Bungee PhysicsAugust 7th, 2012 by Bob Tinker
Last week, Paul, Ed, and I did physics. This is such a rare event that it deserves note. We actually developed a theory, collected data, compared theory to data, came up with new ideas and tested them. We only wish kids everywhere could have the same experience.
This investigation was prompted by Ewa Kedzierska’s presentation at the World Conference on Physics Education in Istanbul in early July*. She presented a student activity on bungee jumping that claimed that the jumper falls faster than a free-falling object. This seems difficult to believe, in spite of video data she presented—collected and graphed by the wonderful COACH software—that clearly showed this to be true. We immediately thought of many reasons why this should be impossible. Imagine jumping without a tethered Bungee cord—jumper and cord would fall in free-fall just as Galileo proved in his famous Tower of Pisa experiment (never mind the fatal consequences—this is physics!). Attaching the far end of the Bungee rope would seem to apply an upward force that could only slow the jumper, not speed her up!
As typical science skeptics, we had to do it ourselves and understand the mechanism, if the effect was true. Following the maxim that was current when CERN supposedly found neutrinos travelling faster than light—“Extraordinary results require extraordinary evidence”—we needed to do the experiment ourselves and get a feel for the situation. So Ed gathered a stepladder, chain (substitute Bungee), tennis ball (for the jumper), and a camera that takes 240 frames per second, and we collected data.
Paul, ever the theoretician, showed that the far end of a horizontal chain link held steady at the near end would fall faster than a free body, and hence, could impart some force to the falling chain. Thus, each chain link, on reaching the bottom of the “U” formed by the falling links, could impart a bit of force on the falling side and make it fall faster than free-fall. Another way of saying this is that each link, when brought to a halt, rotates 180 degrees and can exert some torque on the falling side.
We collected the data, and clearly saw the effect. It is real! And it is huge when the falling mass is small. We photographed side-by-side tennis balls, one attached to a chain and one in free fall. The one with the chain fell faster! Every time. The picture shows a frame from a movie of the experiment, clearly showing Paul about to fall (he didn’t), and the free-falling ball going slower.
Don’t believe us? Do it yourself. We attached a force sensor to the end of the chain and could detect the force from individual links. The force increased non-linearly and dramatically. Stopping the last link required 50 N even though the entire chain weighed only 4 N (see graph). We are still arguing about why the force increases so much for the last few links.
I noticed that sometimes if the falling part of the chain is close to the tethered part, the links at the bottom of the “U” do not rotate, but slide. When they slide, they do not rotate and, hence, should not accelerate the falling chain. We could hear the difference, but our results were inconclusive, because near the end of the fall, the chain doesn’t fall evenly and this causes it to revert to the link-rotation mode.
In our next blog, we’ll present the data and our analysis. Stay tuned.