How would you quantify and predict the internal friction and efficiency of a bungee cord? 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.
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.
Edit: Here is all the given information for this problem:


*

*Average mass of the group of eggs being used: 57.3g

*Standard Deviation: 3.0g

*Height: 10.0m

*Desired height at the egg's lowest point: 0.10m

 A: Neglecting air resistance (whether this is a good idea or not is besides the point), suppose you drop the egg from height 10.0m, and it fell to a height of 0.10m, and then rebounded to a height of 9.0m. What can you deduce from this fact?
Edit: 
Since you want something a bit more along the modelling side, if you know how the tension changes with temperature, you can deduce the change in entropy with change in length at fixed temperature using Maxwell relations. You can assume the rubber band obeys $dU = \delta Q + t dL$ where $t$ is the tension and $L$ is it's length. You can then use more thermodynamic cleverness to determine the change in temperature with length for adiabatic stretching, which allows you to figure out the irreversible component (lost as heat).
Google for thermodynamics+rubber+elasticity should get you started.
More links:
http://physics.oregonstate.edu/~roundyd/COURSES/ph423/lab-2.pdf
ftp://ftp.ccmr.cornell.edu/tmp/MSE-4020/4020-Notes-7-text-book-rubber-elasticity.pdf
