How to Determine Stretch of a Bungee

This experiment was set up to explore the physics of a bungee jump. The goal of the experiment was to develop a method to isolated variables of a model bungee system as to gain insight the relationships between different parts of the bungee system as a whole. Specifically our experiment aimed to determine an appropriate way to determine the stiffness of a bungee cord. One of the most important variables in a bungee jump is the stiffness or flexibility of the bungee used. This variable, which shows that a bungee acts in similar fashion to a spring, is also known as the “k" constant. It can be found in the equation for Hooke’s law (equation A below). The k constant determines how flexible or stiff the bungee cord is. The magnitude of stiffness relating to the bungee cord can make the difference of whether a jumper attached to the bungee experiences a pleasant soft rebound, or one that jerks him with so much force that the jumper experiences bodily damage. Obviously then, a bungee that is extremely stiff is not good for a bungee jump. On the other side of the spectrum, if the bungee is too flexible, the jumper attached to the bungee might fall way too far and smack into the ground. If this was the case he may well have just jumped off and tried to fly, rather than rely on a bungee cord. The question then becomes how one goes about determining what the K-value of a chord is. By using a model bungee system composed of a rubber sting acting as the bungee, and a mass simulating a human attached, the goal is to determine a way to find that k-value. Hooke’s law (Equation A) states that the force necessary to extend or compress a spring by some distance x is proportional to that distance. The derived formulas below shift Hook’s law to show that in our experiment the hanging mass on our bungee will change the proportional constant K relative to the change in position from equilibrium, denoted by x.