Vector Mechanics for Engineers: Statics

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PROBLEM 2.44 Knowing that 25 , α = ° determine the tension ( a ) in cable AC , ( b ) in rope BC . SOLUTION Free-Body Diagram Force Triangle Law of Sines: 5 kN sin115 sin5 sin 60 AC BC T T = = ° ° ° ( a ) 5 kN sin115 5.23 kN sin60 AC T = ° = ° 5.23 kN AC T = W ( b ) 5 kN sin5 0.503 kN sin60 BC T = ° = ° 0.503 kN BC T = W
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PROBLEM 2.45 Knowing that 50 α = ° and that boom AC exerts on pin C a force directed long line AC , determine ( a ) the magnitude of that force, ( b ) the tension in cable BC . SOLUTION Free-Body Diagram Force Triangle Law of Sines: 400 lb sin 25 sin60 sin95 AC BC F T = = ° ° ° ( a ) 400 lb sin 25 169.69 lb sin95 AC F = ° = ° 169.7 lb AC F = W ( b ) 400 sin 60 347.73 lb sin95 BC T = ° = ° 348 lb BC T = W
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PROBLEM 2.53 Two cables tied together at C are loaded as shown. Knowing that W = 840 N, determine the tension ( a ) in cable AC , ( b ) in cable BC . SOLUTION Free-Body Diagram From geometry: The sides of the triangle with hypotenuse CB are in the ratio 8:15:17. The sides of the triangle with hypotenuse CA are in the ratio 3:4:5.
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