Tuesday, March 6, 2012

LOL Energy Diagrams

As I've gotten more into using blogs and twitter as a teacher, I find that they are both such an amazing learning tool for me. This post will make a lot more sense if you read Kelly O'Shea's blog on LOL Diagrams.  As you can see by the comments I made I was taught a slightly different way of making LOL Diagrams in my modeling workshop (See here).

For the following problem:










Here's how I would use LOL's to solve it.  I would first state what objects are in my system (in this case, the spring, the cart, the earth, and the track). I would then  draw the following LOL diagram.











As you can see, the "L's" are exactly the same, however in Kelly's format, you show the objects in the system versus those out of the system.  In this style you show the flow of energy as you move from the initial state (in this case, the energy stored in the compressed spring) to the final state (the cart moving at the top of the loop).

Kelly later gives an example of what the LOL would look like if you do not include the spring within your system.  Here's my take:









Since the spring is no longer part of the system, some "outside object" is doing work on the system.  Also, since the spring is outside the system, it doesn't matter if it's a spring or a rocket or anything else, "something" is providing work to increase the energy of the system.  The way my thermo teacher in college summarized it, if you care what did the work, include it in your system, but then it's not work.

{If that doesn't make sense, if the source of "work" is the spring, then you would call it elastic potential energy or spring energy.  If it were a rocket, you would call it chemical potential energy. etc.}

If we go back and include the spring, but also include friction. Then your LOL diagram would look like this:









As I mentioned in my comment to Kelly's post, I think either method could work. To me, this method makes more sense given the "O" in between the "L's" since it shows how you are getting from the initial to the final state.  I think if you are using Kelly's method, the "O" should go before the first "L".

I'll be the first to admit that I'm learning a lot more from her blog, then I've even thought of sharing on this one.  Just wanted to try to show what I was trying to say.  I'd love to hear from other experience modelers as to which style they use.

3 comments:

  1. I used energy buckets, it ended up being very similar to LOL diagrams. Some of my kids liked the bucket analogy more and some liked the LOL's. I was glad that we did both and they got to choose what works best for them. I really need to post about the energy buckets. Perhaps I'll have some time during spring break. :/ Golly spring is so darn busy! Thank you for taking the time to post this Scott!

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  2. Thanks for the kind words Hope (?). I've heard of energy buckets, but never seen how they work in practice. Would love to see your post!

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  3. Thanks for putting up these examples. I was going to ask you to do that because I was thinking that I still wasn't understanding what you meant.

    But also, I think I still haven't succeeded in explaining the diagram (as used by my students, at least) to you. :(

    If you put the "O" in front of the snapshots, then how could it show how energy is entering or leaving the system between the snapshots? Often we draw LOLLL's (etc). You need to put an "O" between any two snapshots that has a change in total system energy between them. I think you're missing the point of what my students do with the system part of the diagram (the "O"). And in fact, I think yours is the one that could go anywhere. It is just a summary of what is already being said by the L's, so it could go before, in the middle, after, on another line. Wherever. There's nothing there that seems to need to be in between two snapshots.

    On the other hand, I respectfully, but vehemently, disagree with the idea that one shouldn't ever care what is doing work or doing heat (or doing radiation, I guess) on the system. One of the great things about solving with ETM is that you get to be clever about which objects you want to keep inside and which objects you want to keep outside of your system. You can choose a system so that there is no change in total energy (which we often do). You can choose a system so that you know how to calculate the work that would be done on it (another thing that we often do). If you don't care to know what is doing the work, then you've completely limited yourself to quantitative problems where there is no change in total energy. Or to ones where something helpfully (and mysteriously) has told you the amount of work or heat done in Joules. Either way, you've cut out the possibility of students tackling a lot of (most?) interesting problems that they see day-to-day. No offense to your thermo teacher. But I'm not going to purposely make this magical for the kids by alluding to "some 'outside object'".

    And while I believe that you were taught this at a modeling workshop, it is inconsistent with later materials (like in the oscillating particle model where it has them draw an LOLLLLLLLL and asks why they don't need flow diagrams between the other L's (there is only work being done between the first two)—in your method, it seems like there should be one between any two snapshots if it is supposed to show everything that happens between the snapshots). So there is probably a lot of variation in what modelers are doing with energy.

    It just seems like your flow diagrams are really limited to only showing step-by-step changes in how energy is stored. But most problems have more complex changes (the amount of kinetic energy and spring interaction energy is changing simultaneously; there is a continuous increase in thermal energy rather than a sudden isolated incident; gravitational interaction energy and kinetic energy are both decreasing; etc). So it seems like once you get past the first couple of days of using ETM, the flow diagram would become incredibly complicated (and incredibly tedious) to draw.

    Anyway, I don't think there's any particular "right" way to diagram how energy is stored in different snapshots of a situation. (Though there are certainly an infinite number of wrong ways, yeah?)

    Hey, when the kids get back, I'll show this other LOL manifestation to my Honors class (already pros at using ETM) and find out their thoughts about it. I've done that a few times this year (told them about other ways people do various aspects of what we've done and asked for their opinions) and they've had really good, thoughtful things to say. I'll get them near the end of March.

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