After seeing many videos and images of other high school physics classes doing some variation of a bungee jump, we, fellow teacher Jeremy Smith and I, decided to implement one of our own. This turned out to be a great way to wrap up our energy unit as students would be exposed to all three types of mechanical energy in this problem. Our Deadly Gorge Bungee Jump Design was simple, it asked students to design a bungee jump that could work for a range of customers, in this case masses ranging from 100 g to 750 g. Materials were limited to springs(we’re fortunate enough to have several sets of these that work great), string, and an adjustable ring stand.
It was really interesting to watch as the students got started right away. Almost all of the groups began by simply playing with the materials, I often encourage this with new materials in class, just so students can learn on their own how they work. Quickly following this initial play period was the adjust and check period. There were no calculations being done, simply students writing down the height of the jump point and whether it hit the ground or didn’t come close enough. I try not to step in too much with these types of problems, hoping that students will eventually apply the equations to the problem. At the start of the next class period I helped the students talk through a conceptual understanding of the setup, including the variables and energy types. This helped tremendously as groups started to work through the problem on paper. About half of them had it, the other half just couldn’t get past the number of variables. Those groups that struggled ended up coming to see me for some extra help and we talked through it together.
On test day students chose one of 5 random masses and setup their jumps according to their calculations and testing. Not all groups were successful on test day, with some groups dipping into the water, one group hitting the bottom, and a few just missing. It was great to see their reactions and the groups that didn’t get it went immediately to figuring out why it didn’t work.
This setup allowed groups to adjust one of three variables in order to be successful. They could use a different spring, a different length of string, or adjust the height of the ring stand. All three of these methods were employed in my class, the easiest adjustment though is simply to change the height of the ring stand according to calculations, this ends up being a quadratic with two solutions, one being negative.
One aspect of the problem that I’d like to quantify is the acceleration of the mass as it is slowed, as an actual bungee jump needs to do this smoothly so the customer doesn’t experience whiplash.