Um…oops. 
It’s partially-reversible, at least. I strongly suspect that an oscillating mass hanging from a rubber band would still fairly quickly come to rest, even if we minimized all avenues of heat loss from the rubber band (such as by silvering the walls of the vacuum chamber).
But yeah, I’d really like to see the experiment.
Yes, too long, not short enough. There are reports of such things but I think broken and improperly attached cords are a bigger problem.
Also the cord has a pretty high surface area to volume ratio, so it will shed heat quite readily.
How about measuring the rebound differences using objects of identical mass but different shapes/volumes and known air resistance i.e. a range of drag coefficients. Should then be able to use calculus to estimate what would happen with an object of no resistance, and therefore work out the relative energy loss?
That could in principle be done, even with just one object of known shape, but I’m thinking it’d be easier to just get a vacuum chamber. Small ones aren’t too hard to come by.
Right–I should have emphasized that there are still dissipative forces present, but that the actual rebound is from a reversible entropic process. Most likely, you could reduce the dissipative losses to a negligible level by stretching more slowly (since this kind of thing tends to be proportional to v2), but the entropic heating is unavoidable.
This sounds like a spectacular what-if? xkcd.
I’m going to spitball that for the height/length of practical bungee jumping, air resistance on a human is nearly negligible. It might be 5% of the total energy dissipation. It sure isn’t 25%. And I’d actually be surprised if it was as much as 5%. But that’s intuition, not calculation, talking.
The aerodynamic drag equation has a velocity squared term and the rest of the factors can be reasonably assumed to be constants for any given experimental drop. Jumping off a couple-hundred foot building or tower with 50 or 100 feet to fall before the cord starts slowing the test subject just doesn’t give enough time to build up enough velocity for the velocity^2 term to amount to much at the peak velocity. Much less as integrated from zero to max back to zero on the way down and the same zero-some smaller value-zero on each rebound up or down until the motion subsides completely.
Conversely, if people bungee jumped out of helicopters at 10,000 feet above the ground on a 5,000’ cord that stretched to e.g. 9,000’ before rebounding I’d say that air resistance would be a nontrivial fraction of that experiment’s energy dissipation. Both on the first trip down and maybe even on the first trip back up then back down the second time.
I’m inclined to agree, especially since at least half of a jumper’s time is spent in an aerodynamic head-down orientation (rather than a skydiver’s belly-down position).
What makes a bungee jumper eventually stop?
Not tying the other end of the bungee rope to the bridge.
My intuition went the other way and I did the math (please check my calcs). For 50 ft of fall, we will lose around 15% and for 100 ft of fall we will lose around 30% of the energy to drag.
Here are my calcs
Assumed cross section of human body is 2 sq ft (0.19 m2) (Link says says .15 to 0.4 m2 Average absorption cross-section of the human body measured at 1-12 GHz in a reverberant chamber: results of a human volunteer study - PubMed)
Assmed Drag Coefficient of Human Body cd = 1.1 (Link says Person standing, cd = 1.0 – 1.3 and Person (upright position) cd = 1.0 - 1.3, Drag Coefficient)
My calcs are close enough to the wikipedia page " A typical skydiver in a spread-eagle position will reach terminal velocity after about 12 seconds, during which time they will have fallen around 450 m (1,500 ft)" Free fall - Wikipedia.
Please check my math here for integrating the equations and then calculating the constants
https://imgur.com/a/k1O1Y5O
Here is the result in a graphical and tabular form
https://imgur.com/a/VqdSWmF
So the potential energy turns to KE, then we’ve got energy absorbed by the bungee cord itself, then there’s aerobraking…
(Similar to why your car requires a lot of power to force its way through the air while driving at speed).
then there’s lithobraking.
I admit that when I first saw the question, before realizing it was in FQ, I thought the OP meant, "What makes a bungee jumper eventually stop and give up his hobby?"
My answer works with that question, too.
Worth noting that a vacuum chamber will insulate the elastic cord, preventing it from shedding heat, which may affect its elastic properties in some way
All you need is the drag coefficient of the jumper to work out how much air resistance plays into the problem.
From here:
The drag coefficient of a skydiver is approx 0.7 feet down, and 1.0 in a spread eagle position. Knowing this, air density, the weight of the person and their surface area you can calculate drag force, and thus the velocity of someone in that air falling a specified distance. If you compare that to the velocity that would occur in a vacuum, you can figure out how much energy was lost to air resistance.
Then you can model the bungee jump, assuming a frictionless, perfectly elastic bungee cord. It will be a dampening oscillation with energy lost only to the atmosphere.
Then you can drop the person on the real bungee and observe the oscillations, The difference between that result and the modeled result will be the energy lost to the bungee system.
Did I miss anything?
That most people doing a bungee jump are not going to use the skydiver’s spread eagle position.
Right, so I gave the drag coefficient for a heads-down position as well. Use that, or come up with an estimate between the two gased on how you see the body move during the jump.
Hmm… I was thinking that that was exactly what I wanted to study, but on thinking about it more, there are actually three ways that useful energy can be lost: First, through air resistance, second through the elastic processes not being completely reversible, and third through the cord losing heat before it can turn it back into mechanical energy. Both of the elastic loss mechanisms are interesting, and worthy of study.