Final answer:
To verify equilibrium in a concurrent-coplanar force system, the net force in both x and y directions must be zero. A free-body diagram is used to calculate this, checking the reasonableness of the solution afterward.
Step-by-step explanation:
To verify that a system of five concurrent-coplanar forces is in equilibrium, we must ensure that the net force in both the x-direction and y-direction equals zero (net Fx = 0 and net Fy = 0, respectively). Additionally, we should confirm that the net torque (net T) is also zero, satisfying the equilibrium conditions for a static system. This involves a free-body diagram and applying Newton's second law (Σ F = ma) to solve for the unknown forces.
In the given problem, forces F1, F2, F3, F4, and F5 must be represented accurately on a free-body diagram, with their components resolved along the x and y axes. We can then apply the analytical method by adding all the x-components of forces and setting them equal to zero to satisfy Σ Fx = 0. Similarly, we add all the y-components of forces to satisfy Σ Fy = 0.
Performing these calculations enables verification of whether the forces produce a state of equilibrium. If the net forces in both directions and net torque are zero, the system is confirmed to be in equilibrium. We should also check the solution for reasonableness by reviewing the magnitudes, directions, and units of the calculations.