Explanation Given information: The maximum allowable tension in cable A C is 1200 N , and maximum allowable tension in cable B C is 600 N , angle made by A C cable with horizontal is 35 ° and the angle made by B C cable with horizontal is 50 ° . 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 H + 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 V ....... (VIII) Calculation: Substitute 1200 N for T AC ,and 35 ° for θ 1 in the Equation (I) T H,1 = ( 1200 N ) cos ( 35 ° ) = ( 1200 N ) ( 0.81915 ) = 982.98 N Substitute 600 N for T BC ,and 50 ° for θ 2 in the Equation (II) T H,2 = ( 600 N ) cos ( 50 ° ) = ( 600 N ) ( 0.6427 ) = 385.62 N Substitute α for θ 3 , in Equation (III) P H = ( P ) cos ( α ) Substitute 982.98 N for T H,1 , and 385.62 N for T H,2 ,and ( P ) cos ( α ) for P H in the Equation (IV) ( P ) cos ( α ) + 385 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 46P

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 45P

Chapter 2.3, Problem 47P

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(a) The maximum force applied at C .

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(a) The maximum force applied at C.

(b) The corresponding value of angle α.

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Chapter 2 Solutions

(a)

The maximum force applied at C.

(b)

The corresponding value of angle α.