Barometer problems.
The following concerns a question in a physics degree exam at the University of Copenhagen: "Describe how to determine the height of a skyscraper with a barometer." One student replied: "You tie a long piece of string to the neck of the barometer, then lower the barometer from the roof of the skyscraper to the ground. The length of the string plus the length of the barometer will equal the height of the building." This highly original answer so incensed the examiner that the student was failed immediately. The student appealed on the grounds that his answer was indisputably correct, and the university appointed an independent arbiter to decide the case. The arbiter judged that the answer was indeed correct, but did not display any noticeable knowledge of physics. To resolve the problem it was decided to call the student in and allow him six minutes in which to provide a verbal answer that showed at least a minimal familiarity with the basic principles of physics. For five minutes the student sat in silence, forehead creased in thought. The arbiter reminded him that time was running out, to which the student replied that he had several extremely relevant answers, but couldn't make up his mind which to use. On being advised to hurry up the student replied as follows: "Firstly, you could take the barometer up to the roof of the skyscraper, drop it over the edge, and measure the time it takes to reach the ground. The height of the building can then be worked out from the formula H = 0.5g x t squared. But bad luck on the barometer." "Or 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." "But if you wanted to be highly scientific about it, you could tie a short piece of string to the barometer and swing it like a pendulum, first at ground level and then on the roof of the skyscraper. The height is worked out by the difference in the gravitational restoring force T =2 pi sqr root (l /g)." "Or if the skyscraper has an outside emergency staircase, it would be easier to walk up it and mark off the height of the skyscraper in barometer lengths, then add them up." "If you merely wanted to be boring and orthodox about it, of course, you could use the barometer to measure the air pressure on the roof of the skyscraper and on the ground, and convert the difference in millibars into feet to give the height of the building." "But since we are constantly being exhorted to exercise independence of mind and apply scientific methods, undoubtedly the best way would be to knock on the janitor's door and say to him 'If you would like a nice new barometer, I will give you this one if you tell me the height of this skyscraper'." The student was Niels Bohr, the only Dane to win the Nobel Prize for physics.
Walk away from the building with the barometer at arm's length. Once the apparent height of the barometer is the same as the building’s, measure the distance from the building and the height of the barometer and use a little trigonometry.
On a sunny day, place the barometer on the ground. Mark both ends. Stand the barometer upright on the mark closer to the sun, so the shadow will be approaching the other mark. Note the exact time when the shadow reaches the other mark. On the following sunny day, mark the end of the shadow cast by the building at exactly that time. Measure the distance from there to the building. This is the height of the building. Note: The accuracy of this technique depends on the number of days between consecutive sunny days
Hold the barometer one foot in front of yourself and find a position where the building appears to be the same size as the barometer. Now measure the distance to the building (in feet) and multiply by the height of the barometer
Go to a local shop and trade the barometer for the longest measuring tape they have. Take the tape onto the roof of the building. Holding one end, drop the other end over the edge of the building. Raise the measuring tape until the far end is just touching, not resting on, the ground. Read the height of the building from the measuring tape. Note: For particularly tall buildings, this may require a particularly good hardware store.
Hold the barometer straight in front of you and drop it. Measure, very carefully, how long it takes to hit the ground. Go up on the roof and hold the barometer in the same position. Drop it and measure, again very carefully, how long it takes to hit the roof. Since gravity falls off as the square of the distance from the centre of the planet, you can use the difference in times to calculate the height of the building relative to the distance from the base of the building to the centre of the planet. The local library can provide you with the distance to the centre of the planet in the required units. Note: The ratio of the times is the same as the ratio of the distances from the drop points to the centre of the planet.
Drop (and shatter) the mercury barometer at the base of the building on a windless day. Measure the increase in the mercury vapour concentration at the top of the building. Solve the diffusion equation to determine the distance from the shattered barometer to the top of the building.
Place the barometer on the ground floor of the building. Seal all the building's doors and windows. Fill the building with water. Read the pressure measurement from the barometer. This gives the weight of a column of water the same height as the building. Use this and the ratio of the density of mercury to the density of water to calculate the height of the building. Note: It is common courtesy to evacuate the building before using this technique
Go to all the local gift shops. Look for a fancy souvenir barometer, the kind which shows important local landmarks. Find one, which shows the heights of local buildings and considers this building important enough to be listed. Use this barometer.
Clap the barometer against the top of the building. Measure the time taken to hear the echo from the ground. Find the height of the building by multiplying half the echo delay by the velocity of sound
Walk back a measured distance from the building. Using any convenient means, throw the barometer at the top of the building. (Use trial and error until you get the aim right) Measure the angle from the ground and the initial velocity, account for wind and air resistance, use several formulae, and be prepared to account for why you just smashed the sh*t out of the professor's new barometer.
slashed at 11:04 PM .
