Dry Friction – Dependence of the Coefficient of Friction On what factor(s) does the coefficient of (Coulomb) friction primarily depend under standard dry contact conditions?

Introduction / Context:
In machine design and statics, the coefficient of friction μ is used to estimate the maximum friction force F_max = μ N. Misunderstanding what μ depends on can lead to large errors in predicting motion or required effort in mechanisms.

Given Data / Assumptions:

• Classical (Coulomb) dry friction regime.
• Rigid bodies with typical engineering surface finishes.
• No lubrication films that change the regime.

Concept / Approach:
Coulomb’s law models friction as F_max = μ N, where μ is mainly a property of the pair of surfaces and their condition (roughness, cleanliness, presence of oxides). For a given normal load N, μ does not explicitly depend on apparent area of contact in the idealized model because true microscopic contact area adjusts with load.

Step-by-Step Solution:
Identify regime: dry, unlubricated contact. Use Coulomb model: F_max = μ N. Note: μ is characteristic of surface pair and condition; not of nominal area. Hence, dependence is on the nature/condition of the surfaces, not on the apparent area alone.

Verification / Alternative check:
Experiments show friction force roughly scales with normal load and only weakly (if at all) with apparent area. Different materials (steel–steel, wood–steel) and surface finishes exhibit different μ values, confirming surface dependence.

Why Other Options Are Wrong:
Area of contact only: contradicts Coulomb model. Both equally / surface area and load product: not supported by the classical model. None of these: incorrect since surface pair clearly matters.

Common Pitfalls:
Assuming larger area always gives more friction; in dry friction models, it does not. Ignoring surface contamination or oxidation which alters μ.

Final Answer:
Nature and condition of the contacting surfaces only