Problem y C 10 ft The 15-ft boom AB has a fixed 6 ft

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Problem 3.149 y C 10 ft The 15-ft boom AB has a fixed 6 ft z 15 ft 6 ft 10 ft The 15-ft boom AB has a fixed end A. A steel cable is stretched from the free end B of the boom to a point C located on the vertical wall. If the tension in the cable is 570 lb, determine the moment about A of the force exerted by the cable at B.

F d y C Solving Problems on Your Own 10 ft 6 ft A x y z 15 ft 6 ft 10 ft Solving Problems on Your Own The 15-ft boom AB has a fixed end A. A steel cable is stretched from the free end B of the boom to a point C located on the vertical wall. If the tension in the cable is 570 lb, determine the moment about A of the force exerted by the cable at B. Problem 3.149 1. Determine the rectangular components of a force defined by its magnitude and direction. If the direction of the force is defined by two points located on its line of action, the force can be expressed by: F = Fl = (dx i + dy j + dz k) F d

Solving Problems on Your Own C B A x y z 15 ft 6 ft 10 ft Solving Problems on Your Own The 15-ft boom AB has a fixed end A. A steel cable is stretched from the free end B of the boom to a point C located on the vertical wall. If the tension in the cable is 570 lb, determine the moment about A of the force exerted by the cable at B. Problem 3.149 2. Compute the moment of a force in three dimensions. If r is a position vector and F is the force the moment M is given by: M = r x F

TBC = (_15 i + 6 j _ 10 k) = _ (450 lb) i + (180 lb) j _ (300 lb)k 570 N C B A x y z 15 ft 6 ft 10 ft Problem 3.149 Solution Determine the rectangular components of a force defined by its magnitude and direction. First note: dBC = (_15)2 + (6) 2 + (_10) 2 dBC = 19 ft Then: TBC = (_15 i + 6 j _ 10 k) = _ (450 lb) i + (180 lb) j _ (300 lb)k 570 lb 19

MA = rB/A x TBC MA = 15 i x (_ 450 i + 180 j _ 300 k) 570 N C B A x y z 15 ft 6 ft 10 ft Problem 3.149 Solution Compute the moment of a force in three dimensions. Have: MA = rB/A x TBC Where: rB/A = (15 ft) i Then: MA = 15 i x (_ 450 i + 180 j _ 300 k) MA = (4500 lb.ft) j + (2700 lb.ft) k