This approach takes two different springs whose spring constants have already been determined by the class, and asks student to figure out how to make those springs have a similar "effect" on two identical carts. It took me more tries than I like to admit to fully internalize and communicate to my students that, "...

__we aren’t necessarily looking for the carts to get to the end of the track at the same time__. We are looking for the springs to give them the same effect, so

__we’re looking for them to have the same speed once the springs aren’t stretched anymore__. So we should look carefully at their motion relative to each other (not for which one reaches the end of the track first)." However, in the end it seemed reasonably effective and better than just a bit of hand waving saying, "hey kids, the area under the F-x graph MUST mean something, right? Let's call it energy!"

Overall, the insistence in both the Swackhamer reading and Laura's introduction that "energy is a thing, it doesn't come in different types or flavors, it just sits in different containers that we observe different ways" is making it really hard for me to wrap my head around what energy really IS. I've embraced the idea of an operational definition, and the idea that gravitational mass and inertial mass are two different ideas, based on different observational properties of an object, which happen to have the same value. By analogy, we use different observational procedures (operational definitions, in my world) to detect the effects of kinetic, gravitational, and elastic energies. What makes the kinetic, gravitational, and elastic energies have an underlying one-ness that the two kinds of mass do not?

Bryan (@BC_ocs) tweeted a link to a discussion of energy from the Feyman Lectures today. Feyman says: "there is a certain quantity, which we call energy, that does not change in the manifold changes which nature undergoes. That is a most abstract idea, because it is a mathematical principle; it says that there is a numerical quantity which does not change when something happens.

__It is not a description of a mechanism, or anything concrete__; it is just a strange fact that we can calculate some number and when we finish watching nature go through her tricks and calculate the number again, it is the same." Is it too bleak to say that if Feyman couldn't come up with an operational definition of Energy then it's just not possible? If we go to an even more famous physicist, and consider Einstein's E = mc^2, does that give us a route to an operational definition for energy (albeit one that requires a particle accelerator... or at least a radioactive source)? Or is there one hidden in thermodynamics that I just haven't grokked despite taking thermo at least four times in my college / graduate education?

Despite my conceptual unclarity, I enjoyed today's labs. It was fun to see what a difference the different snaky lengths could have in their spring constant -- it makes me want to think more about how the material properties of the substance in a spring interact with the geometry of the spring to make the spring constant. And I had contemplated doing the kinetic and gravitational energy labs with which we ended the day, and been too intimidated by the complexity of the materials required, the lab setup, and the procedure to try them. It was good to see those in action. I still think they're pretty tricky to ask students to figure out good procedures and collect good data for, but I can see that it might be worth the effort to try... I'm looking forward to seeing how the discussion of those gets wrapped up tomorrow.

I'm also wondering what will be prioritized in the last two days of the workshop. We presumably need to wrap up the energy unit tomorrow morning with the lab discussions, and maybe one more deployment? There are two more units in the modeling binder -- uniform circular motion and momentum. I'm curious to see which parts of those seem important enough to the workshop facilitators to touch on in the remaining 1.5 days (minus last day paperwork).

I love that idea of the cart races and will totally use that this year! I hate hand waving but there are times I just don't know how to get them to bridge the gap. We almost had a fight break out at a DMAPT meeting on the definition of energy. So the confusion over that is actually a "thing". I agree with you on the whole mass thing. I see that they are different in theory, but the fact that they end up as the same value makes me think there is something wrong with that theory! Circular motion is tomorrow and Wed. Momentum will have to wait until Oct 18!

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