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

2021
Views:

119

Pages:

1
Author:

Nossardisd7p

COSMOS: Complete Online Solutions Manual Organization System Chapter 9, Solution 198. m= First compute the mass of each component Then γ g V m1 = 0.284 lb/in 3 ( 5 in. × 4.5 in. × 0.9 in.) = 0.1786 lb ⋅ s2/ft 32.2 ft/s 2 m2 = 0.284 lb/in 3 ( 3 in. × 2.5 in. × 0.8 in.) = 0.05292 lb ⋅ s 2/ft 32.2 ft/s 2 m3 = 0.284 lb/in 3  2 π ( 0.6 in.) × 0.5 in. = 0.0049875 lb ⋅ s 2 /ft 2    32.2 ft/s Now observe that the centroidal products of inertia, I x′y′ , I y′z ′ , and I z′x′ , of each component are zero because 0 of symmetry. Now I uv = I u′v′ + muv so that ( Iuv )body = Σmu v . m, lb ⋅ s 2 /ft x , ft y , ft z , ft mx y my z mz x lb ⋅ ft ⋅ s 2 lb ⋅ ft ⋅ s 2 lb ⋅ ft ⋅ s 2 1 0.1786 0.2083 3 0.037 5 0.187 5 1.39531 × 10−3 1.25578 × 10−3 6.97656 × 10−3 2 0.05292 0.3833 3 0.20 0.187 5 4.0572 × 10−3 1.98451 × 10−3 3.80362 × 10−3 3 0.0049875 0.4375 0.225 0.187 5 0.49095 × 10−3 0.21041 × 10−3 0.40913 × 10−3 3.45069 × 10−3 11.18909 × 10−3 Σ Then 5.94347 × 10−3 or I xy = 5.94 × 10−3 lb ⋅ ft ⋅ s 2 or I yz = 3.45 × 10−3 lb ⋅ ft ⋅ s 2 or I zx = 11.19 × 10−3 lb ⋅ ft ⋅ s 2

COSMOS Chapter 9 Solution 198

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