The tension in each segment of the cable and the vertical distance between points
Answer to Problem 5.1P
The tension in segment
The tension in segment
The tension in segment
The vertical distance between points
Explanation of Solution
Concept Used:
Write the expression for the net moment about end
Here
Calculations:
The free body diagram for the system is shown below.
Figure-(1)
Here, the unknown vertical reactions are
The slope of cable
Write the moment about
Consider
Given
Given that
Therefore
Consider
Apply Pythagoras theorem in
Here, the distance between points
Substitute
Take square root on both sides.
Calculate
Substitute
Calculate
Substitute
Calculate
Substitute
The free body diagram at point C is shown below.
Figure-(2)
Apply Sine Law at point
Here, the tension in cable
Determine
Thus the tension in segment
Thus the tension in segment
Analyze point
Figure-(3)
Apply Angle Sum Property in
Substitute
Calculate
Substitute
Calculate
Substitute
Calculate
Substitute
Consider
Figure-(4)
Calculate the length
Substitute
Calculate
Substitute
Analyze point
The free body diagram for point
Figure-(5)
Substitute
Calculate
Substitute
Calculate
Substitute
Apply Sine Law at point
Here, the tension in cable
Determine
Thus the tension in segment
Conclusion:
The tension in segment
The tension in segment
The tension in segment
The vertical distance between points
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Chapter 5 Solutions
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