One of my grandchildren was asked by their teacher to design an experiment to show how helium filled balloons can allow a pumpkin to descend from an 11th floor building and not smash. The first question I asked myself was; how does one do this? The second question was; does this teacher have any idea what she has asked High School freshman?
Now I spent some time trying to solve simply, say for a 9th grader, this problem. So here goes:
1. Lets start with Archimedes, this will be used again and again.
2. So we know that the mass displaced equals the mass in the water. The same principle happens with buoyancy when the balloon is submerged and one seeks the upward force. Now add the balloon, filled with helium, and attach it to a pumpkin. The total is in a gas or fluid so Archimedes applies.
3. Now consider the dynamics of the system and so introduce Newton.
4. Then logically as you increase the balloon size you slow its downward speed and at some point it will actually rise.
5. This then yields a simple solution. I think.
6. If we then ask the question as to size of balloon and weight of pumpkin you get:
and the following:
7. Finally there is the issue as to how slowly must the pumpkin reach the ground so as not to smash. Namely what kinetic energy is the maximum to not smash the pumpkin. Welcome to an experiment.
8. Having spent time on this issue I then wondered where this teacher was coming from. Perhaps this was a game, but in reality it can be a great learning exercise, only if they knew what they were doing!
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