To tie a boat in a harbor, how many times must a rope be wound around a bollard (a vertical rough cylindrical post fixed on the ground) so that a man holding one end of the rope can resist a force exerted by the boat one thousand times greater than the man can exert? First guess, Experiments show that the change ∆S of the force S in a small portion of the rope is proportional to S and to the small angle ∆Φ in Fig. 13. Take the proportionality constant. 0.15.