By Benjamin Crowell

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**Sample text**

Let me see: that would be four thousand miles down, I think” (for, you see, Alice had learned several things of this sort in her lessons in the schoolroom, and though this was not a very good opportunity for showing off her knowledge, as there was no one to listen to her, still it was good practice to say it over)... Alice doesn’t know much physics, but let’s try to calculate the amount of time it would take to fall four thousand miles, starting from rest with an acceleration of 10 m/s2 . This is really only a lower limit; if there really was a hole that deep, the fall would actually take a longer time than the one you calculate, both because there is air friction and because gravity gets weaker as you get deeper (at Problems 49 the center of the earth, g is zero, because the earth is pulling you equally in every direction at once).

The square root of ab). For the sake of definiteness, let’s say both numbers have units of mass. (a) Compute the arithmetic mean of two numbers that have units of grams. Then convert the numbers to units of kilograms and recompute their mean. Is the answer consistent? (b) Do the same for the geometric mean. (c) If a and b both have units of grams, what should we call the units of ab? Does your answer make sense when you take the square root? (d) Suppose someone proposes to you a third kind of mean, called the superduper mean, defined as (ab)1/3 .

01 m2 of leather, then you have probably made a mistake with conversion factors somewhere. 2 Scaling and Order-of-Magnitude Estimates 45 Problems √ The symbols , , etc. are explained on page 52. 74658 1 Correct use of a calculator: (a) Calculate 53222+97554 on a calculator. 55 ? 2 Compute the following things. If they don’t make sense because of units, say so. 0 hours 3 Your backyard has brick walls on both ends. 4 m from the inside of one wall to the inside of the other. 4 cm thick. How far is it from the outside of one wall to the outside of the other?