Effect of Body Mass and Cord Length on Bungee Jump Motion

The physics behind Bungee jumping
To what extent a body’s mass and length of the cord affect the Bungee jumping motion?

 
Abstract:
This essay investigates a body’s motion during a bungee jump in order to answer the question: “To what extent a body’s mass and length of the cord affect the Bungee jumping motion?” the investigation takes place with comparing three different bungee cords ‘s performance in two simulation laboratory experiments. The first is to check the relation between the bungee jumping cord and its relation to Hooke’s law and finding its elastic limit. The second is to inspect the motion in terms of velocity and acceleration changes with varying the weight of the body attached to the cord and changing the length of the cord, since they are the factors to be considered in the research question.
 
Introduction
Scope of work
The vine jumpers of Pentecost Island in Vanuatu inspired the spot of Bungee jumping, as it was viewed by way of a rite of passage to manhood. It is about jumping from a high point such as a bridge, a building or a crane attached to nylon braided, rubber shock cord. It is from a fixed structure most of the time but it is possible to do it from an object floating in the air, for example, a moving crane or a hot air balloon. It became a popular sport the last two decades in the United States of America where people do it for the sake of the excitement and adrenaline pumping sensations. Of course this sport involves a lot of risk and most of the accidents occurring are from miscalculations in the length of the elastic cord, which leads to many horrifying accident when people end up landing on the surface or the cord collapses, it occurred to my mind that exploring such a occurrence might be very interesting.
Objective:
In this essay I aim to look at the physics behind Bungee Jumping. The aim of this essay is to investigate the factors affecting the bungee jump motion. I will be exploring the stages that the bungee jump goes through and the factors affecting it allowing a safe landing but exciting at the same time. This involves data logging from laboratory experiments and graphing data with analysis. Exploring this matter can easily make connections between fundamental concepts of physics and real world phenomena: Bungee Jumping. Therefore attempting to answer, “To what extent a body’s mass and length of the cord affect the Bungee jumping motion?”
Background information
Safety of Bungee jumping
There is no doubt that a thrilling from a height usually more than forty-five meters carries its own risk and can be very dangerous, Bungee jumping is like most adrenaline pumping sports, when done wrong, can be hazardous and even lethal.
Bungee jumping mishaps can occur because of faulty equipment or regardless of safety measures, the injuries that could have been avoided are human errors when the body strapping fails due to improper attachment or flawed harness, Chris Thomas is an example of this horrible incident, he died during a charity jump in Swansea, Wales: because of his weight[1]. Another case is cord length miscalculation and the jumper ends up hitting the ground or the bungee cord just snapped, similarly to what happened to Erin Langworthy, an Australian woman who almost drowned with her feet tied together in Zambezi River at Victoria Falls[2]. In 1989, this activity was banned in France and one state in Australia after three people faced their death[3]. And many other incidents causing people to collapse on concrete and suffer from extreme cranial trauma or even die because the rope was too long, that actually happened to Matthew E. Coleman[4], who died at an Adventure World bungee jump.
However, unavoidable injuries might occur, minor injuries such as skin burn, which is triggered through gripping the cord, happen when Bungee jumpers do not act accordingly to the guidelines given. Some of them stated that they got slapped in the face by the cord.
Other mores serious injuries; such as eyesight damage or temporary retina haemorrhage[5], strokes and traumatic carotid artery dissection happened to fit and healthy youth.
But injury inflicted by the cord, such as choking to asphyxiation, appears not to happen. This can be explained by a combination of factors, including the cord’s minimal torsional stiffness. Also, the minor pendulum motion keeps the cord from contacting the jumper and tangling or strangling him,
No modern-day jump site has seen any serious entanglement, and it is noteworthy that many participants enjoy somersaulting during the free fall without any harm or disaster occurring.
Principle components in the physics of Bungee jumping
To allow the bungee jumping motion to occur the person jumps from a high surface and the cord stretches as he is moving downwards, this demonstrates the cords’ elasticity, which can be defined as the ability of a body or the cord, in this case, to oppose a force exerted on it and change shape and size and to return to its same characteristics when the strain is removed.
The law of elasticity, Hooke’s law, determined by Robert Hooke, an English scientist in 1660, which states that, for relatively small deformations of an object, the displacement or size of the extension is directly proportional to the deforming force applied.

