Rod AB is held in place by the cord AC. Knowing that the tension in the cord is 1350 N and that c = 360 mm, determine the moment about B of the force exerted by the cord at point A by resolving that force into horizontal and vertical components applied (a) at point A, (b) at point C.
(a)
The moment about B of the force exerted by the cord at point A.
Answer to Problem 3.9P
The moment about B of the force exerted by the cord at point A is
Explanation of Solution
Refer Figure 1.
Write an expression to calculate the length of cord.
Here, AC is the length of the cord, OA is the horizontal distance between A and C, OB is the distance between the points O and B and BC is the distance between B and C.
Write an expression to calculate angle
Here,
Write an expression to calculate the tension acting along the cord.
Here,
Write an expression to calculate the position vector between point A and B.
Here,
Write an expression to calculate the moment at point B.
Here,
Conclusion:
Substitute
Substitute
Substitute
Substitute
Substitute
Therefore, the moment about B of the force exerted by the cord at point A is
(b)
The moment about B of the force exerted by the cord at point C.
Answer to Problem 3.9P
The moment about B of the force exerted by the cord at point C is
Explanation of Solution
Refer Figure 2.
Write an expression to calculate the position vector between point A and B.
Here,
Write an expression to calculate the moment at point B.
Conclusion:
Substitute
Substitute
Therefore, the moment about B of the force exerted by the cord at point C is
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