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Quiz03_sol

# Quiz03_sol - QUIZ 3 SOLUTIO S Monday The thin rectangular...

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QUIZ 3 SOLUTIOglyph1197S Monday 09/22/08 The thin rectangular plate is subjected to the four forces shown. Find the moment due to the forces about the axis along the diagonal of the plate passing through O . Key concepts: ( ) × = F r M and ( ) n n F r M × = λ First, find the moment about a point on the axis passing through O and the diagonal end. ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) k F i b j F i b k F j b k F M O ° × + ° × + × + × = 30 cos 2 30 sin 2 0 ( ) ( ) ( ) ( ) k F j b i b j F j b i b ° × + + ° × + + 30 cos 2 30 sin 2 ( ) ( ) ( ) ( ) ( ) + + + + + + = i Fb j Fb k Fb j Fb k Fb i Fb M O 2 3 3 0 3 0 i Fb i Fb i Fb M O + = + = 2 3 1 2 3 Next, note that this distance j b i b + 2 m, so that the unit vector is: ( ) ( ) j i j i b b j b i b n 447 . 0 894 . 0 5 1 5 2 2 2 2 2 + + = + + = . Finally, use the triple scalar product to find the moment about an arbitrary axis: ( ) ( ) n Fb n n M n n F r M O OA axis + = = × = 5 3 2 + + + = m N 5 3 2 5 3 2 4 j i M axis m N 746 . 0 493 . 1 + j i

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Quiz03_sol - QUIZ 3 SOLUTIO S Monday The thin rectangular...

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