COSMOS Chapter 9 Solution 124 | Answer Key - Edubirdie

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

2023
Views:

89

Pages:

1
Author:

Quintin Ware

COSMOS: Complete Online Solutions Manual Organization System Chapter 9, Solution 124. For the element shown: ab  y  y  dm = ρ dV = ρ  a  b  dy = ρ 2 y 2dy h h h    dIx′ = 2 1  y 1 b 2 2  ab  2 1 ab3 4 y  ρ 2  y dy = y dy ρ  b  dm = 2 12  h  12 h 12 h 4  h  Parallel-axis theorem dI x = dI x′ + d 2dm = 1 y where d 2 = y 2 +  b  2 h 2  1 ab3 4 1 y 2  ab ρ 4 y dy +  y 2 + b 2 2  ρ 2 y 2dy 12 h 4 h  h   ρ ab3 ab  =  + ρ 2  y 4dy 4 h  3 h  ρ ab3 ab  h ρ ab3h ρ abh3 I x = ∫ dI x =  + ρ 2  ∫ 0 y 4dy = + 4 15 5 h  3 h 1 ρ abh 3 For pyramid, m = ρv = Thus 1   b 2 3h 2  I x =  ρ abh   +  5  3  5 Ix = 1 m b 2 + 3h 2 5 ( )

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