Explanation Given information : The ring subjected to a vertical force of 200 lb. The tension acting cord AC is 160 lb. Assumption: Consider the point D in between the points B and C . Draw a free body diagram of cords ABC as shown below in Figure 1. Determine the tension force of the member AB by applying the Equation of equilibrium. Along the horizontal direction : ∑ F x = 0 F A B cos θ A B − F A C cos θ A C = 0 F A B cos θ A B = F A C cos θ A C (I) Here, the force acting on the cord AB is F A B , the angle of the cord AB is θ A B , the tension force acting on the cord AC is F A C , and the angle of the cord AC is θ A C . Along vertical direction : ∑ F y = 0 F A B sin θ A B + F A C sin θ A C − W = 0 (II) Here, the vertical force on the ring is W . Determine the length of the cord AC using sine rule. l A C sin θ A B = l A B sin θ A C (III) Calculations : Substitute 40 ° for cos θ A B and 160 lb for F A C in Equation (I). F A B cos 40 ° = 160 cos θ A C F A B = 160 cos θ A C cos 40 ° F A B = 208.8 cos θ A C (IV) Substitute 208.8 cos θ A C for F A B , 40 ° for sin θ A B , 160 lb for F A C , 200 lb for W in Equation (I). 208.8 cos θ A C × sin 40 ° + 160 × sin θ A C − 200 = 0 134.21 cos θ A C + 160 sin θ A C = 200 cos θ A C + 160 134.21 sin θ A C = 200 134.21 cos θ A C + 1.192 sin θ A C = 1.490 (V) Trial and Error method: Trial 1. Try θ A C = 30 ° . Substitute 30 ° for θ A C in Equation (V). cos 30 ° + 1.192 sin 30 ° = 1.490 0.8660 + 0.596 = 1.49 1.46 ≠ 1.49 Hence, it is incorrect. Trial 2. Try θ A C = 32 ° . Substitute 32 ° for θ A C in Equation (V). cos 32 ° + 1.192 sin 32 ° = 1.490 0.848 + 0.632 = 1.49 1.479 ≠ 1.49 Hence, it is incorrect. Trial 3. Try θ A C = 33.25 ° . Substitute 33

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 3.3, Problem 35P

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Chapter 3 Solutions

Engineering Mechanics: Statics & Dynamics (14th Edition)

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The length of the cord AC and the force in the cord AB .

Solution Summary: The author explains how to determine the tension force of the member AB by applying the Equation of equilibrium.

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The length of the cord AC and the force in the cord AB.

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