Explanation Given information : The give force ( F ) value is 800 N. 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 the x direction is x B , the distance of point B from the origin along the y direction is y B , the distance of point B from the origin along the z direction is z B , 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 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 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 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 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 the x direction is x D , the distance of point C from the origin along the y direction is y D , and the distance of point D from the origin along the 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 . Write the Equation of equilibrium condition. Σ F = 0 F A B + F A C + F A D + F = 0 (X) Conclusion : Substitute 4 m for x B , 0 m for x A , (4 m) for y B , 0 m for y A , (–5 m) for z B , 0 m for z A in Equation (I). r A B = ( 4 − 0 ) i + ( 4 − 0 ) j + ( − 5 − 0 ) k = 4 i + 4 j − 5 k Substitute 4 m for x B , 0 m for x A , (4 m) for y B , 0 m for y A , (–5 m) for z B , 0 m for z A in Equation (II). | r A B | = ( 4 − 0 ) 2 + ( 4 − 0 ) 2 + ( − 5 − 0 ) 2 = 16 + 16 + 25 = 7.54 m Substitute (–2 m) for x C , 0 m for x A , (3 m) for y C , 0 m for y A , (–5 m) for z C , 0 m for z A in Equation (III)

Engineering Mechanics: Statics & Dynamics, Student Value Edition Plus Modified Mastering Engineering Revision with Pearson eText -- Access Card Package

14th Edition

ISBN: 9780135841532

Author: HIBBELER, Russell , HIBBLER

Publisher: PEARSON

See similar textbooks

Concept explainers

Plane Trusses

It is defined as, two or more elements like beams or any two or more force members, which when assembled together, behaves like a complete structure or as a single structure. They generally consist of two force member which means any component structure …

Equilibrium Equations

If a body is said to be at rest or moving with a uniform velocity, the body is in equilibrium condition. This means that all the forces are balanced in the body. It can be understood with the help of Newton's first law of motion which states that the res…

Force Systems

When a body comes in interaction with other bodies, they exert various forces on each other. Any system is under the influence of some kind of force. For example, laptop kept on table exerts force on the table and table exerts equal force on it, hence th…

Videos

Question

Chapter 3.4, Problem 61P

To determine

The tension in each cable for equilibrium.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 3.4, Problem 60P

Chapter 3.4, Problem 62P

Students have asked these similar questions

You are tasked with designing a power drive system to transmit power between a motor and a conveyor belt in a manufacturing facility as illustrated in figure. The design must ensure efficient power transmission, reliability, and safety. Given the following specifications and constraints, design drive system for this application: Specifications: Motor Power: The electric motor provides 10 kW of power at 1,500 RPM. Output Speed: The output shaft should rotate at 150 rpm. Design Decisions: Transmission ratio: Determine the necessary drive ratio for the system. Shaft Diameter: Design the shafts for both the motor and the conveyor end. Material Selection: Choose appropriate materials for the gears, shafts. Bearings: Select suitable rolling element bearings. Constraints: Space Limitation: The available space for the gear drive system is limited to a 1-meter-long section. Attribute 4 of CEP Depth of knowledge required Fundamentals-based, first principles analytical approach…

- | العنوان In non-continuous dieless drawing process for copper tube as shown in Fig. (1), take the following data: Do-20mm, to=3mm, D=12mm, ti/to=0.6 and v.-15mm/s. Calculate: (1) area reduction RA, (2) drawing velocity v. Knowing that: ti: final thickness V. Fig. (1) ofthre

A direct extrusion operation produces the cross section shown in Fig. (2) from an aluminum billet whose diameter 160 mm and length - 700 mm. Determine the length of the extruded section at the end of the operation if the die angle -14° 60 X Fig. (2) Note: all dimensions in mm.

Chapter 3 Solutions

Engineering Mechanics: Statics & Dynamics, Student Value Edition Plus Modified Mastering Engineering Revision with Pearson eText -- Access Card Package

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,...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

The tension 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.

Concept explainers

Videos

The tension in each cable for equilibrium.

Want to see the full answer?

Chapter 3 Solutions