COSMOS Chapter 9 Solution 43

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

2024
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71

Pages:

1
Author:

Hundebuchesn

COSMOS: Complete Online Solutions Manual Organization System Chapter 9, Solution 43. Locate centroid: x1 = 8 in. y1 = 3 in. A1 = (16 )( 6 ) = 96 in 2 x2 = −1.5 in. y2 = 2 in. A2 = ( 3)( 4 ) = 12 in 2 x3 = 14 in. y3 = − 5.25 in. A3 = ( 4 )(10.5 ) = 42 in 2 x = ΣxA ΣΑ 8 ( 96 ) − 1.5 (12 ) + 14 ( 42 )  in 3 = = 8.92 in. ( 96 + 12 + 42 ) in 2 y = ( ) ( ) ( ) ΣyA ΣA 3 ( 96 ) + 2 (12 ) − 5.25 ( 42 )  in 3 = = 0.610 in. ( 96 + 12 + 42 ) in 2 I x = I x1 + I x2 + I x3 3 2 3 2 1 1 =  (16 )( 6 ) + ( 96 )( 3 − 0.610 )  in 4 +  ( 3)( 4 ) + (12 )( 2 − 0.610 )  in 4 12 12     3 2 1 +  ( 4 )(10.5 ) + ( 42 )( − 5.25 − 0.610 )  in 4 12   = ( 288 + 548.36 ) + (16 + 23.185 ) + ( 385.875 + 1442.26 )  in 4 = 2703.7 in 4 I x = 2700 in 4 ( ) ( ) ( ) I y = I y1 + I y2 + I 3 3 2 3 2 1 1 =  ( 6 )(16 ) + ( 96 )( 8 − 8.92 )  in 4 +  ( 4 )( 3) + (12 )( −1.5 − 8.92 )  in 4 12 12     3 2 1 +  (10.5 )( 4 ) + ( 42 )(14 − 8.92 )  in 4 12  = ( 2048 + 81.254 ) + ( 9 + 1302.92 ) + ( 56 + 1083.87 )  in 4 = 4581.0 in 4 I y = 4580 in 4

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