# 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
• Are you provided with the bungee cord in advance? If so, then you could test out the device experimentally using a rock or something. You could try making some very rough estimates theoretically, but in the end, it's experiment which has the final say. Even the theoretical calculation will need to take into account some physical details of the cord you are using. What info are you provided? This system can be roughly modeled as a differential equation, and simulated numerically. – DumpsterDoofus Dec 1 '13 at 22:42
• We are not provided a bungee cord in advance. We need to design one using attached rubber bands with only the restrictions mentioned in my question. I was thinking of doing this experimentally, but I would love a predictive calculation if at all possible. I need to put together a design proposal for the cord and and a mathematical starting point would be very helpful albeit rough. I could come up with some arbitrary values for a model but I think an equation with variables would be more helpful at this point. I just don't know where to start in terms of making a model. @DumpsterDoofus – Will Byrne Dec 1 '13 at 23:05
• Is the objective the highest bounce, or the safest landing? Do you want 100% efficient that keeps bouncing for ever, or 0% efficient that dissipates the kinetic energy safely? – ja72 Dec 2 '13 at 2:09
• You can safely say the more rubber bands in parallel the less efficient because of the friction between the strands will convert energy into heat. – ja72 Dec 2 '13 at 2:11
• @WillByrne, there's no single specific model to describe the system you have in mind, simply becuase there's no single way to create the system. You could model the system as a general spring-damper system, but you need to know the damping ratio in that case, which will depend on the properties of the cord you use – Pranav Hosangadi Dec 2 '13 at 2:40

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).