Explanation Given information : The maximum tension sustained by the cables AB and AC is 500 N. The maximum compression supported by the pole AO is 300 N. Show the free body diagram of the forces acting on the cables as in Figure (1). Determine the position vector for point AO . r A O = r O − r A = ( x O i + y O j + z O k ) − ( x A i + y A j + z A k ) = ( x O − x A ) i + ( y O − y A ) j + ( z O − z A ) k (I) Here, the position vector for point O is r O , the position vector for point A is r A , the distance of point O from the origin along x direction is x O , the distance of point O from the origin along y direction is y O , the distance of point O from the origin along z direction is z O , 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 AO . | r A O | = ( x O − x A ) 2 + ( y O − y A ) 2 + ( z O − z A ) 2 (II) Determine the position vector for point AB . r A B = r B − r A = ( x B i + y B j + z B k ) − ( x A i + y A j + z A k ) = ( x B − x A ) i + ( y B − y A ) j + ( z B − z A ) k (III) Here, the position vector for point B is r B , 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 , and the distance of point B from the origin along z direction is z B . Determine the modulus of position vector for point AB . | r A B | = ( x B − x A ) 2 + ( y B − y A ) 2 + ( z B − z A ) 2 (IV) 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 (V) 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 (VI) Force in Rope AO : F A O = F A O [ r A O | r A O | ] (VII) Here, the force in cable AO is F A O . Force in Rope AB : F A B = F A B [ r A B | r A B | ] (VIII) Here, the force in cable AB is F A B . Force in Rope AC : F A C = F A C [ r A C | r A C | ] (IX) Here, the force in cable AC is F A C . Write the Equation of equilibrium condition. Σ F = 0 F A O + F A B + F A C + W = 0 (X) Conclusion : Substitute (2 m) for x O , 0 m for x A , (–1.5 m) for y O , 0 m for y A , (6 m) for z O , and 0 m for z A in Equation (I). r A O = ( 2 − 0 ) i + ( − 1.5 − 0 ) j + ( 6 − 0 ) k = ( 2 i − 1.5 j + 6 k ) m Substitute (2 m) for x O , 0 m for x A , (–1.5 m) for y O , 0 m for y A , (6 m) for z O , and 0 m for z A in Equation (II). | r A O | = ( 2 − 0 ) 2 + ( − 1.5 − 0 ) 2 + ( 6 − 0 ) 2 = 42.25 = 6.5 m Substitute (–6 m) for x B , 0 m for x A , (3 m) for y B , 0 m for y A , (–6 m) for z B , and 0 m for z A in Equation (III). r A B = ( − 6 − 0 ) i + ( 3 − 0 ) j + ( − 6 − 0 ) k = ( − 6 i + 3 j − 6 k ) m Substitute (–6 m) for x B , 0 m for x A , (3 m) for y B , 0 m for y A , (–6 m) for z B , and 0 m for z A in Equation (IV). | r A B | = ( − 6 − 0 ) 2 + ( 3 − 0 ) 2 + ( − 6 − 0 ) 2 = 81 = 9 m Substitute (–2 m) for x C , 0 m for x A , (3 m) for y C , 0 m for y A , (–6 m) for z C , and 0 m for z A in Equation (V). r A C = ( − 2 − 0 ) i + ( 3 − 0 ) j + ( − 6 − 0 ) k = ( − 2 i + 3 j − 6 k ) m Substitute (–2 m) for x C , 0 m for x A , (3 m) for y C , 0 m for y A , (–6 m) for z C , and 0 m for z A in Equation (VI)

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 51P

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The maximum weight of the lamp that can be supported in the given position.

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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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