Solve part a of Prob. 3.78, assuming that two 15-N vertical forces have been added, one acting upward at A and the other downward at C.
(a)
The net couple acting on the rectangular co-ordinates.
Answer to Problem 3.79P
The net couple acting on the rectangular co-ordinates is
Explanation of Solution
Write the equation of the couple acting at the reactangular side
Here, moment of couple at the point
Substitute
Write the equation of the couple acting at the reactangular side
Here, moment of couple at the point
Substitute
Write the equation of the couple vector acting at the reactangular co-ordinates at point
Here, the projection angle is
Substitute
Write the equation of the couple vector acting at the reactangular co-ordinates at point
Substitute
Sketch the moment of additional couple is added to the moment about
Write the equation of the additional couple vector acting at the point
Here, the additional couple vector formed by the force at the point
The negative sign of the force shows that the force acting downward direction.
Substitute
Conclusion:
Write the equation for the net couple acting on the rectangular co-ordinates.
Adding the equations (I), (II), and (III) to obtained the net couple.
Write the equation for the magnitude of net couple.
Therefore, the net couple acting on the rectangular co-ordinates is
(b)
The direction of the two forces acting on the point
Answer to Problem 3.79P
The direction of the two forces acting on the point
Explanation of Solution
Write the equation for direction of the moment of couple formed by the forces at point
Here, the angle formed by the moment of couple due to the force located at the point
Rewrite the equation for
Write the equation for direction of the moment of couple formed by the forces at point
Here, the angle formed by the moment of couple due to the force located at the point
Rewrite the equation for
Write the equation for direction of the moment of couple formed by the forces at point
Here, the angle formed by the moment of couple due to the force located at the point
Rewrite the equation for
Conclusion:
Substitute
Substitute
Substitute
Therefore, the direction of the two forces acting on the point
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Chapter 3 Solutions
Vector Mechanics for Engineers: Statics