Anyway, I couldn't really find it, but I did stumble upon the dissertation of Thomas Thaden, which was related to this sort of thing, and which has a big series of possible outcomes of the race. They're small Quicktime videos and I didn't think that they were big enough or clear enough for what I wanted to do, so I wrote a simulation in VPython.
I think that this is much more interesting than what I was planning to do, which was to just have them predict, argue, and then see the results (peer instruction-esque). Instead, I'll have them check out five different possibilities, poll them, have discussion, and see what kind of consensus comes. Maybe there won't be one, but we'll be defining the gravitational PE that day, based on our lab from the previous day (maybe more on that in another post, if I have time), so that could help. I'm torn about whether to do that first or second, but maybe second is the way to go.
Anyway, the five models in the simulations for the down-and-up track are:
- Correct physics
- Constant speed
- Constant x-dimension speed, constant y-dimension speed while on the ramps (tie)
- Accelerate down the ramp and up the ramp, but back to ball 1's speed on both of the flats
- Accelerate down the ramp and up the ramp (but too much, so that the balls end up tied)