Static friction — select the most complete and correct set of properties of the limiting static friction between two contacting surfaces.

Introduction / Context: Limiting static friction is the maximum frictional force that resists the impending motion of one surface over another just before sliding begins. Understanding its properties is fundamental to solving problems in engineering mechanics and machine design.

Given Data / Assumptions:

• Dry surfaces with no significant adhesion or lubrication effects beyond the classical Coulomb model.
• Normal reaction R acts perpendicular to the interface.
• Motion is impending but not yet occurring.

Concept / Approach: Coulomb’s friction law states that the limiting static friction F_max = μ_s R, where μ_s is the coefficient of static friction. The direction of static friction is such that it opposes the tendency of motion. Additionally, within the idealized model, F_max is largely independent of the apparent (macroscopic) area of contact.

Step-by-Step Solution:

Verification / Alternative Check: Empirical tests across many materials confirm approximately linear proportionality to R and weak dependence on apparent area over practical ranges.

Why Other Options Are Wrong:
Each of (a), (b), (c) is individually true, but incomplete when taken alone.
None of these — Incorrect because (a), (b), and (c) are valid under the Coulomb model.

Common Pitfalls: Confusing apparent with real contact area; misdirecting friction opposite actual motion instead of impending motion.

Final Answer: All of the above.