Concept explainers
For the rectangular plate of Probs. 2.109 and 2.110, determine the tension in each of the three cables knowing that the weight of the plate is 792 N.
Fig. P2.109 and P2.110
The tension in three cables shown in figure
Answer to Problem 2.115P
The tension in cable
Explanation of Solution
The sketch of plate supported by three cables is shown in figure 1.
Free body diagram at
Here,
The weight of the plate is
Let
Let
Write the equation of vector distance
Here,
Write the vector distance of the cable
Here,
Write the vector distance of the cable
Here,
Write the equation of tension in the cable
Here,
Write the equation of
Write the equation of tension in the cable
Here,
Write the equation of
Write the equation of tension in the cable
Here,
Write the equation of
Write the equation of force exerting at point
Here,
Write the equilibrium condition for the forces at
Here, F is the force
The above equation implies that at equilibrium, total force acting on the cable at
Refer figure 2 and write the equation of equilibrium of forces at A.
Conclusion:
Substitute
Calculate the magnitude of
Substitute
Calculate the magnitude of
Substitute
Calculate the magnitude of
Substitute
Substitute
Substitute
(VII) to get
Substitute
Substitute
Substitute
Substitute
Since total force is zero. Equate force along each direction as zero.
Multiply equation (XII) with 12 and equation (XIV) with
Multiply equation (XII) with
Multiply equation (XV) with
Substitute
Substitute
Therefore, the tension in cable
Want to see more full solutions like this?
Chapter 2 Solutions
Loose Leaf for Vector Mechanics for Engineers: Statics and Dynamics
- Solve Prob. 2.4 by trigonometry.(Reference to Problem 2.4):Two structural members B and C are bolted to bracket A . Knowing 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 parallelogram law, (b) the triangle rule.arrow_forward2.66 A 200-kg crate is to be supported by the rope-and-pulley arrangement shown. Determine the magnitude and direction of the force P that must be exerted on the free end of the rope to maintain equilibrium. [Hint: The tension in the rope is the same on each side of a simple pulley. This can be proved by the methods of Chap. 4.] 0.75 m 2.4 m B P αarrow_forwardFor the boom and loading of Prob. 2.97, determine the magnitude of the load P.(Reference to Problem 2.97):The boom OA carries a load P and is supported by two cables as shown. Knowing that the tension in cable AB is 183 lb and that the resultant of the load P and of the forces exerted at A by the two cables must be directed along OA , determine the tension in cable AC.arrow_forward
- 4.45 The uniform, 40-lb ladder is raised slowly by pulling on the rope attached at A. Determine the largest angle 0 that the ladder can attain if the maximum allowable tension in rope BC is 330 lb. Fig. P4.44, P4.45arrow_forward3.49 To loosen a frozen valve, a force F with a magnitude of 70 lb is applied to the handle of the valve. Knowing that 0 = 25°, Mx = -61 lb-ft, and M₂ determine pand d. -43 lb-ft, Fig. P3.49 and P3.50 A = 4 in. 11 in. Show Notebaarrow_forward2.32 The tow truck's front wheels will be lifted off the ground if the moment of the load W about the rear axle exceeds the moment of the 6200-lb weight of the truck. Determine the largest W that may be safely applied. 30 (O) 6200 lb 8 ft -10ft- Fig. P2.32arrow_forward
- 2.43 A steel tube (E = 29 x 106 psi) with a 14-in. outer diameter and a -in. thickness is placed in a vise that is adjusted so that its jaws just touch the ends of the tube without exerting any pressure on them. The two forces shown are then applied to the tube. After these forces are applied, the vise is adjusted to decrease the distance between its jaws by 0.008 in. Determine (a) the forces exerted by the vise on the tube at A and D, (b) the change in length of the portion BC of the tube. Fig. P2.43 -3 in.3 in.3 in. - 3- D 8 kips B 6 kipsarrow_forward3. Three cables are used to tether a balloon as shown. Determine the vertical force P exerted by the balloon at A knowing that the tension in the cable AD is 521 N. 4.20 m 2.40 m T C 4.20 m 5.60 m 3.30 marrow_forward2.51 Two forces P and Q are applied as shown to an aircraft connection. Knowing that the connection is in equilibrium and that P= 600 lb and Q = 800 lb, determine the tension in rods A and B. Answer 30° P ------- A 60° TA B TBarrow_forward
- For the plate of Prob. 2.89, determine the tensions in cables AB and AD knowing that the tension in cable AC is 54 N and that the resultant of the forces exerted by the three cables at A must be vertical.(Reference to Problem 2.89):A rectangular plate is supported by three cables as shown. Knowing that the tension in cable AB is 408 N, determine the components of the force exerted on the plate at B.arrow_forwardA rectangular plate is supported by three cables as shown. Determine the tension in each of the three cables knowing that the weight of the plate is 792.00 N.arrow_forwardPROBLEM 2.89 A rectangular plate is supported by three cables as shown. Knowing that the tension in cable AB is 408 N, determine the components of the force exerted on the plate at B. 480 250 360 130 320 360 450 C Fx = 192 kN, Fy= 288 kN, Fz = - 216 kN Dimensions in mmarrow_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