Friction experiments with a capstan

The force of static friction on a cord wrapped through an angle θ around a rough‐surfaced cylinder increases exponentially with θ. A small tension T₁ at one end of the cord, maintaining contact between cord and cylinder, provides the condition for a substantially larger tension, of maximum value T₂=T₁ exp(μ_sθ), at the other end. The validity of this relationship is studied for the kinetic friction case. The suitability of this system for an undergraduate experiment is discussed, together with practical applications—the donkey engine and the capstan—with a digression on sea chanties.