p01_024

# p01_024 - 24 The metric prefixes(micro pico nano are given...

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Unformatted text preview: 24. The metric prefixes (micro (), pico, nano, . . .) are given for ready reference on the inside front cover of the textbook (see also Table 1-2). The surface area A of each grain of sand of radius r = 50 m = 5010-6 m is given by A = 4(50 10-6 )2 = 3.14 10-8 m2 (Appendix E contains a variety of geometry formulas). We introduce the notion of density (which the students have probably seen in other courses): = m V so that the mass can be found from m = V , where = 2600 kg/m3 . Thus, using V = 4r3 /3, the mass of each grain is 3 4 50 10-6 m kg m= 2600 3 = 1.36 10-9 kg . 3 m We observe that (because a cube has six equal faces) the indicated surface area is 6 m2 . The number of spheres (the grains of sand) N which have a total surface area of 6 m2 is given by N= 6 m2 = 1.91 108 . 3.14 10-8 m2 Therefore, the total mass M is given by M = N m = 1.91 108 1.36 10-9 kg = 0.260 kg . ...
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