# Day 132: Empirical vs. Theoretical

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Today we started regular physics with groups attempting to summarize the relationship between the two masses and changes in velocities for carts involved in a collision. Many groups had variations on the same theme; more below.

We got to a point where some students suggested something resembling conservation of momentum but with the masses paired with the wrong velocities (see the last two pics above); I asked everyone to verify it. One group mentioned that it seems the masses should be switched. We tried it and about half the class seemed to agree that it worked for their data.

Here’s where I’m stuck; I believe that the half that didn’t agree probably thought so because of poor data collection, which is difficult for me to fix in real time particularly because of the relatively large class vs relatively small number of effective setups. Thus I decided to take a different tack, and so far I’m glad I did.

I usually give a quick mention of the difference between empirical and theoretical methods of building models, and this is a perfect place for it. I mentioned that we have something that seems to work for some people based on data. Let’s find out if we can figure something close to it based on theory as well.

We started with drawing free body diagrams for three snapshots, which was good to cycle back to anyway (it’s been a while); the carts traveling on their own before the collision, during the collision, and after the collision. We did two rounds of whiteboard speed dating, my current favorite flavor of whiteboarding, and by the end all but one or two of the groups had something resembling this;

This is where we left off; tomorrow we’ll pick up here to try to derive conservation of momentum, then compare with our empirical model. I hope to start momentum diagrams tomorrow as well, first time!