COSMOS Chapter 9 Solution 46 | Answer Key - Edubirdie

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

2021
Views:

159

Pages:

1
Author:

Nicole Wang

COSMOS: Complete Online Solutions Manual Organization System Chapter 9, Solution 46. Locate centroid: By symmetry, y = 0 A1 = π (100 mm )( 60 mm ) = 6000π mm 2 x1 = 0 x2 = 4 ( 45 mm ) 3π A2 = − x3 = All dimensions in mm π 2 = 60 π mm ( 45mm )2 = −1012.5π mm 2 − 4 ( 30 mm ) 40 mm =− 3π π A3 = − π 2 ( 30 mm )2 = − 450π mm 2 60 40  0 ( 6000π ) + ( −1012.5π ) − ( − 450π ) mm3 ΣxA  π π  x= = = − 2.9990 mm ΣA ( 6000π − 1012.5π − 450π ) mm 2 (a) Have J O = ( J O )1 − ( J O )2 − ( J O )3 4 4 1  1 1 =  π (100 )( 60 ) 1002 + 602  mm 4 −  π ( 45 )  mm 4 −  π ( 30 )  mm 4 4  4  4  ( ) ( ) = π 20 400 000 − 1 025 156 − 202 500 mm 4 = 60232000 mm 4 (b) Have With or J O = 60.2 × 106 mm 4 or J C = 60.1 × 106 mm 4 J O = J C + Ax 2 A = ( 6000π − 1012.5π − 450π ) mm 2 = 4537.5π mm 2 Then ( ) J C = 60 232 000 mm 4 − 4537.5π mm 2 ( − 2.9990 mm ) 2 = 60 232 000 mm 4 − 128209 mm 4 = 60 104 000 mm 4

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