HW_1 Solutions - Scalar Notation: Break into components A...

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Scalar Notation: Break into components A j N i N F j i N F j F i F F A A A A A ) 33 . 530 ( ) 33 . 530 ( ) 707 . 0 * 750 ( ) 707 . 0 * 750 ( ) 45 cos( ) 45 sin( + = + = + = B j N i N F j N i N F j F i F F B B A B B ) 400 ( ) 82 . 692 ( ) 5 . 0 * 800 ( ) 866 . 0 * 800 ( ) 30 sin( ) 30 cos( - = - = - = Adding Similar Components X-dir N F N N F F F F X R X R X B X A X R 15 . 1223 82 . 692 33 . 530 _ _ _ _ _ = + = + = Y-dir N F N N F F F F Y R Y R Y B Y A Y R 33 . 130 400 33 . 530 _ _ _ _ _ = - = + = Magnitude of Resultant Force F R is kN N F F F F F R R Y R X R R 23 . 1 07 . 1230 33 . 130 15 . 1223 2 2 2 _ 2 _ = = + = + = The Direction angle Theta measured counterclockwise from positive x axis is o 08 . 6 15 . 1223 33 . 130 tan tan 1 _ _ 1 = = = - - N N F F X R Y R q
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Position Vector: This can be established from the coordinates of the two points. ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 [ ] [ ] ft k j i r ft k j i r k A B j A B i A B r AB AB Z Z Y Y x X AB 5 7 2 6 1 5 2 3 5 - - = - + - - + - = - + - + - = The total distance is found from the magnitude
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HW_1 Solutions - Scalar Notation: Break into components A...

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