Energy Bar Charts (LOL Diagrams)

“LOL diagrams are my life.” —Honors Physics student from 2010

I have to admit, first of all, that I wasn’t expecting to love energy bar charts (when I first heard about them). I didn’t originally learn to solve energy problems that way, and when I first saw them, I thought it was a silly waste of effort. I especially hated the name (“LOL diagrams”), thinking it just served to emphasize how ridiculous the entire exercise was.

When I tried them with my classes (silly as they seemed, I wasn’t going to ignore them entirely until I found out that they were useless for the kids, too), I was shocked at how effective they were at helping students structure their thinking about how energy is stored, how energy is transferred, and how energy is conserved. The next year, I used them with my Honors Physics students, too. Those classes couldn’t believe that I could have ever taught energy without them. More importantly, when we started tackling more difficult energy problems later that year (calorimetry problems, etc), those students found the new problems to be trivial. They immediately just drew LOL’s and were able to solve the problems every time. The year before (with an incredibly strong class), that topic had been one of the hardest of the year. I was sold.

What are LOL diagrams?

I’ll lay out the first few LOL diagrams that we draw in class. To start, we take this first problem and work through it a few times (the first couple times together, then I let them do the other variations on their own, then we whiteboard them). I’ll put the diagrams first, then outline some of the features below.

A car on a frictionless roller coaster track, launched by a huge spring, makes it to the top of the loop.

With each LOL, we also practice using the diagram to write an equation for the conservation of energy in this situation. So after making that sketch, we update it like so:

Now we tackle the same problem, but we put the spring outside of the system. Energy must be transferred into the system by the object outside of the system. We call this idea of transferring energy into or out of the system “doing work”.

What if we take a different snapshot?

Let’s look at the same initial (spring compressed, cart not yet moving), but change our final snapshot to the cart when it is only halfway up the loop.

Let’s make this LOL make sense with respect to the ones we were drawing for the original situation so we can compare the amount of energy stored as K, Ug, etc.

Enough with the examples for now.

LOL diagrams are a way to represent how the energy is stored in the chosen system during various snapshots and to represent any changes in total energy for the system. Each “L” represents how the energy is stored during a particular snapshot (instant). The “O” shows the objects inside and outside the system. If there are any objects outside the system doing work (or doing heat or, I suppose, doing radiation (though that doesn’t so much come up in my class)), that object is written outside of the “O” with an arrow connecting it to the system and showing the direction of energy transfer. The arrow is labeled with the type of interaction that is causing that transfer of energy (in the example above, the interaction is the spring force (Fs) that the spring exerts on the cart). Even though we don’t start calculating work done right away (we stick to a bunch of qualitative problems at first to work up our LOL chops), getting the habit of labeling the type of interaction is really useful for later.

Oh, and in case it isn’t apparent already, the name “LOL diagram” is descriptive of the shape that the diagram makes. Students love this diagram not only for its utility in setting up solutions using the energy transfer model, but also because it has (what they consider to be) the most excellent name of any of the physics diagrams. After seeing how great they are in action, the name has stopped bothering me, too.

Another great feature of LOL’s is that they are extensible to showing multiple (more than 2) snapshots in the same diagram. So you can have LOLLLLL’s or LOLOLLL’s, etc (with the subsequent O’s only being necessary if the total energy of the system changes between later snapshots).

A quick example: An object is launched upwards using a compressed spring.

We’ll take snapshots at each of the three times shown in the figure.

Conservation of energy equations could be written for any pair of snapshots (L’s) if you were to keep going and do some quantitative work with the problem.

For the rest of this post, I will outline some of the best tips I have for making good use of the diagrams with high school physics students. These are all tweaks or changes that I have made over the past 3 years in the way that I present the diagrams to students.

Keep it quali-quantitative

For a while, I drew my diagrams with bars where the heights were qualitatively important. I noticed that even though I talked about doing that, and even though I did in fact always do that myself, my students almost never did. It generally led to them drawing LOL diagrams that looked “unbalanced” even when energy was not being transfered across the system boundary. They had a lot of trouble with the carefulness required to make those very qualitative drawings work.

Last year, I started having them always divide bars into blocks (as I drew above). That made easy to see whether the drawing was meant to look “balanced” or “unbalanced” since it was always easy to count the blocks.

To keep it clear, I suggest that they draw half-blocks as triangles (as I did in one of the diagrams above). There is no guessing whether a particular block is supposed to be shorter than others or whether the drawing just wasn’t very precise.

Oh, and the “x” on the axis means, “I’ve thought about it, and this is zero.” It keeps the chart from looking like it wasn’t finished.

