By Benjamin Crowell
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Since the flow is steady, the amount of water between the two cross-sections stays constant. Conservation of mass therefore requires that the cross-sectional area of the stream shrink in inverse proportion to the increasing speed of the falling water. self-check A Suppose the you point the hose straight up, so that the water is rising rather than falling. What happens as the velocity gets smaller? What happens when the velocity becomes zero? Answer, p. 849 f / Example 1. 56 Chapter 1 Conservation of Mass How can we apply a conservation law, such as conservation of mass, in a situation where mass might be stored up somewhere?
B) The series of paper sizes starts from an A0 sheet, which has an area of one square meter. Suppose we had a series of boxes defined in a similar way: the B0 box has a volume of one cubic meter, two B1 boxes fit exactly inside an B0 box, and √so on. What would be the dimensions of a B0 box? 35 Estimate the mass of one of the hairs in Albert Einstein’s moustache, in units of kg. 36 According to folklore, every time you take a breath, you are inhaling some of the atoms exhaled in Caesar’s last words.
The big triangle has four times more area than the little one. Correct solution #1: Area scales in proportion to the square of the linear dimensions, so the larger triangle has four times more area (22 = 4). Correct solution #2: You could cut the larger triangle into four of the smaller size, as shown in fig. (b), so its area is four times greater. ) Correct solution #3: The area of a triangle is given by A = bh/2, where b is the base and h is the height. The areas of the triangles are l / A tricky way of solving example 2, explained in solution #2.
7-Simple Nature by Benjamin Crowell