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If you drill a hole horizontally through the branch of a tree, you risk weakening the branch. For minimum weakening, drill the hole through the Ch 12-1 1. upper part, A. 2. middle part, B. 3. lower part, C. 4 … makes no difference.

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If you drill a hole horizontally through the branch of a tree, you risk weakening the branch. For minimum weakening, drill the hole through the Ch 12-1 Answer: 2 The upper half of the horizontal branch is under tension because of its weight, while the lower half is under compression. The middle part is under neither tension nor compression—fibers of wood there experience no stretching or compressing. So drilling a hole through the middle will hardly affect the branch’s strength. Drilling a hole in the upper part, however, weakens the branch because fibers there are stretched and may be pulled apart. And drilling a hole in the lower part may result in squeezed fibers being crushed. Like the horizontal branch, tension and compression occur in the top and bottom parts of an I beam, popular in construction. Material can be scooped from the middle, where it’s needed least, resulting in a beam that is lighter and nearly the same strength. 1. upper part, A. 2. middle part, B. 3. lower part, C. 4 … makes no difference.

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Two identical boxes are brim filled with spherical steel ball bearings—one with uniform big-diameter bearings, and the other with half-size ones. If you pour water and fill each box, which will take more water? Ch 12-4 Thanks to Tom Humphrey. 1. The box of big bearings 2. The box of small bearings 3. Both the same

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Two identical boxes are brim filled with spherical steel ball bearings—one with uniform big-diameter bearings, and the other with half-size ones. If you pour water and fill each box, which will take more water? Ch 12-4 Thanks to Tom Humphrey. Answer: 3 The volume of empty space in both boxes is the same, so the volume of water to fill them is the same. Although there’s more space between the larger bearings, they’re fewer in number. There’s less space between the smaller bearings but there are more of them. It’s a wash. And since the volume of open space in each box is the same, the volume of steel is the same. That means both weigh the same—whether filled with water or not. Let’s exaggerate: Consider a cubical box containing a single sphere of diameter D equal to the length of the box. A simple calculation shows the volume of the sphere is 52% that of the cube, which means 48% open space. Now consider spheres of half size. Rectangularly packed, 8 spheres of diameter D/2 will fill the same cube—like 8 smaller cubes, each with 48% open space. Same total open space. Likewise for smaller spheres, rectangularly packed, where the volume of open space is the same. That means a box full of uniform small spheres weighs the same as the box with the single sphere of diameter D! 1. The box of big bearings 2. The box of small bearings 3. Both the same

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