Find the distance a.
Answer to Problem 7.148P
The distance a is
Explanation of Solution
Given information:
The length of the cable AB is
The value of angle
The collar at A is slides freely and the collar at B is prevented from the moving.
Calculation:
Show the free-body diagram of the cable assembly as in Figure 1.
Refer Equation 7.16 in the textbook.
Write the equation of the catenary cable as follows;
Differentiate the equation with x;
The slope at point A is;
The length of the portion AC is;
The length of the portion CB is;
Find the distance
Substitute 10 ft for L,
Find the distance
Find the distance
Consider the triangle ABD;
Find the value of
Find the distance a using the relation.
Use the trial and error procedure to find the value of a.
Consider the value of c and for the given value of
Find the angle
Trial 1:
Consider a trial value of 1.60 ft for c.
Substitute 1.60 ft for c and
Substitute 1.60 ft for c and 1.410 ft for
Substitute 1.60 ft for c and 1.410 ft for
Substitute 1.60 ft for c and 3.777 ft for
Substitute 1.410 ft for
The calculated value of
Trial 2:
Consider a trial value of 1.70 ft for c.
Substitute 1.70 ft for c and
Substitute 1.70 ft for c and 1.498 ft for
Substitute 1.70 ft for c and 1.498 ft for
Substitute 1.70 ft for c and 3.891 ft for
Substitute 1.498 ft for
The calculated value of
Trial 3:
Consider a trial value of 1.8652 ft for c.
Substitute 1.8652 ft for c and
Substitute 1.8652 ft for c and 1.644 ft for
Substitute 1.8652 ft for c and 1.644 ft for
Substitute 1.8652 ft for c and 4.064 ft for
Substitute 1.644 ft for
The calculated value of
Therefore, the value of c is 1.8652 ft.
Substitute 2.638 ft for
Therefore, the distance a is
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Chapter 7 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
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