Our task was to calculate how many rubber bands were needed to allow a plastic hippo to bungee jump the high of a flight of stairs. The goal was to minimize error and optimize the distance of the fall without exceeding it (ie. not cashing to the floor).
We first attached one rubber band to the foot of the hippo and tested its maximum fall distance. We then added a second rubber band and did the same. We repeated this for the first five rubber bands and then the seventh. We noted that each rubber band averaged an additional 22 cm. to the fall distance. I, myself, speculated that with each rubber band added, the additional distance to the fall was slowly decreasing.
Since the height of the jumping platform to the ground was about 505.46 cm. (199 in.) we calculated that 22 rubber bands would suffice. We found that with seven rubber bands, the hippo dropped a total of 156.5 cm. By calculations, we determined that with 21 rubber bands, (156.5(3)) the hippo would drop a total of 469.5 cm. With an additional 22 cm an extra rubber band would allow - increasing our rubber band count to 22 - we speculated that the hippo would drop a total of 491.5 cm.. This leaves the hippo just 13.96 cm. off of the ground. We determined that with averaging the cm/rubber band, 13.96 cm. from the ground leaves room for unaccounted error.
Below is a recorded account of the bungee jump:
Above is an account of our second jump. It should be added that the first jump was roughly 40 cm. away from the floor however when dropped, the rubber bands bunched up and did not allow for a clean drop. Thus, we dropped again. On the second drop, we ended up a mere17 cm. from the floor. This leads to an error of 3.04 cm. away from the floor based on our calculations.
This activity made me think of limits. When it came to the distance each rubber band added allowed the hippo to drop, the number, ultimately, slowly shrank. However I cannot imagine that if one were to add an obscenely large amount of rubber bands (x rubber bands tending towards infinity) that the last rubber band added would allow a distance of 0 cm more distance dropped. Thus, the limit of what each rubber band would contribute to the drop would have to be greater than zero, but less than the last distance recorded (being 18cm). I should add that I do not know this number and that more testing would be involved to calculate it but this is just a speculation.
Also, it had me wondering about elasticity. According to Anthony Coy, "When the rubber bands were heated, the particles stretched out, making them more elastic and able to withstand greater force" (2005). This has me curious, wondering what would happen to the limit a rubber band might add to the drop when they are heated: would the limit be greater than that of the room-temperature bands or would the limits be equal?
Below is an account for our rough data: