Concept explainers
A 50-kg crate is attached to the trolley-beam system shown. Knowing that a = 1.5 m, determine (a) the tension in cable CD, (b) the reaction at B
Fig.P4.69
(a)
The tension in the cable
Answer to Problem 4.69P
The tension in the cable
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. The weight is acting downwards. The
Write the expression for the angle
Here,
Write the expression for the weight acting on the system.
Here,
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
On rearranging the above equation to find
Therefore, the tension in the cable
(b)
The reaction at
Answer to Problem 4.69P
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.
The figure 1 represents the free body diagram of the system. The weight is acting downwards. The
Write the expression for the angle
Here,
Write the expression for the weight acting on the system.
Here,
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
Rearrange the above equation to find
Therefore, reaction at
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Chapter 4 Solutions
VECTOR MECH....F/ENGNRS-STATICS -CONNECT
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