Final answer:
To determine if a resultant force exists in a force system, such as when analyzing the forces acting on a pipe assembly, one must identify all the forces, use a free-body diagram to visualize them, verify equilibrium, and check the results for correctness in terms of magnitude, direction, and units.
Step-by-step explanation:
The question focuses on replacing the force system acting on a pipe assembly by a resultant. To do this, one must identify forces acting on the structure and understand how they interact. For instance, in the scenario with the grand piano, forces are represented where T is the tension in the rope, W is the weight of the piano, and F is the force the piano exerts on the rope. When dealing with such force systems, it's common to use a free-body diagram to isolate and understand the forces acting on an object.
Remember, a resultant force is a single force that has the same effect as all the forces it replaces. In the case of lifting a grand piano with a rope, if the piano is stationary, then the tension in the rope (T) equals the weight of the piano (W) but with the opposite direction (T = -W), indicating that a resultant force exists.
Determining whether a resultant force exists depends on the forces in the system (option c) and their magnitudes and directions (using vectors). In some cases, based on the characteristics of the forces (such as parallel wires with currents in the same direction), there might be no resultant force (option a or b). The process involves identifying all forces (using a free-body diagram), applying equilibrium conditions (net F = 0 and net τ = 0), choosing a convenient coordinate system, and finally, checking the solution for reasonableness based on the magnitude, direction, and units of forces.