Concept explainers
Cable ACB supports a load uniformly distributed along the horizontal as shown. The lowest point C is located 9 m to the right of A. Determine (a) the vertical distance a, (b) the length of the cable, (c) the components of the reaction at A.
(a)
The vertical distance
Answer to Problem 7.116P
The vertical distance
Explanation of Solution
The free body diagram for the portion AC is depicted below:
Refer fig 1,
Write the equation of net force along vertical direction,
Here, the forces are
Write the equation of momentum,
Here, the tension is
The free body diagram for the portion CB is depicted below:
Refer fig 2.
Write the equation of net force along vertical direction,
Here, the forces are
The free body diagram for the entire cable is depicted below:
Refer fig 3.
Write the equation of momentum,
Here, the distance is
Conclusion:
Substitute
Substitute
Thus, the vertical distance
(b)
The length of the cable.
Answer to Problem 7.116P
The length of the cable is
Explanation of Solution
Write the equation of length of the cable
Here, the length of the cable is
Write the equation of the length of the portion AC,
Here, the coordinates are
Write the equation of the length of the portion CB,
Here, the coordinates are
Conclusion:
Substitute
Substitute
Substitute,
Thus, the length of the cable is
(c)
The component of the reaction a A.
Answer to Problem 7.116P
The component of the reaction a A is
Explanation of Solution
Write the equation of vertical component of reaction A
Write the equation of the horizontal component of reaction A
Conclusion:
Substitute
Substitute
Thus, the component of the reaction a A is
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Chapter 7 Solutions
Vector Mechanics for Engineers: Statics
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