It all started with Galileo's Thought Experiment. Several of Galileo's most important work was in the form of imaginary experiments. One of his most famous experiments was dropping two different weighted balls, one large and heavy, and one small and light, from the same height and seeing which hit the ground first. Galileo was thinking of one of Aristotle's laws:
If a certain weight moves a particular distance in a particular time, a greater weight will move the same distance in a shorter time, and whatever is the proportion which the weights bear one to the other, so too the times will have to each other. For example if the half as heavy weight covers the distance in a certain time, a weight that is twice as heavy will cover the distance in one half the time. (Source)So, following in the footsteps of Galileo, we experimented.
In a real bungee jump event, you have one chance. One jump. No do overs. So the tension of the rope needs to be perfect enough that you come close to the ground but not slam into it. These were also our requirements. We were allowed one jump. To make sure our jump was as accurate as possible, we started gathering data.
We selected our object, Mr. Elephant, and began to take several things into consideration to make our jump the best it could be. We needed to observe how far one rubber band would stretch, how the weight of our object affected the pull of a rubber band, what would happen when another rubber band is added, etc.
To begin, we started with a single rubber band, measured the length at resting, then added another rubber band and observed how the length changed. We continued to do this, recording our data as we went, to generate a ratios with the number of rubber bands used. We took the distance and created a ratio with the number of rubber bands used.
We found that as the number of rubber bands increased, our decimal result grew larger and larger. To make a sound prediction for our one and only jump, we stayed on the safe side and used our smallest decimal result. Through our data we concluded that we would need 16 rubber bands to bungee our elephant 505 cm.
We were wrong.
Our first attempt landed us about 1 meter shy of even touching the ground. Our elephant was safe but we knew we could give him a better bungee experience.
Second time around we used more of a trial and error method. We added two more rubber bands, for a total of 18, and dropped again. Elephant got much closer to the ground. But what would adding one more band do?
Too much. Elephant got a trunk full of concrete. Eighteen was the golden number for Mr. Elephant and a successful jump.
Some noticeable moments from this experiment include:
- It is difficult to prediction how much each rubber band is going to stretch and which rubber bands will stretch the most. Maybe all of the rubber bands we used didn't hold the same tension. It would also be interesting to test this...do all rubber bands from the same bag with the same size hold the same tension?
- Trial and error, as cumbersome as it may be, used to be helpful with out second jump. Had it been a real bungee experience we wouldn't have done this, however, it was quite interesting to see how the addition of one rubber band can alter your results.
- The weight of an object has a huge affect on the number of rubber bands needed. Mr. Elephant was one of the heavier objects. We started at 16 rubber bands for our jump whereas Ms. Barbie's group started with 25.