Explanation Given information: The maximum allowable tension in cable A C is 600 N , and maximum allowable tension in cable B C is 750 N , angle made by A C cable with horizontal is 45 ° and the angle made by B C cable with horizontal is 25 ° . The below figure shows the configuration of the cable and applied force and tension in the cables. Figure-(1) Write the expression for the horizontal component of the tension in cable A C . T H,1 = T AC cos θ 1 …… (I) Here tension in the cable A C is T AC , and the angle of the cable A C with the horizontal is θ 1 . Write the expression for the horizontal component of the tension in cable B C . T H,2 = T BC cos θ 2 …… (II) Here tension in the cable B C is T BC , and angle of the cable B C with the horizontal is θ 2 . Write the expression for the horizontal component of the force P . P H = P cos θ 3 …… (III) Here force is P and θ 3 is the angle of the cable B C with the horizontal. Write the expression for the balanced horizontal force at point C . T H,1 + P = T H,2 …… (IV) Write the expression for the vertical component of the tension in cable A C . T V,1 = T AC sin θ 1 …… (V) Write the expression for the vertical component of the tension in cable B C . T V,2 = T BC sin θ 2 …… (VI) Write the expression for the horizontal component of the force P . P V = P sin θ 3 …… (VII) Write the expression for the balanced vertical force at point C . T V,1 + T V,2 = P …… (VIII) Calculation: Substitute 600 N for T AC ,and 45 ° for θ 1 in the Equation (I) T H,1 = ( 600 N ) cos ( 45 ° ) = ( 600 N ) ( 0.707 ) = 424.264 N Substitute 750 N for T AC , and 25 ° for θ 2 in the Equation (II) T H,2 = ( 750 N ) cos ( 25 ° ) = ( 750 N ) ( 0.9063 ) = 679.730 N Substitute α for θ 3 , in Equation (III) P H = ( P ) cos ( α ) Substitute 424.264 N for T H,1 , and 679.730 N for T H,2 ,and ( P ) cos ( α ) for P H in the Equation (IV) 424.264 N + ( P ) cos ( α ) = 679 To determine (b) The corresponding value of angle α .

2nd Edition

ISBN: 9780073398167

Author: Ferdinand P. Beer, E. Russell Johnston Jr., John T. DeWolf, David Mazurek

Publisher: McGraw-Hill Education

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Chapter 2.3, Problem 44P

To determine

(a)

The maximum force applied at C.

To determine

(b)

The corresponding value of angle α.

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Chapter 2.3, Problem 43P

Chapter 2.3, Problem 45P

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