Thinking back to the blocks, it is also best (in my experience) not to have them represent any actual amount of energy. That is, if there are 3 blocks drawn of K and 1 block drawn of Ug, that doesn’t necessarily mean that there is 3x as much energy stored as kinetic energy than as gravitational interaction energy. Students sometimes really seek to make the graph extremely quantitative, but it ends up being a crippling desire. They should usually be able to draw the complete LOL before knowing any actual numbers in any problem. And when they try to make it extremely quantitative, they end up drawing (or finishing) the diagram at the end of their work (so that it will be “right”) and completely lose the value of drawing the diagram in the first place.

Really, only the change in the amount of energy stored as each flavor matters when diagraming the problem.

So in sum, the diagram is always a qualitative one since the blocks don’t necessarily correspond to a specific quantity of energy.

And the diagram is quantitative in the sense that the total number of blocks in each snapshot does matter. If energy enters the system, there should be more blocks in the subsequent snapshot. If energy leaves, fewer. If there is no total change in energy for the system, then the total number of blocks should be the same in every instant.

Practice the conservation equation

In my experience at least, students have a MUCH easier time of things when they write one big equation from their LOL and use it to solve the problem by plugging other details into the One Big Conservation Equation (rather than getting caught up calculating a million tiny things using the little energy formulas all over the place). It helps them organize their approach and not get lost in the details once they start algebra-ing it up.

So starting this year, I had them practice writing the equation (as I did in the images above) for all of their qualitative LOL’s. So far so good (with Honors Physics). The real test will be to see how much this helps out the regular physics classes (getting there soon after spring break). It helped quite a lot last year when I had them go back and try it (on qualitative problems) once we were halfway through the unit (and struggling mightily).

Calculating the work: Use a graph

Calculating the work by always using a graph (we actually don’t even have an equation for it at all in my Honors Physics classes right now) came about through two things: 1) my trying to embrace graphical solutions wherever feasible and 2) hoping that it would help them understand the value of putting a spring inside the system (and keep them from calculating work that a spring does with Fs*∆x using only the initial (or final) value of Fs—a common trouble for students in previous years).

This move has been a huge success. They seem to have a better understanding of what they are doing. The spring-work problem is basically gone.

Here’s quick screenshot of some student work from this year showing an LOL and a graph calculating the work done. It is missing the label on the arrow, but otherwise looks good (there was more to this problem, but I just grabbed the relevant bit).

Model it correctly

Last bit of advice: always draw your own LOL diagrams correctly (with every detail drawn in that you would want them to draw). I sometimes found this tough when I started using them because I had another way of thinking about it in my head. But when it comes down to it, most of the students will do it the way they (think they) see you do it. If you skip steps, they will skip steps (though maybe not always the same ones). You understand the concepts well enough to skip the steps, but they don’t, so they will just have holey understandings and have trouble doing energy problems (usually the same trouble they would have had if you’d just done this all with equations and no diagrams anyway, so doing it poorly probably isn’t overly harmful, just not helpful). So. My advice is:

ALWAYS write in your system. Try to do it first, before drawing any of the bars.

ALWAYS label the arrow as an object exerting a force on the system when there is work being done

ALWAYS draw the LOL before jumping into equations

The hard part of solving any problem should be drawing an accurate and relevant diagram. Turning the diagram into an equation is super easy. Writing an equation with no diagram (or a cursorily drawn one that skips steps) is as hard as drawing the good diagram, except now with bonus difficulties of abstract symbols, easy-to-make sign mistakes, etc. So load the physics into the diagram and let the algebra be easy and sort itself out from there.

34 thoughts on “Energy Bar Charts (LOL Diagrams)

  1. At our workshop, we were taught to show the flow of energy as you go from the initial to the final state. For instance, in the first example:

    E(elastic) -> E(kinetic) -> E(gravitational)

    I’m sure there are many ways to name the different forces (spring vs elastic…), so I’m in no way squabbling about them, but I’ve found that have them show how the energy is flowing gives me greater insight into how they think the situation is progressing. Just like you make them write the equation afterwords, I also make them identify the system before the LOL diagram. Basically I keep the LOL as a completely separate tool from the system schema. I think it can work both ways, but to me, you should have the “O” first if it is merely a tool to show which objects are in the system.

    I only been using this for one year, so I’d love to hear what others think, as I could easily be wrong.

    1. I’m there there are many different good ways to accomplish something similar. I’ll try to be more specific about what we do in my class.

      Your arrow diagram sounds more like pie charts (I haven’t written that post yet, but it comes before LOL diagrams). Do they continue doing that all year long, even after they have become pros at solving problems with ETM? Or is it more of a stepping stone (as pie charts are for getting to LOLs)? Also, it seems like it would only work for cases where the energy is all stored as a single flavor, then all stored as a different single flavor. Or I’m missing something.

