Explanation Given information : The mass of the crate ( m ) is 130 kg. Show the free body diagram of the forces acting on the cable system as in Figure 1. Determine the position vector for point DA . r D A = r A − r D = ( x A i + y A j + z A k ) − ( x D i + y D j + z D k ) = ( x A − x D ) i + ( y A − y D ) j + ( z A − z D ) k (I) Here, the position vector for point A is r A , the position vector for point D is r D , the distance of point A from the origin along the x direction is x A , the distance of point A from the origin along the y direction is y A , the distance of point A from the origin along the z direction is z A , the distance of point D from the origin along the x direction is x D , the distance of point D from the origin along the y direction is y D , the distance of point D from the origin along the z direction is z D , the vector component along the x direction is i, vector component along the y direction is j, and vector component along the z direction is k. Determine the modulus of position vector for point DA . | r D A | = ( x A − x D ) 2 + ( y A − y D ) 2 + ( z A − z D ) 2 (II) Determine the position vector for point DB . r D B = r B − r D = ( x B i + y B j + z B k ) − ( x D i + y D j + z D k ) = ( x B − x D ) i + ( y B − y D ) j + ( z B − z D ) k (III) Here, the position vector for point B is r B , the distance of point B from the origin along the x direction is x B , the distance of point B from the origin along the y direction is y B , and the distance of point B from the origin along the z direction is z B . Determine the modulus of position vector for point DB . | r D B | = ( x B − x D ) 2 + ( y B − y D ) 2 + ( z B − z D ) 2 (IV) Determine the position vector for point DC . r D C = r C − r D = ( x C i + y C j + z C k ) − ( x D i + y D j + z D k ) = ( x C − x D ) i + ( y C − y D ) j + ( z C − z D ) k (V) Here, the position vector for point C is r C , the distance of point C from the origin along the x direction is x C , the distance of point C from the origin along the y direction is y C , and the distance of point C from the origin along the z direction is z C . Determine the modulus of position vector for point DC . | r D C | = ( x C − x D ) 2 + ( y C − y D ) 2 + ( z C − z D ) 2 (VI) Force in Cable DA : F D A = F D A [ r D A | r D A | ] (VII) Here, the force in cable DA is F D A . Force in Cable DB : F D B = F D B [ r D B | r D B | ] (VIII) Here, the force in cable DB is F D B . Force in Cable DC : F D C = F D C [ r D C | r D C | ] (IX) Here, the force in cable DC is F D C . Determine the weight of the crate in vector form. W = ( − m g ) k (X) Here, the mass of crate is m and the acceleration due to gravity is g . Write the Equation of equilibrium. Σ F = 0 F A B + F A C + F A D + W = 0 (XI) Conclusion : Substitute 2 m for x A , 0 m for x D , (–1 m) for y A , 0 m for y D , 1 m for z A , and 0 m for z D in Equation (I). r D A = ( 2 − 0 ) i + ( − 1 − 0 ) j + ( 1 − 0 ) k = 2 i − 1 j+1k Substitute 2 m for x A , 0 m for x D , (–1 m) for y A , 0 m for y D , 1 m for z A , and 0 m for z D in Equation (II). | r D A | = ( 2 − 0 ) 2 + ( − 1 − 0 ) 2 + ( 1 − 0 ) 2 = 6 = 2.45 m Substitute –2 m for x B , 0 m for x D , (–1 m) for y B , 0 m for y D , 1 m for z B , and 0 m for z D in Equation (III). r D B = ( − 2 − 0 ) i + ( − 1 − 0 ) j + ( 1 − 0 ) k = − 2 i − 1 j+1k Substitute –2 m for x B , 0 m for x D , (–1 m) for y B , 0 m for y D , 1 m for z B , and 0 m for z D in Equation (IV)

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 3.4, Problem 63P

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The tension developed in each cable for equilibrium.

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Chapter 3.4, Problem 62P

Chapter 3.4, Problem 64P

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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