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

2023
Views:

287

Pages:

2
Author:

pravitate8aj13

COSMOS: Complete Online Solutions Manual Organization System Chapter 9, Solution 143. m = ρV = Have γ g V = 0.284 lb/in 3 ×V 32.2 ft/s 2 ( ) = 0.0088199 lb ⋅ s 2/ft ⋅ in 3 V ( ) ( ) ( ) 2 Then m1 = 0.0088199 lb ⋅ s 2 /ft ⋅ in 3 π ( 4 ) ( 2 )  in 3 = 0.88667 lb ⋅ s 2 /ft   2 m2 = 0.0088199 lb ⋅ s 2/ft ⋅ in 3 π (1) ( 3)  in 3 = 0.083126 lb ⋅ s 2/ft   2 m3 = 0.0088199 lb ⋅ s 2 /ft ⋅ in 3 π (1) ( 2 )  in 3 = 0.055417 lb ⋅ s 2/ft   Using Fig. 9-28 and the parallel theorem, have (a) I x = ( I x )1 + ( I x )2 − ( I x )3 2 2 2 1  1 ft  = 0.88667 lb ⋅ s 2 /ft  3 ( 4 ) + ( 2 )  + (1)  in 2 ×     12    12 in.  ( ) 2 2 2 2 1  1 ft  + 0.083126 lb ⋅ s 2 /ft  3 (1) + ( 3)  + (1.5 )  in 2 ×     12    12 in.  ( ) 2 2 2 1  1 ft  − 0.055417 lb ⋅ s 2 /ft  3 (1) + ( 2 )  + (1)  in. ×     12    12 in.  ( ) 2 2 = 0.034106 lb ⋅ ft ⋅ s 2 or I x = 0.0341 lb ⋅ ft ⋅ s 2 continued COSMOS: Complete Online Solutions Manual Organization System ( )1 + ( I y )2 − ( I y )3 Iy = Iy (b) 2 1  1 ft  = 0.88667 lb ⋅ s 2 /ft  ( 4 )  in 2 ×   2   12 in.  ( ) 2 2 1 2  1 ft  + 0.083126 lb ⋅ s 2 /ft  (1) + ( 2 )  in 2 ×   2   12 in.  ( ) 2 2 1 2  1 ft  − 0.055417 lb ⋅ s 2 /ft  (1) + ( 2 )  in 2 ×   2   12 in.  ( ) 2 = 5.0125 × 10−2 lb ⋅ ft ⋅ s 2 or I y = 0.0501 lb ⋅ ft ⋅ s 2 (c) I z = ( I z )1 + ( I z )2 − ( I z )3 2 2 2 1  1 ft  = 0.88667 lb ⋅ s 2 /ft  3 ( 4 ) + ( 2 )  + (1)  in 2 ×    12    12 in.  ( ) 2 2 2 2 2  1  1 ft  + 0.083126 lb ⋅ s 2 /ft  3 (1) + ( 3)  + ( 2 ) + (1.5 )   in 2 ×      12   12 in.  ( ) 2 2 2 2  1  1 ft  − 0.055417 lb ⋅ s 2 /ft  3 (1) + ( 2 )  + ( 2 ) + (1)   in 2 ×      12   12 in.  ( ) 2 2 = 0.034876 lb ⋅ ft ⋅ s 2 or I z = 0.0349 lb ⋅ ft ⋅ s 2