Equilibrium of a wood stack formed by close-packed cylindrical logs

The static equilibrium of cylindrical wood pieces in a close-packed order is analyzed. By considering the coefficient of static friction ${\mu }_L$ between two adjacent logs and the coefficient of static friction ${\mu }_G$ between the logs and the ground, it is demonstrated that the more stringent condition for static equilibrium arises from ${\mu }_L$. This holds true for both systems comprising three logs and those with six logs. The value of the lower threshold ${\tilde{\mu }}_L$ for equilibrium is greater for a system with six logs compared to three logs. This problem could serve as a study project in Newtonian mechanics for first-year college students or for advanced high-school physics students.

Keywords:
Newtonian mechanics; static equilibrium; Euclidean geometry