By Benjamin Crowell
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I said that the surface of a small solid is comparatively greater than that of a large one. The same reasoning applies to the planks. 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.
Also, Galileo is doing something that would be frowned on in modern science: he is mixing experiments whose results he has actually observed (building boats of different sizes), with experiments that he could not possibly have done (dropping an ant from the height of the moon). He now relates how he has done actual experiments with such planks, and found that, according to this operational definition, they are not strong in proportion to their sizes. The larger one breaks. 2 Scaling and Order-of-Magnitude Estimates 37 g / 1.
C) Using the same numbers for d and a, find your maximum speed. 0 × 108 m/s. (Later in this course, you will learn that there are some new things going on in physics when one gets close to the speed of light, and that it is impossible to exceed the speed of light. ) 16 You climb half-way up a tree, and drop a rock. Then you climb to the top, and drop another rock. How many times greater is the velocity of the second rock on impact? Explain. ) 17 If the acceleration of gravity on Mars is 1/3 that on Earth, how many times longer does it take for a rock to drop the same distance on Mars?