If you have ever wondered what type of accelerations are exerted on a body while it is approaching and then bouncing back from a bungee-cord jump, then this lab exercise may appeal to you.  Actually, understanding how to predict and design for certain levels of acceleration in this type of system can provide insight into many practical problems (e.g., suspensions of all types, safety-restraint designs, etc.).

The laboratory study will explore a simple bungee drop.  We will first study a simple mass-spring system, and then experiment with a mass suspended by a bungee cord. Concepts related to making measurements with an accelerometer are introduced, including the need for signal conditioning using a basic amplifier circuit.

Introduction

We will build up to the bungee cord experiments by first using steel coil springs because these tend to have linear elastic behavior. That is, a steel coil spring, either stretched or compressed over a relatively small working range will typically obey a linear Hooke's law relation: F = stiffness*(change in length). We find that most bungee cords don't necessarily follow this type of relation.

Experimenting first with a "linear" mass-spring system will give us experience in using an accelerometer and with measuring signals accurately.  It is possible to run some simple tests to evaluate the sensor calibration, and to make adjustments as needed.

Because these are relatively small-scale lab experiments, the signal levels from the accelerometer used may require amplification.  As such, this will motivate exercises in building, troubleshooting, and testing low power signal amplification circuits.

The Bungee Cord-Mass System

The acceleration of a mass suspended by a bungee cord results from the combination of gravitational, aerodynamic drag, and bungee cord forces.  The latter two effects can vary significantly from one bungee set-up to the next.  In the small-scale experiments conducted in the lab, drag forces are negligible so these can be ignored for the most part.  With regard to the bungee cord, because most bungee cords are made of visco-elastic strands, they may have nonlinear stiffness and damping properties.  Also, the forces exerted by the cord during a bungee jump (or drop) are only exerted when the cord goes taut.  This adds another type of nonlinearity to the problem.  Indeed, when building a model for understanding and prediction, it is important to keep in mind that these two facts will make the system nonlinear.  We can sometimes gain insight into each nonlinearity by designing experiments to investigate these effects independently.

To begin with, experiments will need to be developed to determine the stiffness and damping parameters of the bungee cord(s).  Stiffness, of course, can be measured using simple static loads, and this testing will reveal the cord characteristics (they may have a cubic type nonlinearity with respect to extension of the cord).  Some simple tests based on linear second-order system modeling are commonly used to determine damping; however, this assumes that the system is linear.  Hence, finding a model for the damping in the bungee cord will require us to compare such a model against data measured from an accelerometer.

Unlike some of the earlier "exercises" in this lab course, these lab exercises will leave some of the details to be determined and in this sense approach a true experiment.  The experiment and the materials are fundamental: an accelerometer attached to a mass and bungee cords of different lengths.  Here are the questions that you may keep in mind:

• What is a good model for the bungee cord?
• When dropped from a certain height, what will be the peak acceleration experienced by the mass?
• Can you predict the height that the mass should be dropped from so that the a certain level is approached closely, but not reached?