The Indeterminate Case of Classical Static Friction When Coupled with Tension

It has been noted that the static friction force poses challenges for students and, at times, even their instructors. Unlike the gravitational force, which has a precise and unambiguous magnitude (F_G = mg), the magnitude and direction of the static friction force depend on other forces at play. Friction can be understood rather well in terms of complicated atomic-scale interactions between surfaces. Ringlein and Robbins survey aspects of the atomic origins of friction, and Folkerts explores factors that affect the value of static friction. However, what students typically encounter in an introductory course ignores the atomic origins of friction (beyond perhaps a brief overview of the atomic model). The rules of dry friction (i.e., non-lubricated surfaces in contact) taught in introductory physics were originally published in 1699 by Guillaume Amontons. Amontons’s first law states that the force of friction is directly proportional to the applied load, i.e., f = μF_N, where F_N is the normal force and μ is the coefficient of friction. His second law states that the force of friction is independent of the macroscopic area of contact. These laws were verified by Coulomb in 1781.