Bungee Drop

Cow A Bungee has replaced the Bungee Egg Drop event of preceding years (although it itself has not been run since before 2006) with a new event that requires students do deal not with simply the variable of height, but with two variables - height and weight. Instead of using eggs, competitors will drop a soda bottle, with sand in it. As before, the heights for the two drops can be anywhere from three to seven meters, either the same heighs or two different heights. At the impound, not only will the heights be announced, but also the weights that will be placed in the bottle for each of the drops. These weights will be anywhere from 25 to 500 grams. The goal, as before, is to get your device to drop as close as possible to the floor below, without touching. The team with the lowest score for the sum of the two drops from the ground, wins. All teams that hit the ground with one drop will be ranked behind those that do not touch the ground on either.

General Advice
Read the event description carefully, especially the part about the new definition of 'elasticity' for your bungee device. All sorts of materials can be used, from metal springs to Slinkys to elastic or rubber bands. With the new rules for elasticity, you don't have to make anything but the bottom two meters of the device stretchy, if you so choose.

The important task to be done is calibration. Once you have a set up with some kind of a bungee device, a soda bottle, and hopefully a clamp to attatch the bungee to something at the top, you are ready to begin testing. Calibration this year promises to be more complicated than it has been in past years. If, say, you start calibration with 3.00 meters, you can't only find one mark to make on our bungee for that height - you must make a mark for that height with 25 grams, for that height with 50 grams, etc. Getting the same degree of precision as was possible in past years will now, theoretically, take square the time (assuming you calibrate for, say 15 heights, and 15 masses). Of course, the real solution will to be to find a pattern; a formula. With this rule we hopefully can find, we will be able to simply calculate where to hold the bungee at, given a height and a weight. This formula will obviously differ from device to device.