Sciencegeekgirl is blogging from the AAPT. She talks about showing something interesting to get students thinking, and here is her example:
This reminds me of Dan Meyer’s What Can You Do With This stuff. Anyway, I can’t help it. I must analyze this video. Plus, Fran essentially threw down the gauntlet and called me out on this move. Another reason to analyze this movie is that it is obviously fake. Elephants are one of the few animals that can’t jump. Not even a little bit. They don’t like to have more than 1 foot off the ground. Ok, on to the analysis. As usual, I downloaded the video from youtube and used Tracker Video Analysis. Here is a plot of one series of jumps:
Here, the second jump gives an acceleration of -3.6 trampolines/s2. I didn’t have the scale of this video, so I measured everything in units of the size of the trampoline. Also, the elephant is not a point particle, but I used his or her head for the location of the elephant. This is not a constant position relative to the center of mass, but it is close enough.
Looking at that fit, something looks weird (other than the jumping elephant since elephants can’t jump). The motion at the top of the jump looks like it doesn’t fit. If I just use that top data to get an acceleration, it looks like this:
This gives an acceleration of -1.8 trampolines/s2. I guess the creators of the movie wanted to add emphasis to the motion at the highest point by making it take longer.
So, how big is the elephant and the trampoline? That is difficult to answer. I could assume this is on Earth such that the acceleration would be -9.8 m/s2. But then I would not know which acceleration to match to the Earth’s.
How high did the elephant jump? From the data, it looks like about 1.6 trampolines. I suppose you could use the max height and the time of flight to determine the actual acceleration, but I am not going to do that. You can do that as a homework question (which I won’t grade).
Another interesting question: what is the acceleration of the elephant while in contact with the trampoline and is this acceleration too high to be dangerous? I would assume not, but I have not calculated it. Also, NASA does not publish data (that I am aware of) on g-tolerances of elephants.