Final answer:
To determine if the total force on a system is zero, confirming static equilibrium, a free body diagram and the conditions net F = 0 and net T = 0 should be used, followed by verification that the results are reasonable in terms of magnitude, direction, and units.
Step-by-step explanation:
When checking if the total force exerted on a system is zero, you are verifying a fundamental condition for the state of static equilibrium. This condition asserts that for a system to be in equilibrium, the net external force (net F) must sum up to zero. This concept can be mathematically represented as net F = 0, meaning the vector sum of all individual forces acting on the system (like f1, f2, f3) must equal zero.
To thoroughly check for equilibrium, one must draw a free body diagram to visualize and label all forces and their magnitudes, directions, and points of application. After establishing the free body diagram, the equations for linear equilibrium (net F = 0 or net Fx = 0 and net Fy = 0 for forces along typical x- and y-axes) and the equation for rotational equilibrium (net T = 0 for torques) can be applied. If both conditions are met, the system can be considered in static equilibrium.
Finally, verifying the reasonableness of the results involves looking at the magnitude, direction, and units of the answer. It is crucial to ensure that equilibrium conditions are appropriately applied and that the results align with the physical interpretation of the problem.