The Physics and Mathematics of Ziplining

We study the kinematic and dynamic characteristics of body motion along an inclined hanging cable in the approximation of its masslessness and inextensibility. It is shown that in this case, the motion of the suspended body occurs along an inclined ellipse, the foci of which are the cable attachment points. Herewith, at any given moment, the net tension force of the cable is perpendicular to the instantaneous velocity of the body. Besides, the tension force is a dynamic characteristic of the cable and increases as the body descends along with the increase in the speed. There is also a sharp increase in the tension at the end of the trajectory, which is explained by a decrease in its radius of curvature.