Force systems — can two equal and opposite parallel forces with distinct lines of action be replaced by a single force?

Introduction / Context:This question probes the concept of a couple in engineering mechanics. Two equal and opposite parallel forces whose lines of action are separated form a pure moment (a couple), not a single resultant force.

Given Data / Assumptions:

• Two forces, equal in magnitude and opposite in direction.
• Forces are parallel, with a finite perpendicular distance between their lines of action.
• Rigid body assumption.

Concept / Approach:When two equal and opposite parallel forces are separated by a distance, their net force is zero, but they create a nonzero moment. This moment is called a couple, with magnitude M = F * d, where F is the magnitude of either force and d is the perpendicular distance between their lines of action.

Step-by-Step Solution:

Verification / Alternative check:Try to represent a couple by a single force at any point; you will always introduce an unintended net force, which contradicts the original zero-resultant condition. Only a free vector couple correctly represents the system.

Why Other Options Are Wrong:

• Correct / variants: Misrepresent the mechanics; a single force cannot replicate a pure couple.
• Lines of action intersect: They are parallel; if they intersected, the system would be concurrent, not a couple.

Common Pitfalls:Confusing a couple with two non-parallel forces; believing every force system reduces to a single force plus a moment at the same point (here the net force is strictly zero).

Final Answer:Incorrect