Apparent loss of friction

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The Capstan Equation is given as ( see, Capstan equation - Wikipedia ) :

T_Load = T_Hold * e^{( μ φ )} ( e represents the Exponential Function, * denotes multiplication )

and describes the Tension in a rope that is wrapped around a cylinder where:

T_Load : Tension in the Loaded End of the Rope
T_Hold : Tension in the Held End of the Rope
μ : Coefficient of Friction for the Rope/Cylinder Interface
φ : Total Angle Swept By All Turns of the Rope in Contact with the Cylinder (in radians)

The Tension is at a minimum at the held end of the rope where the rope first makes contact with the cylinder and increases continuously to the maximum Tension in the rope at the loaded end of the rope where the rope loses contact with the cylinder. The Tension in the rope at any point on the cylinder, T_P, can be calculated by inserting into the Capstan Equation the Angle swept from the held point of first contact to the point of interest. Calling this swept Angle φ_P, the Tension at point P is given as :

T_P = T_Hold * e^{( μ φ_P )}