Concept explainers
A 50-kg crate is attached to the trolley-beam system shown. Knowing that a = 1.5 m, determine (a) the tension in cable CD, (b) the reaction at B
Fig.P4.69
(a)
The tension in the cable
Answer to Problem 4.69P
The tension in the cable
Explanation of Solution
Calculation:
If the rigid body subjected to three forces, such a body is commonly called a three-force body. If a two force body is in equilibrium the lines of action of the three forces must be either concurrent or parallel.
The figure 1 represents the free body diagram of the system. The weight is acting downwards. The
Write the expression for the angle
Here,
Write the expression for the weight acting on the system.
Here,
Figure 2 represents a force triangle as shown in the above figure with its interior angles computed from the known directions of the forces. Then use the law of sines to find the unknown forces.
Write the expression for the law of sines from the force triangle.
Conclusion:
Substitute
Substitute
Substitute
On rearranging the above equation to find
Therefore, the tension in the cable
(b)
The reaction at
Answer to Problem 4.69P
The reaction at
Explanation of Solution
Calculation:
If the rigid body subjected to three forces, such a body is commonly called a three-force body. If a two force body is in equilibrium the lines of action of the three forces must be either concurrent or parallel.
The figure 1 represents the free body diagram of the system. The weight is acting downwards. The
Write the expression for the angle
Here,
Write the expression for the weight acting on the system.
Here,
Figure 2 represents a force triangle as shown in the above figure with its interior angles computed from the known directions of the forces. Then use the law of sines to find the unknown forces.
Write the expression for the law of sines from the force triangle.
Conclusion:
Substitute
Substitute
Substitute
Rearrange the above equation to find
Therefore, reaction at
Want to see more full solutions like this?
Chapter 4 Solutions
Vector Mechanics for Engineers: Statics
- A 20-kg ladder used to reach high shelves in a storeroom is supported by two flanged wheels A and B mounted on a rail and by a flangeless wheel C resting against a rail fixed to the wall. An 80-kg man stands on the ladder and leans to the right. The line of action of the combined weight W of the man and ladder intersects the floor at point D. Determine the reactions at A, B, and C.arrow_forwardA 12-m pole supports a horizontal cable CD and is held by a ball and socket at A and two cables BE and BF . Knowing that the tension in cable CD is 14 kN and assuming that CD is parallel to the xaxis (?= 0), draw the free-body diagram needed to determine the tension in cables BE and BF and the reaction at A.arrow_forwardNeglecting friction and the radius of the pulley, determine (a) the tension in cable ADB, (b) the reaction at C.arrow_forward
- The L-shaped member ACB is supported by a pin and bracket at C and by an inextensible cord attached at A and B and passing over a frictionless pulley at D. The tension may be assumed to be the same in portions AD and BD of the cord. If the magnitudes of the forces applied at A and B are, respectively, P = 25 lb and Q = 0, determine (a) the tension in the cord, (b) the reaction at Carrow_forwardThe frame shown supports part of the roof of a small building. Knowingthat the tension in the cable is 150 kN, determine the reaction at thefixed end E.arrow_forwardA force P of magnitude 90 lb is applied to member ACDE that is supported by a frictionless pin at D and by the cable ABE . Since the cable passes over a small pulley at B , the tension may be assumed to be the same in portions AB and BE of the cable. For the case when a= 3 in., determine (a) the tension in the cable, (b) the reaction at D.arrow_forward
- Two links AB and DE are connected by a bell crank as shown. Knowing that the tension in link AB is 720 N, determine (a) the tension in link DE, (b) the reaction at C.arrow_forwardKnowing that the tension in wire BD is 1300 N, determine the reaction at the fixed support C of the frame shown.arrow_forwardA 50-kg crate is attached to the trolley-beam system shown. Knowing that a = 1.5 m, determine (a) the tension in cable CD, ( b) the reaction at B.arrow_forward
- Three loads are suspended as shown from the cable ABCDE . Knowing that dC = 4 m, determine (a) the components of the reaction at E, (b) the maximum tension in the cable.arrow_forwardThe 6-m pole ABC is acted upon by a 455-N force as shown. The pole is held by a ball-and-socket joint at A and by two cables BD and BE . For a = 3 m, determine the tension in each cable and the reaction at A.arrow_forwardA thin ring with a mass of 2 kg and radius r = 140 mm is held against a frictionless wall by a 125-mm string AB . Determine (a) the distance d, (b) the tension in the string, (c) the reaction at C.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