Solution_03 - CIV-100F Section B/E Solutions Fall 2011...

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CIV-100F Solutions Section B/E Fall 2011 Assignment 3 Due on Monday, October 3 rd 2011 Draw a FBD if necessary; Pay attention to significant figures; A ruler is always required. 1- Force Q (Q=90kN) acts along a line which passes through H(2,2,5) and L(6,5,-2). Force is in direction L H , determine vector Q as a Cartesian vector. Solution : ) 2 , 5 , 6 ( ) 5 , 2 , 2 ( = = L H k j i r HL ) 7 ( ) 3 ( ) 4 ( + = 6023 . 8 = HL r kN j i r r Q Q HL HL ) 2 . 73 4 . 31 8 . 41 ( + = = 2- Consider the following points in space: A(-1, 5, -3), B(0, 6, 2), C(7, -3, 3) a) Find the angle formed by vectors AB and AC . Solution : k j i A B r AB 5 1 1 ) 5 , 1 , 1 ( + + = = = k j i A C r AC 6 8 8 ) 6 , 8 , 8 ( + = = = 164 6 ) 8 ( 8 27 5 1 1 2 2 2 2 2 2 = + + = = + + = AC AB r r AC AB AC AB r r r r = θ cos = 164 27 ) 6 5 ( ) 8 1 ( ) 8 1 ( × × + × × =0.45083 θ = 63.20 º b) Find the magnitude of the component of AB in the direction of AC Solution : 34 . 2 20 . 63 cos 27 cos = ° = = θ AB AC r AB
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CIV-100F Solutions Section B/E Fall 2011 Assignment 3 Due on Monday, October 3 rd 2011 Draw a FBD if necessary; Pay attention to significant figures; A ruler is always required. 3- The 7m tree trunk is held stable by 2 cables BC and BA. Knowing that T BA =555N, T BC =660N. Express the two tensions as Cartesian vectors and
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