Today we started the lab aspect of deploying the Energy Transfer Model. We used this handout (modified slightly from the official U of MN lab for energy which is available in large PDF here). Students are asked to derive a formula for predicting the final velocity of a cart at the bottom of a ramp, and then we linearize the formula so the slope is 2g, which is pretty neat. The data works out pretty good. Next they will start planning their own verification lab.
I just love how this whiteboard shows how multiple representations support problem solving and allow for more complete understandings. This is problem 4 from practice 3 here. I got in the practice this year of making students always find the area of the F parallel vs. x graph for work done, because I like the calculus connection and the more completeness of the definition of work as integrating F dot dx (I don’t use dot product here, but it’s a quick extension if they see it again). Also, energy bar charts really revolutionized how well my students understand energy transfer, particularly when the energy of the system is changing due to work being done.
Power is so easy to introduce once students start to understand energy transfer. This year I introduced it in one problem (#7 on practice 3 here) and then expanded on it as well as brought together some other aspects and models in a follow up problem, #8.
My colleague Ben gave me this idea. He showed me how you can write a second energy bar chart for objects that are not in your system and show how the energy that is transferred out of the main system is transferred into the secondary system. No matter the system definition, energy is transferred and stored, but what changes is simply how we are tracking that. This is definitely something I didn’t understand after my first year teaching energy this way (essentially from a 1st law of thermodynamics perspective), and I’m sure it will become more nuanced as I get more used to it. One thing I am thinking about emphasizing more next year is the link between free body diagrams and energy transfer, in that forces in or against the direction of motion cause energy to transfer, though sometimes that is within the system and sometimes adding to or taking from the energy stored in the system, depending on the definition. Lots to think about here.
Students have a hard time believing that the temperature of materials increase when other forms of energy are transferred to thermal energy through friction or collisions. I wanted to show them that the temp does actually increase, so 5-6 years agoI started using a hammer to hit silly putty embedded with a temperature probe. After missing too many times I started dropping a shot put instead, then switched to a bowling ball (more awesome), and this year due to an interaction with Gary (IIFC) I switched from using Silly Putty (which essentially explodes and gets everywhere) to using play doh, much cleaner. It’s pretty great, I usually see about a degree increase in the temp, certainly convincing enough that thermal energy has increased in the play doh.
Today I finished up my packet for ETM, as always heavily borrowed from Kelly’s materials. I also added an introduction to energy bar charts that drew upon how I start the energy unit by summarizing the demonstrations and experiments that start the unit (described in detail here). Secondly, as shown above I wanted to add some problems where students had a force that varies with position and find the work done, and hence the energy transferred, by manually finding the integral. I like that this is closer to the definition of work as int(F dot dx), and that it doesn’t force (hehe) us to only deal with constant F situations.
(Note: This post should have been made earlier, I was quite behind in posting and got lost in the order)
Today I gave my version of Kelly’s Energy is Pain introduction to energy. For me this comes after 5 days of empirically showing how work produces changes in energy, though they don’t know those terms yet. I was careful to do two things in this process; first, I wanted to emphasize (and will keep doing so) that work is always done, though often it is within the system and we simply track the energy storage, not the changes due to work. The above picture illustrates this, as I had first (in blue) considered the air outside of the system, thus energy is transferred out of the system via work done by the air and then stored as thermal energy outside of the system, and then in green went back to what it looks like when we consider the air in the system, so that the work simply transfers the energy to thermal energy stored in the system. Same transfer, same storage, but the question is, are we tracking the storage or the transfer?
I slightly modified the typical money example for this purpose. I picked a student and defined our system as including both myself and the student. I said I had two dollar bills initially. Then I gave the student some money without stating how much, and then we both stated that we had a dollar each. Nothing left the system, but money was still transferred. Then I started over defining myself as the only part of the system. I stated openly that I am transferring a dollar to the student, and had him put it away. In that case we tracked my initial storage, how much left, and the final storage. In both cases the transfer and the storage were the same, but how we tracked them were different.