the premises.Must See To Believe: An absolutely accurate statement.