A cable loop of length 1.5 m is placed around a crate. Knowing that the mass of the crate is 300 kg, determine the tension in the cable for each of the arrangements shown.
(a)
c
The tension in the cable for the given arrangement of the cable loop.
Answer to Problem 2.65P
The tension in the cable
Explanation of Solution
The length of the cable loop is
Above figure represents the free body diagram of the cable loop which is placed around a crate. The forces
Write the expression for the weight acting on the system.
Here,
Figure 2 represents the force triangle of the given free body diagram to find the tension.
Refer from the figure P2.65And Write the expression for finding the cosine angle.
Write the expression for the total length of loop.
From the force triangle it is shown that
Refer the figure 2.
According to the law of sines,
Conclusion:
Substitute
From the figure given in the question the length
Simplify to find
Substitute
Substitute
Therefore, the tension in the cable,
(b)
The tension in the cable for the given arrangement of the cable loop.
Answer to Problem 2.65P
The tension in the cable
Explanation of Solution
The length of the cable loop is
Figure represents the free body diagram of the cable loop which is placed around a crate. The forces
Write the expression for the weight acting on the system.
Here,
Figure2 represents the force triangle of the given free body diagram to find the tension.
Write the expression for finding the cosine angle.
Write the expression for the total length.
From the force triangle it is shown that
From the figure 2a
According to the law of sines,
Conclusion:
Substitute
From the figure given in the question the length
Substitute
Substitute
Therefore, the tension in the cable,
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Chapter 2 Solutions
Vector Mechanics for Engineers: Statics
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