Concept explainers
For the boom and loading shown, determine (a) the tension in cord BD, (b) the reaction at C.
Fig.P4.71
(a)
The tension in the cord
Answer to Problem 4.71P
The tension in the cord
Explanation of Solution
Calculation:
If the rigid body subjected to three forces, such a body is commonly called a three-force body. If a two force body is in equilibrium the lines of action of the three forces must be either concurrent or parallel.
The figure 1 represents the free body diagram of the system.
Write the expression for the angle
Here,
Write the expression for the angle
Write the relations connecting the sides of the triangle.
Figure 2 represents a force triangle as shown in the above figure with its interior angles computed from the known directions of the forces. Then use the law of sines to find the unknown forces.
Write the expression for the law of sines from the force triangle.
Conclusion:
Substitute
Substitute
Substitute
Substitute
On rearranging the above equation to find
Therefore, the tension in the cord
(b)
The reaction at
Answer to Problem 4.71P
The reaction at
Explanation of Solution
Calculation:
If the rigid body subjected to three forces, such a body is commonly called a three-force body. If a two force body is in equilibrium the lines of action of the three forces must be either concurrent or parallel.
Write the expression for the angle
Here,
Write the expression for the angle
Write the relations connecting the sides of the triangle.
Figure 2 represents a force triangle as shown in the above figure with its interior angles computed from the known directions of the forces. Then use the law of sines to find the unknown forces.
Write the expression for the law of sines from the force triangle.
Conclusion:
Substitute
Substitute
Substitute
Substitute
On rearranging the above equation to find
Therefore, reaction at
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