An Analysis of the Physics Behind Bungee Jumping Mathematical Modeling Will Leland, Sanket Prabhu Tarboro High School, William G. Enloe High School 2008

Outline Background/History Model Data Conclusion Constants Equations Force Acceleration Velocity Conclusion http://www.vancouverisland.travel/img/wildplay/bungy.jpg

Problem How do the spring constant, damping constant, and jumper mass affect the path of a bungee jumper? http://alexandre.alapetite.net/cv/photos/19990730-alexandre-alapetite-1.jpg

Origin of Bungee Jumping Created thousands of years ago, by the inhabitants of Pentecost Island A group of 20 young men would take the leap of death Used to please the gods in order to have plentiful crops The land dive would symbolize the jumper’s transition from a child to a man

New Beginning of Bungee Jumping The first modern day bungee jumps were executed on April 1, 1979 by the Oxford University Dangerous Sports Club The sport’s popularity quickly spread across the world The world record for the highest jump is 216 meters of off the Bloukrans River Bridge

Equipment An elastic rope that is usually enclosed in a tough outer cover A simple ankle attachment A body harness Jumping platform http://www.adrenalindreams.com/Gear%20-%20harness%20GEAR%20SPORTS%20ankle%20logo.gif http://www.adrenalindreams.com/iconbingeepurple.gif

Types of Jumps Swallow Dive – classic jump, arms out wide and soar down like a bird Water Touchdown – some sites are confident about the length that the cord will stretch, so at the bottom the jumper goes into the water Sandbagging – extremely dangerous, you jump with a heavy weight, once you get to the bottom, you let go of the weight, the added elastic energy will make you fly much higher than from where you jumped from

What is Force, Velocity, and Acceleration? Force- a push or pull Velocity is the derivative of position Acceleration is the derivative of velocity

Constants K = spring constant - determines elasticity of cord, meaning how far it stretches m = mass - determines mass of jumper b = damping constant - a constant that is put in to represent the loss of energy

Physics Behind the Jump L is the distance from the bridge to the position of the jumper l is the length of the cord at rest While L < l, the only force working on the jumper is projectile motion When L > l, the cord starts to exert an upward force on the jumper The spring constant factors in as it determines the magnitude of the upward force.

Equations For L<l: For L > l:

Bungee Cord Diagram http://www.pa.uky.edu/~moshe/phy231/lecture_notes/bungee_forces.html

The Code:

The Model

Assumptions Bungee cord is in perfect condition Ideal environment so that jumpers only move in one direction

Mass= 80 kg Damping Constant= 25 Kg/s

Spring Constant= 500 N/m Damping Constant= 25 kg/s

Spring Constant= 500 N/m Mass=80 kg

Spring Constant= 500 N/m Damping Constant= 25 kg/s Mass= 80 kg

Spring Constant= 500 N/m Damping Constant= 25 kg/s Mass= 80 kg

Spring Constant= 500 N/m Damping Constant= 25 kg/s Mass= 80 kg

Spring Constant= 500 N/m Damping Constant= 25 kg/s Mass= 80 kg

Spring Constant= 500 N/m Damping Constant= 25 kg/s Mass= 80 kg

Changes Based on Findings Add wind factor, so we would be able to manipulate a z factor as well. Work on the rope so that when it came up it would produce slack and fold over Model a water touchdown

Summary Bungee jumping was created thousands of years ago and still continues today as a popular and exhilarating sport Spring constant, damping constant, and mass vary the jumper’s fall by different magnitudes.

Conclusion It was found that a high damping constant and mass results in the jumper coming to equilibrium faster A larger spring constant limits the jumper’s oscillation amplitude. The period looks to have linear relationships with the spring constant and mass

What We Learned The basics of VPython, Excel, and PowerPoint The physics behind bungee jumping and how to manipulate the parameters The long, rich history of bungee jumping

References http://library.thinkquest.org/C0123122/historybungee.htm http://www.bungeezone.com/history/ http://www.bungeeamerica.com/nowhr.htm http://www.pa.uky.edu/~moshe/phy231/lecture_notes/bungee_forces.html

Acknowledgments Special thanks to: Dr. Russ Herman and Mr. David Glasier for their generous aid in class and on this project Also thanks to: the 2008 SVSM staff for providing an excellent social and learning environment Thanks to our parents for the opportunity