“Be kind, for everyone you meet is fighting a hard battle” - Often attributed to Plato but likely from Ian McLaren (pseudonym of Reverend John Watson)

Thursday, November 18, 2010

I don't have a barometer but I have an iPhone

There's an old apocryphal tale of a high school physics student taking a test who's asked "how would you use a barometer to measure the height of a building?" The expected answer is "measure the barometric pressure at the bottom and the top, use the pressure lapse rate with altitude to determine the height." This was not the answer given by the student. When his teacher marked the answer as incorrect, the student protested, telling the teacher that there are many ways to use a barometer to find the height of a building. The teacher was curious and asked the student to name a few. The student came up with (in addition to the obvious answer above):
  • On a sunny day, set the barometer on a sidewalk and measure the height of the barometer and its shadow. Measure the building's shadow, apply the ratio.
  • Drop the barometer from the roof, time its descent to the street and use s=.5*g*t^2.
  • From the roof, tie the barometer to a string, lower it until it almost touches the street. Set it swinging and measure the period, and apply t=2*Pi*(L/g)^0.5
  • Measure the height of the barometer, use the core stair to count barometer heights to the top of the building, multiply.
  • The easiest? Take the barometer to the building manager and say "I have a fine barometer here, and if you'll tell me the height of your building, I'll give it to you."
Not having a barometer handy, I didn't do any of those, but I used the Pasco SPARKvue program on my iPhone to measure and record the acceleration during an elevator trip from the third floor to the 11th of the Hilton Americas-Houston where I'm staying. The program will email the data in CSV format. I then used Excel to numerically integrate the acceleration and the velocity to find displacement. The distance worked out to  be 100' 1 1/2" for the eight floors, a floor height of about 12.5'. This is a little more than I'd have estimated. The hotel has 19 floors and, I assume, a mechanical penthouse, so I'm going with 19*12.5 + 10 (the mechanical penthouse will be shorter) for a total of 247.5'.

The top (and steady) speed reached by the elevator (a Schindler) was 7.9 m.p.h. The peak acceleration was about 0.8 m/s^2, less than 0.1 "g". And if my iPhone were as smart as it (and Steve Jobs) thinks it is, it could distinguish acceleration from gravity in a closed elevator cab. Oh, wait...

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