For the cables of Prob. 2.44, find the value of α for which the tension is as small as possible (a) in cable BC, (b) in both cables simultaneously. In each case, determine the tension in each cable.
(a)
The value of the angle
Answer to Problem 2.57P
The value of the angle
Explanation of Solution
The arrangement of the system is given in Fig. P2.44. The tension in the cable
The free body diagram of the arrangement shown in Fig. P2.44 is given in the Figure
Since the point
The angle between the
Write the expression for the angle
Apply law of sine to the force triangle in Figure 2.
Conclusion:
From the force triangle the angle
Substitute
Solve equation (I) for
Substitute
Solve equation (I) for
Therefore, the value of the angle
(b)
The value of the angle
Answer to Problem 2.57P
The value of the angle
Explanation of Solution
The free body diagram corresponding to the given arrangement is given in Figure 1
The force triangle become isosceles when the tension in both the cables become the minimum, since the tensions will be equal on both the cables in such situation.
The force triangle corresponding to the minimum tension in both cables
Apply the law of sine to the force triangle given in Figure 3.
Conclusion:
From inspection on the force triangle in Figure 3, the angle
Solve equation (III) for
Solve equation (III) for
Therefore, the value of the angle
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Chapter 2 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
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