University:
Michigan State University
Course:
ERG 160 | Success in Science, Technology, Engineering, and Mathematics
Academic year:

2024
Views:

141

Pages:

2
Author:

lankstoetp13

COSMOS: Complete Online Solutions Manual Organization System Chapter 9, Solution 23. y1 : x = a, At y = 2b: 2b = ma or m= 2b a Then y1 = 2b x a y2 : x = 0, y = b: b = k ( 0 ) + c or At x = a, y = 2b: 2b = ka 2 + b At k = or y2 = Then Now c=b b a2 b 2 b x + b = 2 x2 + a2 a2 a ( ) 2b  a b A = ∫ ( y2 − y1 ) dx = ∫ 0  2 x 2 + a 2 − x dx a  a ( ) a  b 1  b  =  2  x3 + a 2 x  − x 2   a 0 a  3 = Now b 1 3 1  b a + a3  − a 2 = ab 2 3 a 3  a a I y = ∫ x 2dA = ∫ 0 x 2 ( y2 − y1 ) dx = 2b  x  dx  a 2 2 2 ∫ 0 x  a2 ( x + a ) − a  b a b  1 1  2b x 4  = 2  x5 + a 2 x3  −  3 a  5  a 4 0 = b  a5 1 5  2b a 4 1 3 ab + a  − = 2  3  a 4 30 a  5 continued COSMOS: Complete Online Solutions Manual Organization System And 1  1 I x = ∫ dI x = ∫  y23 − y13  dx 3 3   = 1 a  b3 2 x + a2 ∫ 0  6 3 a = 1 b3 a  1 6  x + 3x 4a 2 + 3x 2a 4 + a 6 − 8x3  dx ∫ 3 a3 0  a3  ( ) 3 − 8b3 3  x  dx a3  ( ) a 1 b3  1  x 7 3 2 5 3 4 3 8 4 6  + + + − Ix = a x a x a x  3  3  4x  3 a  a  7 5 3  0  = Finally   1 b3  1  a 7 3 7 26 3 + a + a 7 + a 7  − 2a 4  = ab 3  3  3 a  a  7 5   105 JP = Ix + I y = 26 3 1 3 ab + ab 105 30 or J P = And kP = JP = A ab 210 ab 7a 2 + 52b 2 210 a + 52b 2 ( ) ) 1 ab 3 or k P = 7a 2 + 52b 2 70