Explanation Given information : The weight of the crate ( W ) is 300 lb. Show the free body diagram of the forces acting on the cable system as in Figure 1. 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 (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 z B , 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, the 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 + ( z B − 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 the 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 the 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 | ] X (IX) Here, the force in cable AD is F A D . Write the weight of the crate in vector format. W = − 300 k lb Write the Equation of equilibrium condition. Σ F = 0 F A B + F A C + F A D + W = 0 (X) Calculations : Substitute –3 ft for x B , 0 ft for x A , (–6 ft) for y B , 0 ft for y A , (2 ft) for z B , and 0 ft for z A in Equation (I). r A B = ( − 3 − 0 ) i + ( − 6 − 0 ) j + ( 2 − 0 ) k = − 3 i − 6 j + 2 k Substitute –3 ft for x B , 0 ft for x A , (–6 ft) for y B , 0 ft for y A , (2 ft) for z B , and 0 ft for z A in Equation (II). | r A B | = ( − 3 − 0 ) 2 + ( − 6 − 0 ) 2 + ( 2 − 0 ) 2 = 49 = 7 ft Substitute (2 ft) for x C , 0 ft for x A , (–6 ft) for y C , 0 ft for y A , (3 ft) for z C , and 0 ft for z A in Equation (III)

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 3.4, Problem 54P

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The tension developed in each cable for equilibrium.

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Chapter 3.4, Problem 53P

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Chapter 3 Solutions

Engineering Mechanics: Statics & Dynamics (14th Edition)

Ch. 3.3 - In each case, draw a free-body diagram of the ring...Ch. 3.3 - Write the two equations of equilibrium, Fx = 0 and...Ch. 3.3 - The crate has a weight of 550 lb. Determine the...Ch. 3.3 - The beam has a weight of 700 lb. Determine the...Ch. 3.3 - If the 5-kg block is suspended from the pulley B...Ch. 3.3 - The block has a mass of 5 kg and rests on the...Ch. 3.3 - If the mass of cylinder C is 40 kg, determine the...Ch. 3.3 - Determine the tension in cables AB, BC, and CD,...Ch. 3.3 - The members of a truss are pin connected at joint...Ch. 3.3 - The members of a truss are pin connected at joint...

Ch. 3.3 - Determine the magnitude and direction of F so...Ch. 3.3 - The bearing consists of rollers, symmetrically...Ch. 3.3 - The members of a truss are connected to the gusset...Ch. 3.3 - The gusset plate is subjected to the forces of...Ch. 3.3 - The man attempts to pull down the tree using the...Ch. 3.3 - The cords ABC and BD can each support a maximum...Ch. 3.3 - Determine the maximum force F that can be...Ch. 3.3 - The block has a weight of 20 lb and is being...Ch. 3.3 - Determine the maximum weight W of the block that...Ch. 3.3 - The lift sling is used to hoist a container having...Ch. 3.3 - A nuclear-reactor vessel has a weight of 500(103)...Ch. 3.3 - Determine the stretch in each spring for...Ch. 3.3 - The unstretched length of spring AB is 3 m. If the...Ch. 3.3 - Determine the mass of each of the two cylinders if...Ch. 3.3 - Determine the stiffness kT of the single spring...Ch. 3.3 - If the spring DB has an unstretched length of 2 m....Ch. 3.3 - Determine the unstretched length of DB to hold the...Ch. 3.3 - A vertical force P = 10 lb is applied to the ends...Ch. 3.3 - Determine the unstretched length of spring AC if a...Ch. 3.3 - The springs BA and BC each have a stiffness of 500...Ch. 3.3 - The springs BA and BC each nave a stiffness of 500...Ch. 3.3 - Determine the distances x and y for equilibrium if...Ch. 3.3 - Determine the magnitude of F1 and the distance y...Ch. 3.3 - The 30-kg pipe is supported at A by a system of...Ch. 3.3 - Each cord can sustain a maximum tension of 500 N....Ch. 3.3 - The streetlights A and B are suspended from the...Ch. 3.3 - Determine the tension developed in each cord...Ch. 3.3 - Prob. 30P Ch. 3.3 - Prob. 31P Ch. 3.3 - Prob. 32P Ch. 3.3 - The lamp has a weight of 15 lb and is supported by...Ch. 3.3 - Each cord can sustain a maximum tension of 20 lb....Ch. 3.3 - Prob. 35P Ch. 3.3 - Prob. 36P Ch. 3.3 - Prob. 37P Ch. 3.3 - Prob. 38P Ch. 3.3 - The ball D has a mass of 20 kg. If a force of F =...Ch. 3.3 - The 200-lb uniform container is suspended by means...Ch. 3.3 - The single elastic cord ABC is used to support the...Ch. 3.3 - A scale is constructed with a 4-ft-long cord and...Ch. 3.3 - The concrete wall panel is hoisted into position...Ch. 3.3 - Prob. 2CP Ch. 3.3 - Prob. 3CP Ch. 3.3 - Prob. 4CP Ch. 3.4 - Determine the magnitude of forces F1, F2, F3, so...Ch. 3.4 - Determine the tension developed in cables AB, AC,...Ch. 3.4 - Prob. 9FP Ch. 3.4 - Prob. 10FP Ch. 3.4 - Prob. 11FP Ch. 3.4 - The three cables are used to support the 40-kg...Ch. 3.4 - Determine the magnitudes of F1, F2, and F3 for...Ch. 3.4 - If the bucket and its contents have a total weight...Ch. 3.4 - Determine the stretch in each of die two springs...Ch. 3.4 - Prob. 47P Ch. 3.4 - Determine the tension in the cables in order to...Ch. 3.4 - Determine the maximum mass of the crate so that...Ch. 3.4 - Determine the force in each cable if F = 500 lb.Ch. 3.4 - Prob. 51P Ch. 3.4 - Determine the tens on developed in cables AB and...Ch. 3.4 - If the tension developed in each cable cannot...Ch. 3.4 - Prob. 54P Ch. 3.4 - Determine the maximum weight of the crate that can...Ch. 3.4 - The 25 kg flowerpot is supported at A by the three...Ch. 3.4 - If each cord can sustain a maximum tension of 50 N...Ch. 3.4 - Determine the tension developed m the three cables...Ch. 3.4 - Determine the tension developed in the three...Ch. 3.4 - Prob. 60P Ch. 3.4 - Prob. 61P Ch. 3.4 - If the maximum force in each rod con not exceed...Ch. 3.4 - Prob. 63P Ch. 3.4 - If cable AD is tightened by a turnbuckle and...Ch. 3.4 - Prob. 65P Ch. 3.4 - Prob. 66P Ch. 3.4 - Determine the maximum weight of the crate so that...Ch. 3.4 - The pipe is held in place by the vise. If the bolt...Ch. 3.4 - Prob. 2RP Ch. 3.4 - Prob. 3RP Ch. 3.4 - Prob. 4RP Ch. 3.4 - Prob. 5RP Ch. 3.4 - Prob. 6RP Ch. 3.4 - Determine the force in each cable needed to...Ch. 3.4 - If cable AB is subjected to a tension of 700 N,...

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The tension developed in each cable for equilibrium.

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

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The tension developed in each cable for equilibrium.

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Chapter 3 Solutions