Chapter01 - 1. The metric prefixes (micro, pico, nano, .)...

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1. The metric prefixes (micro, pico, nano, …) are given for ready reference on the inside front cover of the textbook (see also Table 1–2). (a) Since 1 km = 1 × 10 3 m and 1 m = 1 × 10 6 μ m, () 33 6 9 1km 10 m 10 m 10 m m 10 m. == = μμ The given measurement is 1.0 km (two significant figures), which implies our result should be written as 1.0 × 10 9 m. (b) We calculate the number of microns in 1 centimeter. Since 1 cm = 10 2 m, 22 6 4 1cm=10 m= 10 m 10 mm m . −− = We conclude that the fraction of one centimeter equal to 1.0 m is 1.0 × 10 4 . (c) Since 1 yd = (3 ft)(0.3048 m/ft) = 0.9144 m, 65 1.0 yd = 0.91m 10 m m 9.1 10 m.
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2. (a) Using the conversion factors 1 inch = 2.54 cm exactly and 6 picas = 1 inch, we obtain () 1 inch 6 picas 0.80 cm = 0.80 cm 1.9 picas. 2.54 cm 1 inch §· § · ¨¸ ¨ ¸ ©¹ © ¹ (b) With 12 points = 1 pica, we have 1 inch 6 picas 12 points 0.80 cm = 0.80 cm 23 points. 2.54 cm 1 inch 1 pica § · § · ¨ ¸ ¨ ¸ © ¹ © ¹
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(b) and that distance in chains to be () 4.0 furlongs 201.168 m furlong 40 chains. 20.117 m chain d == 3. Using the given conversion factors, we find (a) the distance d in rods to be 4.0 furlongs 201.168 m furlong 4.0 furlongs = 160 rods, 5.0292 m rod d
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4. The conversion factors 1 gry 1/10 line = , 1 line=1/12 inch and 1 point = 1/72 inch imply that 1 gry = (1/10)(1/12)(72 points) = 0.60 point. Thus, 1 gry 2 = (0.60 point) 2 = 0.36 point 2 , which means that 22 0.50 gry = 0.18 point .
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5. Various geometric formulas are given in Appendix E. (a) Expressing the radius of the Earth as () 63 3 6.37 10 m 10 km m 6.37 10 km, R = × its circumference is 34 2 2 (6.37 10 km) 4.00 10 km. sR ππ == × = × (b) The surface area of Earth is 2 23 8 2 4 4 6.37 10 km 5.10 10 km . AR =π =π × = × (c) The volume of Earth is 3 33 1 2 3 44 6.37 10 km 1.08 10 km . VR × = ×
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6. From Figure 1.6, we see that 212 S is equivalent to 258 W and 212 – 32 = 180 S is equivalent to 216 – 60 = 156 Z. The information allows us to convert S to W or Z. (a) In units of W, we have () 258 W 50.0 S 50.0 S 60.8 W 212 S §· == ¨¸ ©¹ (b) In units of Z, we have 156 Z 50.0 S 50.0 S 43.3 Z 180 S
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2 2 Vr z π = where z is the ice thickness. Since there are 10 3 m in 1 km and 10 2 cm in 1 m, we have () 32 5 10 m 10 cm 2000km 2000 10 cm. 1km 1m r §· § · == × ¨¸ ¨ ¸ ©¹ © ¹ In these units, the thickness becomes 2 2 10 cm 3000m 3000 10 cm z = × which yields ( ) 2 52 2 2 3 2000 10 cm 3000 10 cm 1.9 10 cm . 2 V π × = × 7. The volume of ice is given by the product of the semicircular surface area and the thickness. The area of the semicircle is A = π r 2 /2, where r is the radius. Therefore, the volume is
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8. We make use of Table 1-6. (a) We look at the first (“cahiz”) column: 1 fanega is equivalent to what amount of cahiz? We note from the already completed part of the table that 1 cahiz equals a dozen fanega. Thus, 1 fanega = 1 12 cahiz, or 8.33 × 10 2 cahiz. Similarly, “1 cahiz = 48 cuartilla” (in the already completed part) implies that 1 cuartilla = 1 48 cahiz, or 2.08 × 10 2 cahiz. Continuing in this way, the remaining entries in the first column are 6.94 × 10 3 and 3 3.47 10 × .
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This note was uploaded on 05/11/2010 for the course PHYS 2101,2102 taught by Professor Giammanco during the Spring '10 term at LSU.

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Chapter01 - 1. The metric prefixes (micro, pico, nano, .)...

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