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

2019
Views:

298

Pages:

2
Author:

Tyshawn Shaffer

COSMOS: Complete Online Solutions Manual Organization System Chapter 9, Solution 56. (a) Using shape data from Fig. 9.13A xA = 1.78 in. AA = 8.44 in 2 xC = − 0.499 in. AC = 3.09 in 2 a  xP =  6 −  in. 2  AP = ( 0.75a ) in 2 x= From the condition ΣxA =0 ΣΑ or ΣxA = 0  (1.78 in.) (8.44 in 2 ) − ( 0.499 in.) ( 3.09 in 2 ) +  6 −  or a 2 − 12a − 35.950 = 0 a  2  in. 0.75a in = 0 2  ( ) a = 14.4823 in. a = 14.48 in. or and (b) AP = ( 0.75 in.)(14.4823 in.) = 10.8617 in 2 Locate centroid y= ΣyA = ΣΑ 6  in.  3.09 in 2 − ( 0.375 in.) 10.8617 in 2 2  (8.44 + 3.09 + 10.8617 ) in 2 (1.78 in.) (8.44 in 2 ) +  ( ) ( ) = 0.90302 in. continued COSMOS: Complete Online Solutions Manual Organization System I x = ( I x ) A + ( I x )C + ( I x ) P Now ( ) 2 =  28.2 in 4 + 8.44 in 2 (1.78 in. − 0.90302 in.)    ( ) 2 + 15.2 in 4 + 3.09 in 2 ( 3.0 in. − 0.90302 in.)    3 2 1 +  (14.4823 in.)( 0.75 in.) + 10.8617 in 2 ( 0.375 in. + 0.90302 in.)  12  ( ) = ( 28.2 + 6.4912 ) + (15.2 + 13.5877 ) + ( 0.5091 + 17.7408 )  in 4 = 81.729 in 4 I x = 81.7 in 4 or and ( ) A + ( I y )C + ( I y ) P Iy = Iy ( ) ( ) 2 2 =  28.2 in 4 + 8.44 in 2 (1.78 in.)  + 0.866 in 4 + 3.09 in 2 ( 0.499 in.)      2 1 14.4823 in.   3  +  ( 0.75 in.)(14.4823 in.) + 10.8617 in 2  6 in. −   2    12 ( ) = ( 28.2 + 26.741) + ( 0.866 + 0.7694 ) + (189.842 + 16.7319 )  in 4 = 263.15 in 4 or I y = 263 in 4