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

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Unformatted text preview: CIV-100F Section B/E Solutions Fall 2011 Assignment 3 Due on Monday, October 3rd 2011 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 H → L , determine vector Q as a Cartesian vector. Solution: H = (2,2,5) L = (6,5,−2) rHL = (4)i + (3) j − (7)k rHL = 8.6023 Q=Q rHL = (41.8i + 31.4 j − 73.2)kN rHL 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: r AB = B − A = (1,1,5) = 1i + 1 j + 5k r AC = C − A = (8,−8,6) = 8i − 8 j + 6k r AB = 12 + 12 + 52 = 27 r AC = 82 + (−8)2 + 6 2 = 164 cos θ = r AB ⋅ r AC (1 × 8) − (1 × 8) + (5 × 6) = =0.45083 r AB r AC 27 × 164 θ = 63.20º b) Find the magnitude of the component of AB in the direction of AC Solution: ABAC = rAB cos θ = 27 cos 63.20° = 2.34 Draw a FBD if necessary; Pay attention to significant figures; A ruler is always required. CIV-100F Section B/E Solutions Fall 2011 Assignment 3 Due on Monday, October 3rd 2011 3- The 7m tree trunk is held stable by 2 cables BC and BA. Knowing that TBA=555N, TBC=660N. Express the two tensions as Cartesian vectors and determine the angle formed by BA and BC. Solution: First identify the coordinates of all points: A (-0.75, 0, 6) B (0,7,0) C (4.25, 0, 1) Represent the forces in the cables as vectors: rBA = A − B = (−0.75,−7,6)m = (−0.75i − 7 j + 6k )m rBC = C − B = (4.25,−7,1)m = (4.25i − 7 j + 1k )m rBA = (−0.75) 2 + (−7)2 + 6 2 = 9.25m rBC = 4.252 + (−7) 2 + 12 = 8.25m u BA = rBA = −0.081081i − 0.75675 j + 0.64865k rBA u BC = rBC = 0.51515i − 0.84848 j + 0.12121k rBC T BA = T BA u BA = (−45i − 420 j + 360k )N T BC = T BC u BC = (340i − 560 j + 80k )N cos θ = rBA ⋅ rBC (−0.75i − 7 j + 6k ) ⋅ (4.25i − 7 j + 1k ) = = 0.67895 (9.25)(8.25) rBA rBC θ = cos −1 (0.67895) = 47.24° Draw a FBD if necessary; Pay attention to significant figures; A ruler is always required. ...
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Solution_03 - CIV-100F Section B/E Solutions Fall 2011...

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