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:
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Solve equation (XVIII) to get
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Similarly substitute
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The vector form of the reaction force is
Therefore, the tension in cable BD is
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Chapter 4 Solutions
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