HW_2 Solutions - For 3D moments I will use r cross F M A =...

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For 3D moments I will use r cross F [ ] [ ] [ ] [ ] [ ] N i k j k M Nm k j i x j i M N k j i F m k j i r xF r M P P AB AB A 720 720 ) 120 ( 60 ) ( 600 300 600 2 . 1 2 . 0 600 300 600 0 2 . 1 2 . 0 - - + - - = - + + = - + = + + = = Combining Similar terms [ ] Nm k j i M P 660 120 720 - + - = Want to find moment about x-axis Convert to meters [ ] [ ] [ ] [ ] [ ] Nm i j i k M Nm k j i x k j M N k j i F m k j i r xF r M P P AB AB A ) 6 . 3 ( ) 2 . 1 ( 15 . 0 ) 3 . 0 ( ) ( 2 12 4 3 . 0 075 . 0 2 12 4 3 . 0 075 . 0 0 - - + + - = + - + = + - = + + = = Combining Similar terms [ ] Nm k j i M P 3 . 0 2 . 1 75 . 3 - + = Need only i term or dot with unit vector i. Nm M P 75 . 3 =
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Sum the moments about point A They have to be equal to zero so there is no couple [ ] [ ] [ ] [ ] [ ] Nmm k Nk Nmm Nj i x j i M N Nj i F mm j j j i r xF r M P AB AB A 1125 3 . 43 0 ) ( 15 75 3 . 43 0 15 30 sin 50 25 25 30 cos 50 0 - = + - - = = + = - - - - = = = o o All Similar terms drop k and equate N N Nmm N mm 0 . 26 ) ( 1125 ) ( 3 . 43 = = Sum the moments about point A Goes to zero, neglect force at B 0 = A M
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HW_2 Solutions - For 3D moments I will use r cross F M A =...

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