Final answer:
To determine the single force equivalent to a force-couple system and its point of application on a lever, one needs to sum the forces and their moments, ensuring rotational and translational equilibrium are maintained.
Step-by-step explanation:
The question pertains to the force-couple system and how to determine the single equivalent force along with its point of application on a lever. As we have learnt, any real system of forces and moments can be replaced by a single force and a couple at some point. The couple's moment is simply the sum of the moments of the original forces about that point. This can typically be accomplished by summing the forces in the system and relocating the resultant to a point where it creates a moment equal to that of the system's original moment about that same point. The lever arm should be considered as well, with the force applied as close as possible to the pivot point to optimize torque, taking into account the forces described in Figures 12.9 and 12.10.
When finding the equivalent single force, it's crucial to ensure that the force's line of action is chosen in such a way that it yields the same external effect on the body as the original system. This includes both the forces acting and the caused rotations. Therefore, the point of application is not arbitrary but must be chosen to satisfy both the translational and rotational equilibrium of the original system.