Explanation Given information : The mass of the pot ( m ) is 50 kg. The given value of d is 2.5 m. Show the free body diagram of the forces acting on the cables as in Figure (1). Using Figure (1), Determine the position vector for point AB . r A B = r B − r A = ( x B i + y B j + d k ) − ( x A i + y A j + z A k ) = ( x B − x A ) i + ( y B − y A ) j + ( d − z A ) k (I) Here, the position vector for point B is r B , the position vector for point A is r A , the distance of point B from the origin along x direction is x B , the distance of point B from the origin along y direction is y B , the distance of point B from the origin along z direction is d , the distance of point A from the origin along x direction is x A , the distance of point A from the origin along y direction is y A , the distance of point A from the origin along z direction is z A , the vector component along x direction is i, vector component along y direction is j, and the vector component along z direction is k. Determine the modulus of position vector for point AB . | r A B | = ( x B − x A ) 2 + ( y B − y A ) 2 + ( d − z A ) 2 (II) Determine the position vector for point AC . r A C = r C − r A = ( x C i + y C j + z C k ) − ( x A i + y A j + z A k ) = ( x C − x A ) i + ( y C − y A ) j + ( z C − z A ) k (III) Here, the position vector for point C is r C , the distance of point C from the origin along x direction is x C , the distance of point C from the origin along y direction is y C , and the distance of point C from the origin along z direction is z C . Determine the modulus of position vector for point AC . | r A C | = ( x C − x A ) 2 + ( y C − y A ) 2 + ( z C − z A ) 2 (IV) Determine the position vector for point AD . r A D = r D − r A = ( x D i + y D j + z D k ) − ( x A i + y A j + z A k ) = ( x D − x A ) i + ( y D − y A ) j + ( z D − z A ) k (V) Here, the position vector for point D is r D , the distance of point D from the origin along x direction is x D , the distance of point C from the origin along y direction is y D , and the distance of point D from the origin along z direction is z D . Determine the modulus of position vector for point AD . | r A D | = ( x D − x A ) 2 + ( y D − y A ) 2 + ( z D − z A ) 2 (VI) Force in Cable AB : F A B = F A B [ r A B | r A B | ] (VII) Here, the force in cable AB is F A B . Force in Cable AC : F A C = F A C [ r A C | r A C | ] (VIII) Here, the force in cable AC is F A C . Force in Cable AD : F A D = F A D [ r A D | r A D | ] (IX) Here, the force in cable AD is F A D . Determine the weight of the pot. W = m g (X) Here, the acceleration due to gravity is g . Write the Equation of equilibrium condition. Σ F = 0 F A B + F A C + F A D + F = 0 (XI) Conclusion : Substitute (6 m) for x B , 0 m for x A , (0 m) for y B , 0 m for y A , (2.5 m) for d , and 0 m for z A in Equation (I). r A B = ( 6 − 0 ) i + ( 0 − 0 ) j + ( 2.5 − 0 ) k = ( 6 i + 0 j + 2.5 k ) m Substitute (6 m) for x B , 0 m for x A , (0 m) for y B , 0 m for y A , (2.5 m) for d , and 0 m for z A in Equation (II). | r A B | = ( 6 − 0 ) 2 + ( 0 − 0 ) 2 + ( 2.5 − 0 ) 2 = 42.25 = 6.5 m Substitute (–6 m) for x C , 0 m for x A , (–2 m) for y C , 0 m for y A , (3 m) for z C , and 0 m for z A in Equation (III). r A C = ( − 6 − 0 ) i + ( − 2 − 0 ) j + ( 3 − 0 ) k = ( − 6 i − 2 j + 3 k ) m Substitute (–6 m) for x C , 0 m for x A , (–2 m) for y C , 0 m for y A , (3 m) for z C , and 0 m for z A in Equation (IV)

Engineering Mechanics: Statics and Study Pack (13th Edition)

13th Edition

ISBN: 9780133027990

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Chapter 3.4, Problem 52P

To determine

The force acting in each cable for equilibrium.

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Chapter 3 Solutions

Engineering Mechanics: Statics and Study Pack (13th Edition)

Ch. 3.3 - Determine the force in each supporting cable.Ch. 3.3 - Determine the shortest cable ABC that can be used...Ch. 3.3 - Neglect the size of the pulley.Ch. 3.3 - Determine the unstretched length of the spring.Ch. 3.3 - If the mass of cylinder C is 40 kg, determine the...Ch. 3.3 - Also, find the angle .Ch. 3.3 - Determine the magnitudes of F1 and F2 for...Ch. 3.3 - Determine the magnitude of F1 and its angle for...Ch. 3.3 - Determine the force in each of the cables AB and...Ch. 3.3 - Prob. 4P

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