Physics Model for Rope Jumping Game

Abstract

We developed a simple physics model to explain the profile of the rope played in the rope jumping game.  Firstly, we derived a second order non-linear differential equation to explain the rope motion. Analytical solutions can be obtained if the displacement of all points along the rope is small. For arbitrary deviations, a numerical solution must be employed, and at the present paper, we used a simple excel-visual basic program. We found that the profiles of the simulation results is very similar to the real profile which can be observed in a number of sources on the internet. A critical value separating the condition where the rope length remains unchange and the condition when the rope changes suddenly with rw2/T was identified. A scaling relationship was also identified in the changing region with the critical exponent of -0.31. The existence of the critical point and the critical exponent in the changing region informs that the change in the rope profile resembles the phase transition phenomenon