By Benjamin Crowell
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Extra resources for 7-Simple Nature
Even though they are not cubes, the large one could be sawed into eight small ones, each with half the length, half the thickness, and half the width. The small plank, therefore, has more surface area in proportion to its weight, and is therefore able to support its own weight while the large one breaks. Scaling of area and volume for irregularly shaped objects You probably are not going to believe Galileo’s claim that this has deep implications for all of nature unless you can be convinced that the same is true for any shape.
Show that the units of this expression make sense. Problem 10. 12 (a) Based on the definitions of the sine, cosine, and tangent, what units must they have? (b) A cute formula from trigonometry lets you find any angle of a triangle if you know the lengths of its sides. Using the notation shown in the figure, and letting s = (a + b + c)/2 be half the perimeter, we have tan A/2 = (s − b)(s − c) s(s − a) . Show that the units of this equation make sense. In other words, check that the units of the right-hand side are the same as your answer to part a of the question.
07 m His Aunt Wanda is good with numbers, but has never taken physics. She doesn’t know the formula for the distance traveled under constant acceleration over a given amount of time, but she tells her nephew his answer cannot be right. How does she know? Problem 12. 14 You are looking into a deep well. It is dark, and you cannot see the bottom. 0 seconds later. How deep√is the well? Problems 47 15 You take a trip in your spaceship to another star. Setting off, you increase your speed at a constant acceleration.
7-Simple Nature by Benjamin Crowell