A simple theoretical model of a bungee jump

Abstract

A bungee jump is described in terms of a simple theoretical model of a small body attached to an ideally elastic massive cord. In the first phase of the jump the cord remains unstretched and the sum of the kinetic and gravitational potential energy is assumed to be constant. In the second phase of the jump the cord is stretched and the elastic potential energy of the cord has to be included. The transition between both phases is described by an inelastic collision. Zusammenfassung. Der Seilsprung wird mit einem einfachen theoretischen Modell eines kleinen Körpers an einem idealen elastischen massiven Seil erörtert. In der ersten Phase des Sprungs ist das Seil ungespannt und wird die Summe der kinetischen und potentiellen Energie als konstant angenommen. In der zweiten Phase wird das Seil gespannt und muss seine elastische Energie berüksichtigt werden. Der Übergang zwischen beiden Phasen wird mit einem inelastischen Stoss beschrieben.

The dynamics of a bungee rocket

“…The dotted curves in figure 2 show the graphs for this solution, which correspond closely to those previously obtained for the real rocket. Note particularly the region of constant acceleration around position C. The potential energy of the vertical cords when stretched to position A, given by 1 2 Nk(h − 0 ) 2 = 173.3 kJ, is less than the 205.8 kJ for the real rocket; therefore the maximum velocity and maximum height are also smaller.…”

“…, where v = ẏ is the velocity. Equating E(θ ) to E A and using (1) and (2), we can solve for the kinetic energy (and v) as a function of θ from The solid curves presented in figure 2 show the velocity v, calculated from (5), and acceleration a = ÿ/g, from (4), as functions of position y, from (1).…”

“…By now the bungee jump has become a fairly well known activity of the adrenalin junkies, and a neat theoretical model has been published in this journal [1].…”

Understanding the physics of bungee jumping

“…As Strnad [8] showed, this formula needs the notion of elliptic functions and is beyond secondary school level. However, two interesting limiting cases for the falling time T are the free fall of an object over a distance L ( 0 µ ↓ ) and the falling chain fixed on one side and free on the other side ( µ → ∞ ):…”

“…Kockelman and Hubbard [7] included the effects of the elastic properties of the rope, jumper air drag, and jumper push-off. Strnad [8] described a theoretical model of a bungee jump that takes only the mass of the bungee rope into account. The first phase of bungee jumping can also be related to other phenomena such as the dynamics of a falling, perfectly flexible chain suspended at one end and released with the two ends near to each other at the same vertical elevation [9][10][11][12][13][14].…”