For the cables of Prob. 2.44, find the value of α for which the tension is as small as possible (a) in cable BC, (b) in both cables simultaneously. In each case, determine the tension in each cable.
(a)
The value of the angle
Answer to Problem 2.57P
The value of the angle
Explanation of Solution
The arrangement of the system is given in Fig. P2.44. The tension in the cable
The free body diagram of the arrangement shown in Fig. P2.44 is given in the Figure
Since the point
The angle between the
Write the expression for the angle
Apply law of sine to the force triangle in Figure 2.
Conclusion:
From the force triangle the angle
Substitute
Solve equation (I) for
Substitute
Solve equation (I) for
Therefore, the value of the angle
(b)
The value of the angle
Answer to Problem 2.57P
The value of the angle
Explanation of Solution
The free body diagram corresponding to the given arrangement is given in Figure 1
The force triangle become isosceles when the tension in both the cables become the minimum, since the tensions will be equal on both the cables in such situation.
The force triangle corresponding to the minimum tension in both cables
Apply the law of sine to the force triangle given in Figure 3.
Conclusion:
From inspection on the force triangle in Figure 3, the angle
Solve equation (III) for
Solve equation (III) for
Therefore, the value of the angle
Want to see more full solutions like this?
Chapter 2 Solutions
EBK VECTOR MECHANICS FOR ENGINEERS: STA
- Three cables are connected at A, where the force P is applied as shown. Determine the tension each cable.arrow_forward1.Referring to the figure below, knowing that a = 20", determine the tension in (a) in cable AC. (b) in горе ВС. 1200 Ib 2. Referring to the block below, determine (a) the required value of a if the resultant of the three forces shown is to be parallel to the incline, (b) the corresponding magnitude of the resultant. 3. A transmission tower shown below, is heid by three guy wires anchored by bolts at 8, C, and D. (a) If the tension in wire AB is 525 Ib, determine the components of the force exerted by the wire on the bolt at 8. (b) A transmission tower is held by three guy wires anchored by bolts at 8, C, and D. If the tension in wire AD is 315 Ib, determine the components of the force exerted by the wire on the bolt at D. 100 t 20 25 20 60arrow_forward4.110 A 7-ft boom is held by a ball and socket at A and by two cables EBF and DC; cable EBF passes around a frictionless pulley at B. Determine the tension in each cable.arrow_forward
- Two cables are tied together at C and loaded as shown. Determine the tension (a) in cable AC, (b) in cable BCarrow_forwardB 2 m 30° 3 kN 2 m A 4 kN 2 m For the following truss system, determine the tension TAB in the cable AB. 2 marrow_forwardSolve Prob. 3.53 when the tension in cable AB is 306 lb.(Reference to Problem 3.53):A farmer uses cables and winch pullers B and E to plumb one side of a small barn. If it is known that the sum of the moments about the x axis of the forces exerted by the cables on the barn at points A and D is equal to 4728 lb·ft, determine the magnitude of TDE when TAB = 255 lb.arrow_forward
- Knowing that the tension in cable AC is 300 lb, determine the smallest angle between cable AC and the boom AB. The smallest angle is?arrow_forward2. Cable AB passes over the small ideal pulley C without a change in its tension. The length of cable AD is 10m. What is the tension Tin cable CD?arrow_forward50° P2.3 and P2.4 2.4 Two structural members B and C are bolted to bracket A. Know- ing that both members are in tension and that P = 6 kips and Q = 4 kips, determine graphically the magnitude and direction of the resultant force exerted on the bracket using (a) the paral- lelogram law, (b) the triangle rale.arrow_forward
- Solve 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_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_forwardQ.2 A barge shown in Fig.2 is pulled by two tugboats. If the resultant of the forces exerted by the tugboats is a 5000 N force directed along the axis of the barge, determine the tension in each of the ropes knowing that a= 45. (25 Marks) 30 Fig.2arrow_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