Final answer:
The problem requires the calculation of the sum of horizontal and vertical forces and the net torque on a system. The steps involve using the torque formula and summing the individual torques with respect to an origin, taking into consideration each force's magnitude, direction, and point of application.
Step-by-step explanation:
The question relates to the concept of torque in physics, which is a measure of the turning force on an object that can cause it to rotate about an axis or pivot. Torque (T) is calculated using the formula T = rF sin θ, where r is the distance from the pivot point to the point where the force is applied, F is the magnitude of the force, and θ is the angle between the force vector and the arm of the lever. In scenarios involving equilibrium, the net force and net torque are zero (net F = 0 and net τ = 0 respectively).
For the given problem, one would start by identifying all the forces acting in the horizontal and vertical directions, drawing a free body diagram if needed, applying the right signs for each force depending on its direction, and then finding the sum of horizontal and vertical forces separately. Once the forces are summed up, the next step would be to calculate the torque for each force about the center using the provided distances and then summing all the individual torques to get the net torque about the center.