# Homework Help: How would you quantify and predict the efficiency of a bungee cord?

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1. Dec 1, 2013

### Will2596

I am in an introductory physics class and we have been working with Gravitational Potential Energy, Elastic Potential Energy, Kinetic Energy and the Law of Conservation of Energy in relation to bungee cords. Recently, we delved into the topic of efficiency and with it I came upon the following stumbling block.

For a project, we need to design a bungee cord for an egg (Average mass: 57.3g +/- 3.0g) falling from a height of 10.0m, and try to get the egg's stopping point as close as possible to the ground. We also need to take efficiency into account. There is no exact wording to the question/problem, it was an open-ended question posed to the class.

Now I completely understand the basics of the calculation. Pick a desired stretch, use that to determine cord length, use that to determine the spring constant of the cord, etc. However, when you bring efficiency into account things get more complicated. Energy definitely escapes the system as the egg falls and the cord is stretched. Energy escapes in the cord as a result of internal friction, and during the fall as a result of air resistance. I think air resistance should be negligible given the mass of the egg and the shortness of the drop. I have scoured the internet for a model to determine the energy loss of the system due to internal friction to no avail. So...My question is, how can I quantify and predict the internal friction of the bungee cord, then use that to determine the % efficiency of my system?

Sorry if my question's a little long and/or misplaced and/or I'm making some kind of mistake in my thinking here. This is my first post on the site.

2. Dec 1, 2013

### Spinnor

If you want the egg to stop just before ground use a bungee cord that is very strong and will not extend at all, the down side to this is the egg will experience a sudden deceleration at the end, probably not good for the egg unless sealed in a solid epoxy capsule.

For a little on losses see,

http://en.wikipedia.org/wiki/Hysteresis#Elastic_hysteresis

I think the key to getting the egg as low as possible is to use the strongest and longest cord possible without the egg decelerating too much or going too far. You did not mention how the egg will be attached.

Ideally you would want a bungee cord that would only extend and not rebound by converting all the potential energy into heat on the first trip down. I don't think bungee cords are that good at dissipating energy?

For an idea of losses see,

Last edited by a moderator: Sep 25, 2014
3. Dec 1, 2013

4. Dec 1, 2013

### Simon Bridge

You have to measure it.

If this is a practical project, you are probably supplied with the materials to build the bungee cord from. Typically rubber bands or knicker elastic or something cheap like that. Is that the case?

If so:

Such materials will exceed their elastic limit almost right away when stretched - so you understanding of ideal springs will not help you. A mass dropped will extend the cord much farther than predicted by assuming an ideal spring.

Since you are restricted in your materials - you need to conduct a series of experiments to investigate how different combinations of the materials will stretch. You need to know how far they will stretch when dropped.

This approach will automatically take account of the efficiency of the material...