A flagpole is guyed by three cables. If the tensions in the cables have the same magnitude P, replace the forces exerted on the pole with an equivalent wrench and determine (a) the resultant force R, (b) the pitch of the wrench, (c) the point where the axis of the wrench intersects the xz-plane.
(a)
The resultant force.
Answer to Problem 3.140P
The resultant force is
Explanation of Solution
The diagram for the force-couple system is given below:
Refer fig 1.
Write the equation of resultant force.
Here, the resultant force is
Conclusion:
Substitute,
The magnitude of the resultant force,
Thus, the resultant force is
(b)
The pitch of the wrench.
Answer to Problem 3.140P
The pitch of the wrench is
Explanation of Solution
Write the equation of pitch of the wrench.
Here, the pitch of the wrench is
Since, the
Here, the constant is
Write the expression for the constant is,
Write the equation of momentum.
Here, the momentum is
Rewrite the expression for the momentum of the wrench is,
Conclusion:
Substitute,
Substitute,
Thus, the pitch of the wrench is
(c)
The point at which the axis of wrench intersects the xz-plane.
Answer to Problem 3.140P
The axis of wrench intersects the xz-plane at
Explanation of Solution
Refer fig 1,
Write the equation for the force couple system for the wrench.
Here, the momentum is
Write the expression for the momentum at which the wrench intersects the xz-plane.
Here, the position vector is
Write the expression for the position vector is,
Here, the coordinates are
Conclusion:
Substitute,
Substitute,
Substitute,
Comparing the coefficients of the x and z components both sides,
Therefore, he axis of wrench intersects the xz-plane at
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Chapter 3 Solutions
Loose Leaf for Vector Mechanics for Engineers: Statics
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- International Edition---engineering Mechanics: St...Mechanical EngineeringISBN:9781305501607Author:Andrew Pytel And Jaan KiusalaasPublisher:CENGAGE L