Static friction — identify the statement that is NOT a law: Which of the following is NOT a valid law of limiting static friction between two dry solid surfaces?

Introduction / Context:
For dry, rigid bodies at impending motion, classical Coulomb friction provides empirical “laws” for limiting static friction. These guide quick calculations in statics and dynamics. This question asks you to identify a statement that does not belong to these laws.

Given Data / Assumptions:

• Dry, clean, nominally rigid surfaces in contact.
• Impending motion (limiting static friction), not kinetic friction.
• No significant adhesion, temperature, or surface contamination effects.

Concept / Approach:

Classical laws: (1) The frictional force opposes impending motion; (2) Limiting friction F_lim is proportional to the normal reaction N, with coefficient μ_s roughly constant for given surfaces; (3) F_lim is largely independent of apparent area of contact for clean, rigid bodies; (4) At the instant of impending motion, speed is zero and speed effects are irrelevant (unlike kinetic friction at higher speed). Hence any statement claiming dependence on apparent area is not a law in this idealization.

Step-by-Step Solution:

Verification / Alternative check:

Experiments with varying block footprint but same normal load show nearly unchanged limiting friction in the ideal regime, corroborating area-independence.

Why Other Options Are Wrong:

(a), (c), and (d) match Coulomb laws; (e) is consistent at the threshold since sliding speed is zero.

Common Pitfalls:

Confusing real microscopic contact area (which may affect μ_s) with apparent geometric area; mixing static and kinetic friction behaviors.

Final Answer:

Limiting friction depends on the apparent area of contact