COSMOS Chapter 9 Solution 47 | Michigan State University - Edubirdie

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

2022
Views:

249

Pages:

1
Author:

Athena Harrison

COSMOS: Complete Online Solutions Manual Organization System Chapter 9, Solution 47. Locate centroid: (a) Have x1 = 4 in. y1 = −1.15 in. A1 = (16 )( 2.3) = 36.8 in 2 x2 = 4 in. y2 = 3.2 in. A2 = x3 = 2 in. y3 = 1.6 in. 1 (12 )( 9.6 ) = 57.6 in 2 2 1 A3 = ( 6 )( 4.8 ) = −14.4 in 2 2 x= 3 ΣxA  4 ( 36.8 ) + 4 ( 57.6 ) + 2 ( −14.4 )  in 348.8 in 3 = = − = 4.360 in. ΣA 80 in 2 ( 36.8 + 57.6 − 14.4 ) in 2 y= 3 ΣyA  −1.15 ( 36.8 ) + 3.2 ( 57.6 ) + 1.6 ( −14.4 )  in 118.96 in 3 = =− = 1.487 in. 2 ΣA 80 in 80 in 2 I x = ( I x )1 + ( I x )2 − ( I x )3 = 1 1 1 (16 )( 2.3)3 in 4 + (12 )( 9.6 )3 in 4 − ( 6 )( 4.8)3 in 4 3 12 12 = 64.891 in 4 + 884.736 in 4 − 55.296 in 4 = 894.33 in 4 ( )1 + ( I y )2 − ( I y )3 Iy = Iy 1 1 3 2 3 3 1 =  ( 2.3)(16 ) + 2.3 (16 )( 4 )  in 4 + ( 9.6 )(12 ) in 4 − ( 4.8 )( 6 ) in 4 12 12 12  = 1373.87 in 4 + 1382.4 in 4 − 86.4 in 4 = 2669.9 in 4 Now J O = I x + I y = 894.33 in 4 + 2669.9 in 4 = 3564.2 in 4 (b) J O = 3560 in 4 Have J O = J C + Ad 2 Then 2 2 J C = 3564.2 in 4 − 80 in 2 ( 4.360 in.) + (1.487 in.)    where ( d2 = x2 + y2 ) = 3564.2 in 4 − 1697.66 in 4 = 1866.54 in 4 J C = 1867 in 4

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