Analytical Mech Homework Solutions 108

Analytical Mech Homework Solutions 108 - 6 8.7 For a...

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6 8.7 For a rectangular parallelepiped: dv hdxdy = h is the length of the box in the z -direction z x y 2b 2a () 1 22 2 R xy =+ ( ) 2 xa yb z xayb I R dv x y hdxdy ρρ == =− + ∫∫ 3 24 2 33 a z a b 2 I h bx dx hab a b  =   + ( )( ) 4 a b h abh m 3 z m I ab For an elliptic cylinder: Again dv hdxdy = , and 1 2 R 2a 2b z y x On the surface, 1 + = 1 2 2 2 1 y b 1 2 2 2 1 2 2 2 1 1 y b z y b 2 I R dv x y hdxdy ρ = + 31 32 2 12 1 3 b z b yy I ha a y bb    +    d y 2 22 2 2 2 3 aa hb y d y b y y −− d y + From a table of integrals: 33 1 222 4 1 sin 48 8 byd y by b y b b −= + − + 13 1 1 2 sin 48 8 by y d y b + + y 42 2 2 38 8 4 z b 2 I h a b a ρπ π =
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This note was uploaded on 01/06/2012 for the course PHYSICS 4360C taught by Professor Johnanderson during the Fall '11 term at UNF.

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