Physics Model for Rope Jumping Game

Fathan Akbar,Ardi Khalifah,Mikrajuddin Abdullah

doi:10.29303/jppipa.v7i2.559

Fathan Akbar, Ardi Khalifah + Show 1 more

Open Access

https://doi.org/10.29303/jppipa.v7i2.559

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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

Highlights

There are a number of ancient children's games that are starting to be forgotten today
We developed a simple physics model to explain the profile of the rope played in the rope jumping game
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

Summary

Introduction

There are a number of ancient children's games that are starting to be forgotten today. The resulted equation can be directly applied to the condition of the rope forming the upper formation by replacing the gravitational acceleration with its negative. By using the general solution obtained and considering that the two ends have a slope with a different sign (the slope at x = 0 is negative and at x = L is positive) this condition is fulfilled if only a half wave and is formed L =. With this condition, the tension in the rope fulfills the equation ρω2L2 2.

Simulation and Discussion Results

Conclusion