Vector Mechanics for Engineers: Statics

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PROBLEM 2.1 Two forces are applied to an eye bolt fastened to a beam. Determine graphically the magnitude and direction of their resultant using ( a ) the parallelogram law, ( b ) the triangle rule. SOLUTION ( a ) ( b ) We measure: 8.4 kN R = 19 α = ° 8.4 kN = R 19 ° W
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PROBLEM 2.6 Two control rods are attached at A to lever AB . Using trigonometry and knowing that the force in the right-hand rod is F 2 = 80 N, determine ( a ) the required force F 1 in the left-hand rod if the resultant R of the forces exerted by the rods on the lever is to be vertical, ( b ) the corresponding magnitude of R . SOLUTION Using the Law of Sines 1 80 sin sin38 sin F R α β = = ° 90 10 80 , 180 80 38 62 α β = ° − ° = ° = ° − ° − ° = ° Then: 1 80 N sin80 sin38 sin62 F R = = ° ° ° or ( a ) 1 89.2 N F = W ( b ) 55.8 N R = W
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PROBLEM 2.17 Solve Problem 2.2 using trigonometry Problem 2.2: The cable stays AB and AD help support pole AC . Knowing that the tension is 500 N in AB and 160 N in AD , determine graphically the magnitude and direction of the resultant of the forces exerted by the stays at A using ( a
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