Final answer:
To replace loading with a resultant force and couple moment at point O, sum all forces for the resultant force and calculate torques of each force about point O for the couple moment, using equilibrium conditions where net force and net torque are zero.
Step-by-step explanation:
The student's question pertains to statics in engineering mechanics, focusing on the concept of resultant force and couple moments. When asked to replace a loading by an equivalent resultant force and couple moment at a point, one often utilizes the conditions for equilibrium, which state that the net force and the net torque (or moment) must be zero in a system at rest or moving at a constant velocity.
To find the equivalent resultant force, sum up all the forces acting on the body. As for the equivalent couple moment, calculate the torque created by each force about the reference point, and then sum these torques. This calculation might involve using vector cross products or simply multiplying the magnitude of force by the perpendicular distance from the reference point to the line of action of the force.
For example, in the given scenario where we consider the force acting on a pendulum or a bob, it describes how the weight mg can be split into components mg cos θ along the string and mg sin θ tangent to the arc, where the tension cancels the component along the string, leaving only the tangential component contributing to the restoring force.
When considering the moment or torque, we take into account the lever arm distance and the angle at which the force is applied, as demonstrated in the solution for a door where the torque depends on the radius and the force applied.
The complete question is: Replace the loading by an equivalent resultant force and couple moment at point O. Suppose that F1={8i−4k}kNF1={8i−4k}kN and F2={−2i+4j−2k}kNF2={−2i+4j−2k}kN.