Concept explainers
For the rectangular plate of Probs. 2.109 and 2.110, determine the tension in each of the three cables knowing that the weight of the plate is 792 N.
Fig. P2.109 and P2.110
The tension in three cables shown in figure
Answer to Problem 2.115P
The tension in cable
Explanation of Solution
The sketch of plate supported by three cables is shown in figure 1.
Free body diagram at
Here,
The weight of the plate is
Let
Let
Write the equation of vector distance
Here,
Write the vector distance of the cable
Here,
Write the vector distance of the cable
Here,
Write the equation of tension in the cable
Here,
Write the equation of
Write the equation of tension in the cable
Here,
Write the equation of
Write the equation of tension in the cable
Here,
Write the equation of
Write the equation of force exerting at point
Here,
Write the equilibrium condition for the forces at
Here, F is the force
The above equation implies that at equilibrium, total force acting on the cable at
Refer figure 2 and write the equation of equilibrium of forces at A.
Conclusion:
Substitute
Calculate the magnitude of
Substitute
Calculate the magnitude of
Substitute
Calculate the magnitude of
Substitute
Substitute
Substitute
(VII) to get
Substitute
Substitute
Substitute
Substitute
Since total force is zero. Equate force along each direction as zero.
Multiply equation (XII) with 12 and equation (XIV) with
Multiply equation (XII) with
Multiply equation (XV) with
Substitute
Substitute
Therefore, the tension in cable
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