Two cables are tied together at C and are loaded as shown. Determine the range of values of P for which both cables remain taut.
Fig. P2.49 and P2.50
The range of values of the force
Answer to Problem 2.50P
The range of values of the force
Explanation of Solution
In the arrangement in Fig. P2.50, the forces acting at the point
The free body diagram corresponding to the given arrangement is shown in Figure 1.
When the system is in equilibrium, the total forces acting on the system will be zero. Moreover, the equilibrium condition imply that the components of the forces along
Write the expression for the equilibrium state along
Here,
Apply the condition in equation (I) to the given system.
Apply the condition in equation (II) to the given system.
Write the condition for the cable
Write the condition for the cable
The condition for both the cables to remain taut is that, there should be a tension greater than zero in each of the cables.
Conclusion:
Set
Add equation (VII) and (VIII).
Solve equation (IX) for
Solve equation (VIII) for
Set
Add equation (XI) and (XII).
Solve equation (XIII) for
Solve equation (XII) for
The magnitude of
Therefore, the range of values of the force
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Chapter 2 Solutions
Vector Mechanics for Engineers: Statics
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