| The professor is good on theory, but short on practice. He set an exam question "Given a barometer, determine the height of City University's clock tower". He expects us to know that atmospheric pressure drops about 1 millbar every 26 feet of altitude at sea level. Thus a measured difference of 3 mb would show the tower to be 78 feet high. In practice, you can't read a barometer to better than ½ mb accuracy, implying +/- 13 feet on the measurement, or +/- 17%. We decided to show him some more accurate alternatives and criticise his theory-heaviness simultaneously ;-)
• Tie the barometer to a piece of string, swing it as a pendulum, and calculate the value of g at the street level and at the top of the clock tower. From the difference between the two values of g deduce the height of the clock tower (in theory). Accuracy +/- 10,000 % ?
• Take the barometer to the top of the clock tower. Drop the barometer, timing its fall with a stopwatch. Then using the formula H = ½gt2 calculate the height H of the clock tower. Accuracy +/- ¼ sec on the stopwatch, so +/- 11% or 8 feet.
• On a sunny day measure the height of the barometer, the length of its shadow, and the length of the shadow of the clock tower. Now, by geometry, determine the height of the clock tower. Accuracy probably +/- 2% = 1 ½ feet.
• Walk up the clock tower stairs, marking off the length of the barometer up the stairwell. Count the marks, giving the height of the clock tower in barometer units. Finally, multiply by the size of the barometer. Accuracy +/- 2 inches.
• Take the barometer to the top of the clock tower, attach a long rope to it (the barometer!), lower the barometer to the pavement, now reel it in, measuring the length of the rope, which gives the height of the clock tower directly. Accuracy +/- 1 inch.
• Bribe the university janitor by giving him the new, unused, barometer if he tells you the height of the clock tower by looking it up on the building's plans. Accuracy? Perfect!  |