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Unformatted text preview: 1 chapter1 1 1. The metric prefixes (micro, pico, nano, . . . ) are given for ready reference on the inside front cover of the textbook (see also Table 12). (a) Since 1 km = 1 × 10 3 m and 1 m = 1 × 10 6 μ m, 1 km = 10 3 m = (10 3 m)(10 6 μ m / m) = 10 9 μ m . The given measurement is 1 . 0 km (two significant figures), which implies our result should be written as 1 . × 10 9 μ m. (b) We calculate the number of microns in 1 centimeter. Since 1 cm = 10 2 m, 1 cm = 10 2 m = (10 2 m)(10 6 μ m / m) = 10 4 μ m . We conclude that the fraction of one centimeter equal to 1 . μ m is 1 . × 10 4 . (c) Since 1 yd = (3 ft)(0 . 3048 m / ft) = 0 . 9144 m, 1 . 0 yd = (0 . 91 m)(10 6 μ m / m) = 9 . 1 × 10 5 μ m . 2. The customer expects 20 × 7056 in 3 and receives 20 × 5826 in 3 , the difference being 24600 cubic inches, or 24600 in 3 2 . 54 cm 1 inch 3 1 L 1000 cm 3 = 403 L where Appendix D has been used (see also Sample Problem 12). 3. Using the given conversion factors, we find (a) the distance d in rods to be d = 4 . 0 furlongs = (4 . 0 furlongs)(201 . 168 m / furlong) 5 . 0292 m / rod = 160 rods , (b) and that distance in chains to be d = (4 . 0 furlongs)(201 . 168 m / furlong) 20 . 117 m / chain = 40 chains . 4. (a) Recalling that 2 . 54 cm equals 1 inch (exactly), we obtain (0 . 80 cm) 1 inch 2 . 54 cm ! 6 picas 1 inch 12 points 1 pica ! ≈ 23 points , (b) and (0 . 80 cm) 1 inch 2 . 54 cm ! 6 picas 1 inch ≈ 1 . 9 picas . 5. Various geometric formulas are given in Appendix E. (a) Substituting R = 6 . 37 × 10 6 m 10 3 km / m = 6 . 37 × 10 3 km into circumference = 2 πR , we obtain 4 . 00 × 10 4 km. (b) The surface area of Earth is 4 πR 2 = 4 π 6 . 37 × 10 3 km 2 = 5 . 10 × 10 8 km 2 . (c) The volume of Earth is 4 π 3 R 3 = 4 π 3 6 . 37 × 10 3 km 3 = 1 . 08 × 10 12 km 3 . 6. (a) Using the fact that the area A of a rectangle is width × length, we find A total = (3 . 00 acre) + (25 . 0 perch)(4 . 00 perch) = (3 . 00 acre) (40 perch)(4 perch) 1 acre ! + 100 perch 2 = 580 perch 2 . We multiply this by the perch 2 → rood conversion factor (1 rood / 40 perch 2 ) to obtain the answer: A total = 14 . 5 roods. (b) We convert our intermediate result in part (a): A total = (580 perch 2 ) 16 . 5 ft 1 perch ! 2 = 1 . 58 × 10 5 ft 2 . Now, we use the feet → meters conversion given in Appendix D to obtain A total = 1 . 58 × 10 5 ft 2 1 m 3 . 281 ft 2 = 1 . 47 × 10 4 m 2 . 7. The volume of ice is given by the product of the semicircular surface area and the thickness. The semicircle area is A = πr 2 / 2, where r is the radius. Therefore, the volume is V = π 2 r 2 z where z is the ice thickness. Since there are 10 3 m in 1 km and 10 2 cm in 1 m, we have r = (2000 km) 10 3 m 1 km !...
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.
 Fall '08
 SPRUNGER
 Physics

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