Mathematic Methods HW Solutions 24

Mathematic Methods HW Solutions 24 - Chapter 5 (b) x = y =...

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Chapter 5 24 4.1 (b) ¯ x = ¯ y = 4 a/ (3 π ) (c) I = Ma 2 / 4 (e) ¯ x = ¯ y = 2 a/π 4.2 (c) ¯ y = 4 a/ (3 π ) (d) I x = Ma 2 / 4, I y = 5 Ma 2 / 4, I z = 3 Ma 2 / 2 (e) ¯ y = 2 a/π (f) ¯ x = 6 a/ 5, I x = 48 Ma 2 / 175, I y = 288 Ma 2 / 175, I z = 48 Ma 2 / 25 (g) A = ( 2 3 π - 1 2 3) a 2 4.3 (a), (b), or (c) 1 2 Ma 2 4.4 (a) 4 πa 2 (b) (0 , 0 ,a/ 2) (c) 2 Ma 2 / 3 (d) 4 πa 3 / 3 (e) (0 , 0 , 3 a/ 8) 4.5 7 π/ 3 4.6 π ln 2 4.7 (a) V = 2 πa 3 (1 - cos α ) / 3 (b) ¯ z = 3 a (1 + cos α ) / 8 4.8 I z = Ma 2 / 4 4.10 (a) V = 64 π (b) ¯ z = 231 / 64 4.11 12 π 4.12 (c) M = (16 ρ/ 9)(3 π - 4) = 9 . 64 ρ I = (128 ρ/ 15 2 )(15 π - 26) = 12 . 02 ρ = 1 . 25 M 4.13 (b) πa 2 ( z 2 - z 1 ) - π ( z 3 2 - z 3 1 ) / 3 (c) 1 2 a 2 ( z 2 2 - z 2 1 ) - 1 4 ( z 4 2 - z 4 1 ) a 2 ( z 2 - z 1 ) - ( z 3 2 - z 3 1 ) / 3 4.14 π (1 - e - 1 ) / 4 4.16 u 2 + v 2 4.17 a 2 (sinh 2 u + sin 2 v ) 4.19 π/ 4 4.20 1 / 12 4.22 12(1 + 36 π 2 ) 1 / 2 4.23 Length = ( R sec α ) times change in latitude 4.24 ρGπa/ 2 4.26 (a) 7 Ma 2 / 5 (b) 3 Ma 2 / 2 4.27 2 πah (where h = distance between parallel planes) 4.28 (0 , 0 ,a/ 2) 5.1 9 π 30 / 5 5.2 π r 7 / 5 5.3 π (37 3 / 2 - 1) / 6 = 117 . 3 5.4 π/ 6 5.5 8 π for each nappe 5.6 4 5.7 4 5.8 b 3 6 + 9 ln( 2 + 3) B / 16 5.9 π 2 5.10 2 πa 2 ( 2 - 1) 5.11 (¯ x, ¯ y, ¯ z ) = (1 / 3 , 1 / 3 , 1 / 3) 5.12 M = 3 / 6, (¯ x, ¯ y, ¯ z ) = (1 / 2 , 1 / 4 , 1 / 4) 5.13 ¯ z = π 4( π - 2) 5.14 M = π 2 - 4 3 5.15 I z /M = 2(3 π - 7) 9(
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This note was uploaded on 02/29/2012 for the course MHF 2312 taught by Professor Dr.chet during the Fall '11 term at UNF.

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