Concept explainers
PROBLEM 4.106
The 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.
The tension in each of the cable and the reaction at A.
Answer to Problem 4.106P
The tension in cable BD is
Explanation of Solution
Refer figure1 shown below. The figure shows that the pole ABC is acted upon by a certain force. The pole is balanced by cables BD and BE about a ball and socket joint A. The forces along the cables can be resolved into its x and y components.
The sum of moments along line AC is zero at equilibrium.
Here,
Write the equation to find the position vector of point B.
Here,
Write the equation to find the position vector of point C.
Here,
Write the equation to find the position vector
Here,
Write the equation to find the magnitude of vector
Here,
Write the equation to find the position vector
Here,
Write the equation to find the magnitude of vector
Here,
Write the equation to find the position vector
Here,
Write the equation to find the magnitude of vector
Here,
Write the equation to find the force acting along line CF.
Here,
Write the equation to find the tension in cable BD.
Here,
Write the equation to find the tension in cable BE.
Here,
Write the equation to find the sum of moments along the point A.
Here,
Since the sum of moments at point A is zero, rewrite equation (XI).
Substitute for
Find the determinant value of equation (XIII) and equate the coefficients of unit vectors
Equate the coefficients of unit vector
Here,
Equate the coefficient of unit vector
Add equations (XIV) to twice of equation (XV) to get the value of tensions in cables.
The sum of all external forces is zero. Therefore sum of tensions in cables, force at P and S is zero.
Here,
Conclusion:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Solve equation (XVIII) to get
Substitute
Substitute
Substitute
Substitute
Similarly substitute
Substitute
The vector form of the reaction force is
Therefore, the tension in cable BD is
Want to see more full solutions like this?
Chapter 4 Solutions
EBK VECTOR MECHANICS FOR ENGINEERS: STA
- the frame shown supports part of the roof of a small building. Knowing that the tension in the cable is 150 kN, determine the reaction at the fixed end E.arrow_forwardA lever AB is hinged at C and attached to a control cable at A . If the lever is subjected to a 500-N horizontal force at B , determine (a) the tension in the cable, (b) the reaction at C.arrow_forwardA 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_forward
- The 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 3-m boom is acted upon by the 4-kN force shown. Determine the tension in each cable and the reaction at the ball-and-socket joint at A.arrow_forwardThe 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_forward
- Neglecting friction and the radius of the pulley, determine (a) the tension in cable ADB, (b) the reaction at C.arrow_forwardA uniform circular rod of weight 8 lb and radius 10 in. is attached to a pin at C and to the cable AB. Determine (a) the tension in the cable,(b) the reaction at C.arrow_forwardA 48-in. boom is held by a ball-and-socket joint at C and by two cables BF and DAF passes around a frictionless pulley at A . For the loading shown, determine the tension in each cable and the reaction at C.arrow_forward
- A lever AB is hinged at C and attached to a control cable at A . If the lever is subjected to a 75-lb vertical force at B , draw the freebody diagram needed to determine the tension in the cable and the reaction at C.arrow_forward4.7 A hand truck is used to move a compressed-air cylinder. Knowing that the combined weight of the truck and cylinder is 180 lb. determine (a) the vertical force P that should be applied to the handle to maintain the cylinder in the position shown, (b) the corresponding reaction at each of the two wheels.arrow_forward4.108 - A 2250 N marquee, 2,4 x 3 m, is held in a horizontal position bytwo horizontal hinges at A and B and by a cable CD attached to a point D located 1,5m directly above B. Determine the tension in the cable and the components of the reactions at the hinges.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