Explanation Given information : The mass of the flowerpot ( m ) is 25 kg. Show the free body diagram of the forces acting on the cord as in Figure 1. Determine the weight of the flowerpot in vector form. F = ( − m g ) k (I) Here, the mass of the flowerpot is m and the acceleration due to gravity is g . Force in Cable AB : F A B = F A B ( sin θ y B j + cos θ z B k ) (II) Here, the angle for force in cable AB along the y direction is θ y B and the angle for force in cable AB along the z direction is θ z B . Force in Cable AC : F A C = F A C ( ( − sin θ x C ) i − ( cos θ y 1 C sin θ y 2 C ) j + ( cos θ z 1 C cos θ z 2 C ) k ) (III) Here, the angle for force in cable AC along the x direction is θ x C , the angle for force in cable AC along the y direction is θ y 1 C and θ y 2 C , and the angle for force in cable AC along the z direction is θ z 1 C and θ z 2 C . Force in Cable AD : F A D = F A D ( ( sin θ x D ) i − ( cos θ y 1 D sin θ y 2 D ) j + ( cos θ z 1 D cos θ z 2 D ) k ) (IV) Here, the angle for force in cable AD along the x direction is θ x D , the angle for force in cable AD along the y direction is θ y D , and the angle for force in cable AD along the z direction is θ z D . Write the Equation of equilibrium. Σ F = 0 F A B + F A C + F A D + F = 0 (V) Conclusion : Substitute 25 kg for m and 9.81 m / s 2 for g in Equation (I). F = ( − 25 × 9.81 ) k = ( − 245 .25 kg ⋅ m / s 2 × 1 N 1 kg ⋅ m / s 2 ) k = ( − 245.25 k ) N Substitute 45 ° for θ y B and 45 ° for θ z B in Equation (II). F A B = F A B ( sin 45 ° j + cos 45 ° k ) = F A B ( 0.707 j + 0.707 k ) Substitute 30 ° for θ x C , 30 ° for θ y 1 C , 60 ° for θ y 2 C , 30 ° for θ z 1 C , and 60 ° for θ z 2 C in Equation (III). F A C = F A C ( ( − sin 30 ° ) i − ( cos 30 ° sin 60 ° ) j + ( cos 30 ° cos 60 ° ) k ) = F A C ( − 0.5 i − 0.75 j+0 .433k ) Substitute 30 ° for θ x D , 30 ° for θ y 1 D , 60 ° for θ y 2 D , 30 ° for θ z 1 D , and 60 ° for θ z 2 D in Equation (IV)

INTERNATIONAL EDITION---Engineering Mechanics: Statics, 14th edition (SI unit)

14th Edition

ISBN: 9780133918922

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 3.4, Problem 56P

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The force acting in each cord for equilibrium.

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Chapter 3.4, Problem 55P

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INTERNATIONAL EDITION---Engineering Mechanics: Statics, 14th edition (SI unit)

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The force acting in each cord for equilibrium.

Solution Summary: The author shows the free body diagram of the forces acting on the cord as in Figure 1.

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The force acting in each cord for equilibrium.

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