COSMOS Chapter 9 Solution 146

COSMOS: Complete Online Solutions Manual Organization System Chapter 9, Solution 146. m = ρV = m1 = γ g V 0.100 lb/in 3 ( 4 in.)(1 in.)( 3 in.) 32.2 ft/s 2 = 37.267 × 10−3 m2 = 0.100 lb/in 3 ( 2 in.)(1.2 in.)( 3 in.) 32.2 ft/s 2 = 22.360 × 10−3 m3 = lb ⋅ s 2 ft 0.100 lb/in 3 π 2 × ( 0.9 in.) ( 2 in.) 2 2 32.2 ft/s = 7.9028 × 10−3 m4 = lb ⋅ s 2 ft lb ⋅ s 2 ft 0.100 lb/in 3 π 2 × ( 0.5 in.) ( 3 in.) 2 2 32.2 ft/s = 3.6587 × 10−3 lb ⋅ s 2 ft continued COSMOS: Complete Online Solutions Manual Organization System Have I z = ( I z )1 + ( I z )2 + ( I z )3 + ( I z )4 2 2 2 1   −3 lb ⋅ s  2 −3 lb ⋅ s  2 2 2 2 2  1 ft  =   37.267 × 10  4 + 1 in +  37.267 × 10  2 + 0.5 in    ft  ft  12    12 in.   ( ) ( ) 2 2 1   lb ⋅ s 2  2 2 2 2 2  1 ft  −3 lb ⋅ s  2 2 1.2 in 22.360 10 1 1.6 in +   22.360 × 10−3 + + × +      ft  ft  12    12 in.   ( ) ( ) lb ⋅ s 2   1 16  1 2 2  +  7.9028 × 10−3 0.9 in.) + ( 2 in.)    − 2 ( ft   4 9π  12   2 2 2   4 × 0.9  2    1 ft  2  −3 lb ⋅ s  +  7.9028 × 10  (1 in.) +  2.2 +   in   ft   3π      12 in.   lb ⋅ s 2   1 16  2  +  3.6587 × 10−3 0.5 in.)   − 2 ( ft   2 9π   2 2 2   4 × 0.5  2    1 ft  2  −3 lb ⋅ s  +  3.6587 × 10  ( 3.5 in.) + 1 +   in   ft   3π      12 in.   ( ) ( =  1.46653 × 10−3 + 70.393 × 10−6 + 552.79 × 10−6  ( ) ( ) ) + 21.400 × 10−6 + 420.75 × 10−6 + 2.0318 × 10−6 + 348.58 × 10−6  lb ⋅ ft ⋅ s 2  = 2.88 × 10−3 lb ⋅ ft ⋅ s 2 I z = 2.88 × 10−3 lb ⋅ ft ⋅ s 2