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

2024
Views:

371

Pages:

2
Author:

Lamghari6kx

COSMOS: Complete Online Solutions Manual Organization System Chapter 9, Solution 156. First compute the mass of each component m = ρstV = ρst tA Have Then m1 = ( 7860 kg/m 3 ) ( 0.003)( 0.08 )( 0.09 )  m 3 = 0.169776 kg  1  m2 = 7860 kg/m 3 ( 0.003)  × 0.09 × 0.036   m 3 2   = 0.03820 kg Now observe that (I ) = (I ) = (I ) x′y ′ y ′z ′ 1 (I ) = (I ) y ′z ′ 2 z ′x′ (I ) Also x1 = y1 = z2 = 0 x′y ′ 2 ( ) = ρ sT t I x′y′ 2 1 =0 =0 ( I x′y′ )2,area = − 721 b22 h22 From Sample Problem 9.6 Then z ′x′ 1 2,area 1  1  = ρst t  − b22 h22  = − m2 b2 h2 36  72  0.09   x2 =  −0.045 +  m = −0.015 m 3   continued COSMOS: Complete Online Solutions Manual Organization System Finally  1 I xy = Σ I xy + mx y = ( 0 + 0 ) +  − ( 0.03820 kg )( 0.09 m )( 0.036 m )  36 ( )  0.036 m   + ( 0.03820 kg )( −0.015 m )   3   ( ) = −3.4379 × 10−6 − 6.876 × 10−6 kg ⋅ m 2 = −10.3139 × 10−6 kg ⋅ m 2 or I xy = −10.31 × 10−6 kg ⋅ m 2 And ( ) I yz = Σ I y′z ′ + m y z = ( 0 + 0 ) + ( 0 + 0 ) = 0 or I yz = 0 I zx = Σ ( I z ′x′ + m z x ) = ( 0 + 0 ) + ( 0 + 0 ) = 0 or I zx = 0