Bungee Project Description

 

Introduction

 

In industrial, engineering, and business applications it is sometimes necessary to develop a mathematical model to predict how a system, economy, or invention will perform. The mathematical model is based on a set of sample data and the model that is developed is then used to predict behavior in new situations. In this activity we will need to develop a mathematical model (an equation) to describe the amount of stretch there is in a bungee cord of varying length. You will be provided with a participant (an egg) and harness, bungee cord (several rubber bands), and a meter stick. Your goal is to develop an equation that can be used to predict the number of rubber bands needed to provide an exciting and safe jump from a height to be determined later in the class. Of course part of the thrill of bungee jumping is to see how close the participant can come to the ground without actually contacting the ground.

 

Developing Your Model

 

Your group will need to make several jumps varying the number of rubber bands and measuring the total elongation of the cord for each jump. Be sure to record the number of rubber bands involved and the maximum length of the unit for each jump. After you have done several jumps enter your data into your calculator and plot the data. Use the calculator to find the equation that will best fit your data.

 

Exploring Your Model

 

Now that you have an equation, what does the slope of the line represent with regard to the bungee-jumping problem? Measure the length of the egg and the netting. Does this measurement seem to correspond to any part of the model you have? With what part of the model would you expect it to correspond? Why?

 

Testing Your Model

 

Toward the end of class we will put your model to the test. You will be given a height from which your jumper is to make the leap. Your group will need to decide how many rubber bands are required for a safe jump. Points will be awarded for a safe jump. Additional points will be awarded for the group that has a safe jump as well as the minimum ground clearance. Scoring will be as follows:

 

POINTS FOR SUCCESSFUL JUMPS 10-The jump is within 1 inch. 9-The jump is 1 to 3 inches. 8-The jump is 3 to 7 inches. 7-The jump is 7 to 10 inches. 6-The jump is 10 to 13 inches. 5-The jump is more than 13 inches. 2 Bonus Points The jump that is closest to the ground with out touching the ground. 7-A minor impact. Small crack or can hear it touch. 6-Impact with the ground that results in a fairly large crack. 5-Impact that results in the egg shattering.

 

Report

 

A group report is expected that includes the data used to obtain the model, the calculations used to determine the number of rubber bands required for the contest jump, and the answers to the questions in the Exploring Your Model section above.