The Physics of Bungee Jumping
Outcomes: 1. Analyze natural and technological systems to interpret and explain their structure. (116-7) 2. 3. 4. 5. 6. 7. 8. 9. Describe and evaluate the design of technological solutions and the way they function, using energy principles. (116-6) Analyze and describe examples where technological solutions were developed based on scientific understanding. (116-4) Distinguish between problems that can be solved by the application of physics-related technologies and those that cannot. (118-8) Analyze and describe examples where energy-related technologies were developed and improved over time. (115-5, 116-4) Analyze the risks and benefits to society and the environment when applying scientific knowledge or introducing a particular technology (118-2) Construct and test a prototype of a device and troubleshoot problems as they arise. (212-14) Analyze quantitatively the relationships among mass, height, gravity, spring constant, gravitational potential energy and elastic potential energy. (326-1) Solve problems using the law of conservation of energy, including changes in elastic potential energy.
Would you plunge off a bridge attached only by a soft springy cord that could stretch three to four times its free length? If you understood the physics behind such a daring feat you just might! Bungee jumping involves attaching oneself to a long cord and jumping from extreme heights. It is related to a centuries old practice from the Pentecost Island in the Pacific Archipelago of Vanuatu. On this island, the men jump to show their courage and to offer thanks to the gods for a good harvest of yams. In 1979, members of the Oxford University Dangerous Sport Club jumped off a bridge near Bristol, England, apparently inspired by a film about “vine jumpers”. In the early 1990’s, the sport gained popularity in the United States and Canada. Today it is still dubbed the “ultimate adrenaline rush” (Menz, 1993). PHYSICS 2204 CURRICULUM GUIDE
The old adage of “less is more” certainly applies to bungee jumping. The only equipment required is a springy cord and a harness. However it is very important that the equipment used be strong and secure. The harnesses are similar to those used in mountain climbing, including the caribiner which is the main link between the cord and the harness. The cord itself is soft and springy and is secured tightly to the jumper’s body. Jumpers today are typically aided by double hookups. If an ankle jump is chosen, the body harness is used as a backup. If the body harness is chosen, a chest/shoulder harness becomes the backup. Though there have been some accidents related to bungee jumping (three deaths in France in 1989), they can be traced to human error in attachment, total height of jump available, or a mismatch between the cord and jumper. Minor injuries like skin burn or being hit by the cord happen when 107
jumpers do not follow instructions. Skin burn for example is caused by gripping the cord. Understanding and adhering to some basic physics principles would prevent such problems.
Energy Distribution The main physics concepts involved in bungee jumping are the gravitational potential energy of the jumper and the elastic potential energy of the stretched cord. Initially the jumper is attached to the cord which is attached to a supporting structure on the same level as the jumper’s center of mass. Standing on the platform, the jumper possesses gravitational potential energy given by,
the jump the velocity of the jumper, and therefore the kinetic energy, is zero. At that point the gravitational potential energy possessed at the top has been totally converted into the elastic potential of the cord. Since energy is conserved in the jump, the gravitational potential energy of the jumper must equal the elastic potential energy of the cord.
E top = E bottom mgh =
E p = mgh
where is the...