Under these conditions the object returns to its original shape and size upon removal of the load.
If the force exerted exceeds a certain amount, known as the elastic limit, it would create a permanent deformation to the body even when there is no force applied on the body. The elastic limit differs from a body to another because both of the resistance to stress and it depends on what the body is made of. Elastic materials expand thinner and thinner until rupturing at their breaking point.
The strength of materials is the measurement of a body’s capacity to bear strain and stress. Stress is the internal force applied by a segment of an elastic body upon the connecting part and strain is the dimension’s deformation caused by stress. Elastic materials are the materials whose stress disappears after the exerted force is removed.
In bungee jumping the cord is subjected to pull, this is identified as tension. When the cord has weight attached and it is being pushed, this is known as a compressive stress. During the jump, the external forces twist the body around an axis, it is known as the torsional stress.
Experiment 1: Hooke’s Law
This experiment is carried out to calculate the elasticity of the bungee cord and its elastic limit.
Variables

The force exerted on the bungee cord

The extension of the cord due to the force applied

The same bungee cord used for different weights
Shape of the weight used
Height of the cord from the ground
Apparatus Used
Since the Hooke’s law experiment apparatus is usually equipped with a retort stand, which is a stand that has a ruler and a pointer attached to the spring, but since I am using a bungee cord instead of the spring, I used a regular clamp and I had seven different masses labeled 0.1 kg, a digital measuring scale with 0.01 kg uncertainty, three different car bungee cords purchased at the local hardware shop, a ruler0.0005m and a flat surface to perform the experiment on.
Method
First of all, I measure the length of the car bungee cord is provided with two hooks at each of the extremities, therefore I hang the cord with one hook on the clamp, I measure the weight holder then I hang it to the bottom hook line the I add one weight cylinder, afterwards I carefully measure the length of the cord. Next I measure each weight on the scale and I measure the extension on the cord each time the weight is added. All the measurements are recorded during the experiment.
Experiment 2: Bungee Jumping Simulation
Variables

Length of the cord
Thickness of the cord
Force applied to the cord

Time taken to complete a bungee jump
Velocity of the body
Acceleration of the body

The same bungee cord used for different weights
Shape of the weight used, using the same set of weights
Height of the weights from the motion sensor, it is controlled by placing the Vernier motion sensor on a laboratory chair with the ability to move it around and adjust its height.
Apparatus Used
Vernier motion sensor connected to a computer with a data logging software[6] installed which will be crucial for more accurate timing and graphing purposes than manual timing. Also, the same Bungee cords used in the previous Hooke’s law experiment are used since characteristics are already measured and this experiment is relating to the previous one, a meter ruler can be used to insure that the apparatus is perpendicular to the motion sensor. Blu-tack and tape is also needed.

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Method
A clamp is put on a flat surface, to prevent it from falling I and the bungee cord is hung from it with the weight holder suspended at the bottom of the cord, both of the hooks attached to both ends of the cord are secured with Blu-Tack to prevent the apparatus from falling and act as the harness in this simulation. The Vernier motion sensor is put on the laboratory chair, and before starting the experiment, activate the motion sensor and oscillate the cord with the suspended weight holder to test the sensitivity of data logging and test the range of motion detection. Afterwards the weight is elevated to the beginning of the cord and it is released with minimum to no force. This step is repeated by adding weights and the weights are secured with a thin strip of tape to avoid them falling off.
Conclusion:
Bibliography
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1

[1] “Fatal Bungee Jump was “accident” ” BBC News. BBC, 25 Feb. 2005. Web. 19 Nov. 2014.
[2] “Aussie Plunges into Raging Waters after Bungy Cord Snaps.” N.p., 9 Jan. 2012.Web
[3] “For Thrills, Lovers and Others Leap.” The New York Times. The New York Times, 30 July 1991. Web. 19 Nov. 2014.
[4] “Relatives Grieve after Fatal Bungee Accident.” Baltimore Sun. N.p., 16 May 2000. Web. 19 Nov. 2014.
[5] “Injuries Resulting from Bungee-cord Jumping.” ANNALS OF EMERGENCY MEDICINE 22.6 (1993): 1060-063. Print.
[6] Logger Pro 3. Portland, Or.: Vernier Software, 2003. Computer software.