6. What happens when you take the common logrythm?

Question

And also...


7. Atmospheric pressure p at an altitude a is given by:

p(a) = p(sub o)e ^ -0.00005a

where p (sub 0) is the pressure at sea level = 14.7 lb/in^2. Explain how a barometer, or some device for measuring armospheric pressure, can be used to find the height of a skyscraper.

Answer 1

you areexpressing the no aspower of 10

2.find the pressure atthe top of the skyscraper
plug in the value in the equation
solve to get the height

Answer 2

Common logarithm of N means find a number a such that 10^a = N

A barometer might not be sensitive enough to measure the height of a skyscraper.
First you'd have to consider the altitude at the ground level of the skyscraper, compared with sea level. Find the pressure at ground level.
Next, take the barometer to the top of the sky scraper. If there is any measurable difference in pressure, you can use this formula. Solve for a:
p(a) = p_o e^(-.00005a)
p(a)/p_o = e^(-.00005a)
ln (p(a)/p_o) = -.00005a
(1/(-.00005a))(ln(p(a)/p_o) = a
-20000 ln((p(a)/p_o)) = a
It is as I thought.
If there is no measurable difference between p(a) at the top of your skyscraper, and p(a) at the base of your skyscraper, this formula would not give you any meaningful result. At any rate, the coeffieicnt of 20000 (ft) suggests to me that this formula would not be sensitve to differences of several hundred feet.
If there's no measurable difference, your barometer isn't sensitive enough to measure the slight difference in air pressure.
Then you'd have to do like the joke along these lines says -- throw the barometer off the skyscraper, measuring the time it takes to fall, then calculating the height of the skyscraper in feet is h = 16t^2. (this is just a studnet's joke, and it's been making the rounds for ages. Actually, you wouldn't throw away a barometer when a rock would do for this test. And you might hurt someone on the sidewalk!)

Answer 3

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