Concept explainers
For the boom and loading shown, determine (a) the tension in cord BD, (b) the reaction at C.
Fig.P4.71
(a)
The tension in the cord
Answer to Problem 4.71P
The tension in the cord
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.
Write the expression for the angle
Here,
Write the expression for the angle
Write the relations connecting the sides of the triangle.
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
Substitute
On rearranging the above equation to find
Therefore, the tension in the cord
(b)
The reaction at
Answer to Problem 4.71P
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.
Write the expression for the angle
Here,
Write the expression for the angle
Write the relations connecting the sides of the triangle.
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
Substitute
On rearranging the above equation to find
Therefore, reaction at
Want to see more full solutions like this?
Chapter 4 Solutions
VECTOR MECHANICS FOR ENGINEERS: STATICS
- Q1/ A vertical, circular gate with water on one side as shown. Determine the total resultant force acting on the gate and the location of the center of pressure, use water specific weight 9.81 kN/m³ 1 m 4 marrow_forwardI need handwritten solution with sketches for eacharrow_forwardGiven answers to be: i) 14.65 kN; 6.16 kN; 8.46 kN ii) 8.63 kN; 9.88 kN iii) Bearing 6315 for B1 & B2, or Bearing 6215 for B1arrow_forward
- (b) A steel 'hot rolled structural hollow section' column of length 5.75 m, has the cross-section shown in Figure Q.5(b) and supports a load of 750 kN. During service, it is subjected to axial compression loading where one end of the column is effectively restrained in position and direction (fixed) and the other is effectively held in position but not in direction (pinned). i) Given that the steel has a design strength of 275 MN/m², determine the load factor for the structural member based upon the BS5950 design approach using Datasheet Q.5(b). [11] ii) Determine the axial load that can be supported by the column using the Rankine-Gordon formula, given that the yield strength of the material is 280 MN/m² and the constant *a* is 1/30000. [6] 300 600 2-300 mm wide x 5 mm thick plates. Figure Q.5(b) L=5.75m Pinned Fixedarrow_forwardHelp ارجو مساعدتي في حل هذا السؤالarrow_forwardHelp ارجو مساعدتي في حل هذا السؤالarrow_forward
- Q2: For the following figure, find the reactions of the system. The specific weight of the plate is 500 lb/ft³arrow_forwardQ1: For the following force system, find the moments with respect to axes x, y, and zarrow_forwardQ10) Body A weighs 600 lb contact with smooth surfaces at D and E. Determine the tension in the cord and the forces acting on C on member BD, also calculate the reaction at B and F. Cable 6' 3' wwwarrow_forward
- Help ارجو مساعدتي في حل هذا السؤالarrow_forwardQ3: Find the resultant of the force system.arrow_forwardQuestion 1 A three-blade propeller of a diameter of 2 m has an activity factor AF of 200 and its ratio of static thrust coefficient to static torque coefficient is 10. The propeller's integrated lift coefficient is 0.3.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