Resultant of two collinear opposite forces: Two forces P and Q (P > Q) act along the same straight line but in opposite directions. What is the magnitude of their single resultant?

Introduction / Context:
When two forces act collinearly and oppositely, they combine algebraically along that line. The stronger force partially cancels the weaker, leaving a single resultant acting in the direction of the stronger force. This principle underpins many equilibrium checks in trusses, cables, and straight-line pulls.

Given Data / Assumptions:

• Two forces P and Q on the same line.
• P > Q; directions are opposite.
• Rigid-body statics; no other forces.

Concept / Approach:

The net force along one dimension is the signed sum of components. Take the positive direction as that of P. Then the resultant R = P − Q, positive, acting in the direction of P. If Q were greater, the magnitude would be Q − P acting in Q’s direction.

Step-by-Step Solution:

Verification / Alternative check:

Free-body diagram confirms that the larger of the two determines direction, while magnitude is the absolute difference.

Why Other Options Are Wrong:

(a) P + Q would apply if the forces acted in the same direction; (b) and (c) are dimensionally incorrect for a resultant; (e) Q − P would be negative under our convention, contradicting P > Q.

Common Pitfalls:

Forgetting to account for direction; reporting a negative number as a magnitude without indicating direction.

Final Answer:

P − Q