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
<LCPO> VECTOR MECH,STAT+DYNAMICS
- 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 = 542 N, determine P and Q. (Hint: The tension is the same in both portions of cable BAC.) 150 mm 140 mm B 240 mm 130 mm 420 mm P Warrow_forwardTwo 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_forwardSolve Prob. 2.103, assuming that a= 8 in.(Reference to Problem 2.103):A 36-lb triangular plate is supported by three wires as shown. Determine the tension in each wire, knowing that a= 6 in.arrow_forward
- A container of weight W is suspended from ring A , to which cables AC and AE are attached. A force P is applied to the end F of a third cable that passes over a pulley at B and through ring A and that is attached to a support at D. Knowing that W = 1000 N, determine the magnitude of P. (Hint: The tension is the same in all portions of cable FBAD).arrow_forwardKnowing that the tension in cable AE of Prob. 2.123 is 75 lb, determine (a) the magnitude of the load P, (b) the tension in cables BAC and AD.(Reference to Problem 2.123):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.arrow_forward1. Two tape spools are attached to an axle supported by bearings at A and D. Assume that the bearing at A does not exert any axial thrust. The radius of spool B is 1.5 in and the radius of spool C is 2 in. Knowing that TB = 20 lb., determine (a) the tension, Tc, and (b) the reactions at A and D. 4.5 in. A TC 6 in. B 4.5 in. Ans: Tc = 15 lb, A= 0î +14 j+4.5k lb D = 0î +6j+10.5k lb Darrow_forward
- Collars 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_forwardA container of weight W is suspended from ring A, to which cables AC and AE are attached. A force P is applied to the end F of a third cable that passes over a pulley at B and through ring A and that is attached to a support at D. Knowing that W=1000 N, determine the magnitude of P. (Hint: The tension is the same in all portions of cable FBAD.)arrow_forwardshow work please Answer is T=180 lb -6 ft Ĵ 3.. The 8 ft rod AB and the 6 ft rod BC are hinged at B and supported by cable DE, and by ball-and- socket joints at A and C. Knowing that h= 10.5 ft, determine the tension in the cable. 2 ft B Ċ 210 lb 3 ft 3 ftarrow_forward
- 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.arrow_forwardTwo steel pipes AB and BC, each having a mass per unit length of 28 kg/m, are welded together at B and supported by three wires. Knowing that a = 0.4 m, determine the tension in each wire. (Round the final answers to two decimal places.)arrow_forward4. Collars A and B are connected by 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 and z = 12 in, (b) the corresponding magnitude of the force P required to maintain equilibrium of the system. 20 in.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