Engineering mechanics – properties of a couple (pure moment) Which of the following statements correctly describe a force couple in statics and dynamics?
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AThe algebraic sum of the forces forming a couple is zero.
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BThe algebraic sum of the moments of the two forces about any point is the same (i.e., a pure moment).
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CA couple cannot be balanced by a single force; it can be balanced only by another couple of equal magnitude and opposite sense.
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DAll of the above
Answer
Correct Answer: All of the above
Explanation
Introduction / Context:A couple is a fundamental concept in engineering mechanics. It consists of two equal, parallel, and opposite forces separated by a distance, creating a pure moment with no net resultant force. This question checks your understanding of the defining properties and implications of a couple in equilibrium and motion analysis.
Given Data / Assumptions:
- Two forces are equal in magnitude, opposite in direction, and non-collinear.
- The perpendicular distance between their lines of action is constant.
- Rigid-body assumptions; forces are coplanar for simplicity.
Concept / Approach:The net force of a couple is zero because forces cancel vectorially. However, they produce a moment M = F * d about any point. Since the resultant force is zero, the moment of a couple is free vector: its magnitude and sense are independent of the moment center. A single force cannot nullify a pure moment; only another couple of equal magnitude and opposite sense can.
Step-by-Step Solution:
Show force summation: ΣF = +F − F = 0.Compute moment about an arbitrary point O: ΣM_O = F * d (taking proper sign). This value is the same about any O for a given couple.For balance, require ΣF = 0 and ΣM = 0. A single force would violate ΣF = 0; hence, only an opposite couple can balance.Verification / Alternative check:Replace a wrench (force + couple) by an equivalent system. Removing the force leaves a pure couple. To counter it, another couple of opposite sense is required; adding a single force reintroduces a resultant.
Why Other Options Are Wrong:
- Each of A, B, and C is correct individually; the best composite choice is “All of the above”.
Common Pitfalls:Assuming the couple’s moment depends on the reference point. Unlike a force’s moment, a couple’s moment is invariant with respect to the moment center.
Final Answer:All of the above