How would you quantify and predict the efficiency of a bungee cord?

[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.

 

[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,

 

[Spinnor]

Also see,

https://www.physicsforums.com/showthread.php?t=351202

https://www.physicsforums.com/showthread.php?t=316822

from,

https://www.google.com/search?q=bun...ABQ&ved=0CAYQ_AUoAA&biw=1024&bih=544&dpr=1.25

 

[Simon Bridge]

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?

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...

 

[Nickie]

I would approach this problem by first defining efficiency in the context of a bungee cord. Efficiency can be defined as the ratio of the useful output energy to the total input energy. In this case, the useful output energy is the potential energy stored in the bungee cord that is used to slow down and stop the falling egg. The total input energy is the initial potential energy of the egg at the height of 10.0m.

To quantify and predict the efficiency of a bungee cord, we need to consider the energy losses in the system. As you mentioned, there are two main sources of energy loss: internal friction in the bungee cord and air resistance during the fall. Let's discuss each of these in more detail.

Internal friction in the bungee cord can be quantified by the spring constant of the cord. The spring constant is a measure of how easily the cord stretches when a force is applied to it. A higher spring constant means the cord will stretch less for a given force, which means less energy will be lost due to internal friction. So, choosing a bungee cord with a higher spring constant can improve the efficiency of the system.

Air resistance can also contribute to energy loss in the system. However, as you mentioned, it is likely to be negligible in this case due to the small mass of the egg and the short drop distance. If you want to be more precise, you can estimate the air resistance using the drag equation and then subtract it from the total input energy to get a more accurate efficiency calculation.

In order to predict the efficiency of your system, you can use the equations for gravitational potential energy and elastic potential energy to calculate the expected stopping point of the egg. Then, you can compare this with the actual stopping point achieved in the experiment to determine the efficiency. If the actual stopping point is lower than the predicted stopping point, it means that some energy was lost due to internal friction and/or air resistance, resulting in a lower efficiency.

In summary, to quantify and predict the efficiency of a bungee cord, we need to consider the energy losses due to internal friction and air resistance. By choosing a bungee cord with a higher spring constant and accounting for air resistance, we can optimize the efficiency of the system. Good luck with your project!