Cable BAC passes through a frictionless ring A and is attached to fixed supports at B and C, while cables AD and AE are both tied to the ring and are attached, respectively, to supports at D and E. Knowing that a 200-lb vertical load P is applied to ring A, determine the tension in each of the three cables. (Hint: The tension is the same in both portions of cable BAC.)
Fig. P2.136
The tension in each of the three cables
Answer to Problem 2.136RP
The tension in each of the three cables are
Explanation of Solution
The free body diagram is sketched in the figure 1 below
From the free body diagram the tension along of cable
Write the expression for the magnitude of tension acting along
Here,
Write the expression for the direction of tension
Here,
Thus equation 1 can be rewritten as
Write the expression for the magnitude of tension acting along
Here,
Write the expression for the magnitude of tension acting along
Here,
Similarly, the expression for the magnitude of tension acting along
Here,
Under equilibrium, the total force will balances and the sum of all forces will be equal to zero.
Conclusion:
Write the vector representation of
The magnitude of vector
Write the vector representation of
The magnitude of vector
Write the vector representation of
The magnitude of vector
Write the vector representation of
The magnitude of vector
Substitute
Substitute
Substitute
Substitute
Substitute
Rearrange equation (VI) to obtain
Rearrange equation (VIII) to obtain
Substitute equation (IX) and (X) in equation (VII)
Substitute
Substitute
Therefore, the tension in each of the three cables are
Want to see more full solutions like this?
Chapter 2 Solutions
Loose Leaf for Vector Mechanics for Engineers: Statics
- A 36-lb triangular plate is supported by three wires as shown. Determine the tension in each wire, knowing that a=6 in.arrow_forwardTwo cables are tied together at C and are loaded as shown. Part 1. If W=160 lb, determine the tension (a) in cable AC and (b) in cable BC. Part 2. Determine the range of values for W such that the tension will not exceed 240 lb in either cable.arrow_forwardCollars A and B are connected by a 25-in.-long wire and can slide freely on frictionless rods. If a 60-lb force Q is applied to collar B as shown, determine (a) the tension in the wire when x =9 in., (b) the corresponding magnitude of the force P required to maintain the equilibrium of the system.arrow_forward
- A container of weight W is suspended from ring A. Cable BAC passes through the ring and is attached to fixed supports at B and C . Two forces P= Pi and Q QK are applied to the ring to maintain the container in the position shown. Knowing that W = 376 N, determine P and Q. (Hint: The tension is the same in both portions of cable BAC.)arrow_forwardA telephone cable is clamped at A to the pole AB . Knowing that the tension in the right-hand portion of the cable is T2 = 1000 lb, determine by trigonometry (a) the required tension T1 in the left-hand portion if the resultant R of the forces exerted by the cable at A is to be vertical, (b) the corresponding magnitude of R.arrow_forwardA transmission tower is held by three guy wires attached to a pin at A and anchored by bolts at B, C, and D. If the tension in wire AB is 945 lb, determine the vertical force P exerted by the tower on the pin at A. y 25 ft 20 ft 100 ft B 60 ft C D 20 ft 18 ft 74 ft x The vertical force P exerted by the tower on the pin is 762.84 lb.arrow_forward
- Two cables are tied together at C and are loaded as shown. Knowing that P= 500 N and a= 60°, determine the tension in (a) in cable AC, (b) in cable BC.arrow_forwardA slender rod BC with a length of L and weight W is held by two cables as shown. Knowing that cable AB is horizontal and that the rod forms an angle of 40° with the horizontal, determine (a) the angle 0 that cable CD forms with the horizontal, (b) the tension in each cable.arrow_forwardThree cables are connected are connect at A, where the forces P and Q are applied as shown below. Knowing that Q=0, find the valueof P for which the tension of the cable in AD is 427N.arrow_forward
- Two steel pipes AB and BC , each having a mass per unit length of 8 kg/m, are welded together at B and supported by three vertical wires. Knowing that a= 0.4 m, determine the tension in each wire.arrow_forwardA load Q is applied to pulley C, which can roll on cable ACB. The pulley is held in the position shown by a second cable CAD, which passes over pulley A and supports a load P. Knowing that P = 750 N, determine (a) the tension in cable ACB, (b) the magnitude of load Q.arrow_forwardAt C two cables are tied and loaded as shown in Fig. figure. Knowing that Q = 60 lb, determine the tension (a) in cable AC and b) in cable BC.arrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY