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HW3 - Problem 2-98 The cable attached to the tractor at B...

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Unformatted text preview: Problem 2-98 The cable attached to the tractor at B cxerts force F on the framework. Express this force as a Cartesian vector N Given: F = 350 1b . a = 35 ft ; A b = 50 ft t; 6' = 20 deg ' 5‘ ‘ F 3 ‘ in Solution: x Find the position vector and then the force bsin(6) rAB = bcos(0) Fv = F —a rAB erBI Problem 2-100 Determine the position (x, y, 0) for fixing cable BA so that the resultant of the forces exerted on the pole is directed along its axis, from B toward 0, and has magnitude F R. Also, what is the magnitude of force F 3? y fir Given: F] = 500 N F2 = 400 N = 1000 N a = 1m [7 = 2 m c = 2 m d = 3 m Solution: Initial Guesses F3 = 1 N x = l m y = 1 In Given -—c F2 a F3 FR = 0 + — —b + —— y [cZF+d2] —d, [\Ia2+b2+d2] —d (x2+y2+d2] —d x 1.9 3=Find(,,F3xy) ()=(24)m F3=38ON y . Problem 2-107 Given the three vectors A, B, and D, show that A-(B + D) = (A B) + (A. D). Solution: Since the component of (B + D) is equal to the sum of the components of B and D, then A-(B + D) = A-B + A-D (QED) Also, A~(B + D) = (Axi + ij + Azk)[(Bx + Dx)i + (By + Dy)!" + (Bz + Dz)k] Ax(Bx + Dx) + Ay(By + Dy) + AZ(BZ + DZ) 102 = (AxBx + AyBy + A2192) + (AxDx + AyDy + AzDz) II (A. B) + (A- D) (QED) Problelh 2-119 Deterrnine the projected component of the force F acting along the axis AB of the pipe. Given F = 80 N a = 4 m b = 3 m c = 12 m d = 2 m e = 6 in Solution: Find the force and the unit vector —e —6 ‘ —35.3 rA rA= -—a——b rA= -—7 m FV=FIr I Fv= —41.2 N d— c —10 A —58.8 —e —6 . —0.9 l'AB rAB = —b rAB = —3 m “AB = '1‘ I “AB = —0.4 d 2 AB 0.3 Now find the projection using the Dot product. FAB = Fv' “AB ...
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