Blue Rock - Climber Fall with Elastic Rope · Physics Brawl 2012 #FoL.3
Physics · mechanics
Problem
Center of mass of a mountaineer climbing on a rock is h = 24 m above ground. The last belay (place where the climber's rope runs through a metallic circle attached to the rock) is at a height h₀ = 20 m. The climber slips and falls. How closest to the ground does he get during his fall? Young's modulus of the rope is E = 100 MPa, its radius r = 0.5 cm and mass of the climber m = 70 kg. Neglect mass of the rope and all friction. Assume that the rope is attached to the climber in his center of mass. All distances are given with respect to a securing device which is attached to the ground and does not move during the fall. The local gravitational acceleration is g = 9.81 m·s⁻².