Diagramming Energy Theater

Yesterday UE1 did Energy Theater for the first time, and after that, they were invited to diagram what their group had done. I wasn't there at the time so I don't know exactly how the exercise was introduced; Lindsay said it was pretty open-ended. I think the diagrams that they produced were fantastic. Because I am interpreting their diagrams in light of my own diagramming conventions and convictions, I am going to talk about my own way of diagramming Energy Theater first.

I have become attached to a form of diagram that I call an Energy Tracking Diagram. (UE1 calls any kind of diagram that records an Energy Theater performance an Energy Tracking Diagram, but I'm going to stick to my special label.)

• Individual units of energy are represented as individual letters, with the specific letter representing the form of energy.
• Energy transfers and transformations are represented with arrows. All arrows have a letter at the head and the tail. Arrows that have different letters at the head and the tails indicate transformations. Arrows that cross the boundaries of object-areas indicate transfers.
• The process by which a transfer or transformation occurs (e.g., mechanical work, conduction) is indicated by the color or pattern of the arrow.
• Time order of energy processes is represented by sequences of arrows. (The time order of processes that occur along separate tracks is not represented.)
• Relative amounts of energy may be represented by duplicating letters or tracks, or by adding coefficients to the letters representing energy.

Here is an Energy Tracking Diagram (ETD) that I drew for a basketball being pushed down underwater at constant speed. (If you are concerned about my having put the G's inside the objects, feel free to ask me about that.)

Abby has other examples on her blog; here is a PowerPoint version of an ETD for a compressing spring.

Now to the teachers' diagrams! In this post I am going to focus more on the representational features and less on the substance of the physics ideas that is represented. To examine a diagram more closely, click on it, and you'll see it full size.

(Bummer about the glare on this one.) At first, looking at those converging arrows on the left side, I thought they were not conserving energy (four units of energy going into one). But then I saw that the four units of energy are all there in the cart - just not at the end of that particular arrow. Instead of prioritizing that each energy unit follows a "track," this diagram prioritizes the physical location at which the transfer occurred: the contact point between the finger and the cart. Renee Michelle says that in their ET, they all pointedly (ha) walked through the finger. Thus it makes perfect sense that they drew the objects instead of drawing schematic areas the way I usually do. Another thing I notice about this diagram is the use of color in the arrows. For them, color indicates form. In the letters, this is redundant (because which letter it is already tells you the form), but in the arrows, the color shows that the energy starts out as one form and transforms at a certain spot (the black "transformation point") into the other form. So the arrows, for them, represent the energy, whereas for me, the arrows represent the kind of process by which energy transfers or transforms.

This one doesn't show the path each energy unit takes; instead, each energy unit gets an identifying number, which has a corresponding number in other objects. So there is a C1 in the hand, a K1 in the car, and a T1 in the air. It seems that K1 goes to S1 and K6 goes to T6, so the energy units are treated as though they were traceable individually. The big block arrows seem to represent forces (one is marked R, maybe for resistance?), and the thin black arrows seem to show energy transfer. As in the first diagram, letter-color is used redundantly with the letter itself to indicate the form of energy. (It's less apparent in this diagram because two of the forms are black, and one is dark blue.)

This one uses schematic areas instead of pictures of objects, and shows energy tracks. I find it hard to follow visually - the criscrossing lines and the fact that they are dotted makes them look like a maze of snail trails to me. But I believe they are used consistently. What interests me about this diagram is the fact that the car appears twice. What's with that?

This diagram helps me make sense of the other one, because the air and the car are shown twice, so now I understand that I am being shown a kind of a time sequence. First there is the hand; then there is the car moving on the floor through the air; then there is the stopped car sitting on the floor in the air. This suggests to me that in this diagram the swirly arrows are time arrows; the energy in the car goes to the future car. 

This diagram seems to have a similar form: a sort of time sequence, but with not all of the objects present at each time - only the "spotlighted" object. This representation reminds me of energy discussions I've seen in the context of Rube Goldberg machines, in which people think of the energy as almost being passed like a baton from one "active" object to the next.

This one is a more explicit time sequence. This group uses coefficients to indicate quantity, rather than repeating the letters as the other groups do. They use a delta symbol to indicate a transformation (maybe  because it means "change"?) and an arrow to indicate a transfer. Again, both letter and color indicate form; coefficients are written in a distinctive color.

Every single diagram shows the energy being conserved, supporting my conviction that once you start using the substance metaphor you pretty much can't help conserving energy. I'm curious what's going on with thinking in terms of partial time sequences, since it seems to be popular this year.