      The “O” is definitely not a system schema (see forces post to see how we do system schemas). Though Matt Greenwolfe does actually put a system schema in the center, not an O. But I think that’s more work than is necessary (for where my students are at this point). And yes, the O certainly does come first. But it also needs to be between the two snapshots so that it can show energy being transferred into or out of the system (aka “flowing” into or out of the system). A system schema is definitely a completely separate tool. I don’t find that my students still need it at this point (though in the regular classes, we might draw it once in a while during an energy problem, still) It is not merely a tool to show which objects are in the system. It shows how the energy of the system is changing or not changing between the two snapshots.

      Hopefully that helps make more clear what I was trying to talk about. But keep asking away! 🙂

  2. The way they explained it to us, it’s not a pie chart, it’s an energy flow chart. You show the path the energy takes. If work or heat are occurring, you show it entering/leaving across the boundary with a Q or W outside and an arrow across the circle in the direction of Q or W.

    As far as I know, the pie charts just show how much (what percent) of each flavor of energy is present in a given situation. We were told the “O” shows how those flavors are changing by showing the pathway of energy. For the first example, the energy is initially stored in the spring, as the cart begins to move, the spring energy is transforming into kinetic energy. As it starts to go up the loop, some of that kinetic energy is becoming gravitational potential energy. Thus the flow of energy is entirely inside the system and all three letters would be inside the circle. If friction is included, you would have a second branch coming off of kinetic energy for (what our workshop leader called) internal energy. If that internal energy later escapes outside your system, that branch would leave the circle as heat. {Since you don’t care where it went (or else that object(s) would be part of your system), it’s labeled “Q”}

    To be brief, you’re visually showing how the energy flowed as your system went from the first “L” to the second.

    1. Hmm. Interesting. I think for where my students are, that seems like an excessive amount of writing for each problem (as does putting an entire system schema in the middle instead of the “O”). So your “O” doesn’t show the objects in the system at all? Just the types of energy, again, with arrows? Isn’t that information all already conveyed through the initial and final “L” in the diagram? How many snapshots do you tell them to break that into between the two snapshots you chose? And if you don’t care what (outside of the system) is storing the energy, it seems like you are losing something huge in terms of understanding (and tools for figuring out whether energy is really being transferred in or out or not at all).

  3. You ROCK Kelly! These are very helpful, and a little un-nerving to read, since it sometimes (often) points out things that I could have done much better. Your posts are so valuable and I know will help me become a better modeler. Thank you for taking the time to do this.

    I also used an analogy of energy buckets, which when we draw them out, as we always do, look almost exactly like LOL diagrams. It is nice to give the kids both tools, and have them choose in the end which one makes more sense to them. I’ll write a post about the buckets, but probably not till my spring break in April. Sorry.

    1. Thanks. I’d like to see your energy bucket diagrams (no hurry—I totally understand—this post only finally happened because we are on our spring break).

      LOL’s are one of the best additions I’ve ever made to my class. Honestly. The first year that I used them in Honors, we hadn’t really switched over to Modeling yet. We were mostly doing the old curriculum that we had, but we did one unit of Modeling-like work for energy. Before the unit test, the kids told me that they thought I had “done a really good job teaching [them] energy” and that they “really get it”. And they really did, as evidenced by how easy energy problems were for them compared to (a) all the rest of the material that year and (b) how hard energy problems were for students in the couple years before that. Now my former Honors kids go to their Honors Chemistry class the next year and convince their new teacher to that they should be drawing LOL diagrams for problems there. So apparently they really see this as something über-useful (and not just something they’re doing because I ask them to do it). 🙂

  4. I like how your circle defines the system and how energy can flow into and out of the system from the surroundings. This reinforces the “system” concept and the ” surroundings” concept. I use the same method, but did not list the objects in the system in my circle. I will from now on.

    One suggestion that I have is to show your arrows going into and out of the system as bars with an arrow head on the end. For example in your third diagram the work done by the spring would be a 4-barred arrow going into the system.

    Thanks. I learned a lot (and I like the LOL descriptor).


  5. I’ve been thinking about your LOLs a lot the past couple of days and I’ve come up with a question that I think I would have a hard time with if a student asked it to me: “Why is the earth always in the system”, or phrasing it differently: “Could I put the earth outside the O”. I might be overlooking something (and I haven’t done a modeling workshop since I’m not a US resident), but I find it quite hard to answer in a way that’s intuitive for a high school student.

    Take the following example: a cart is cruising along a frictionless path (not caring about how it got its initial speed) and then comes to a halt when colliding with a spring *snapshot*. We would say that kinetic energy of the cart has been converted into potential energy of the spring. This works with the spring inside or outside of the system (allowing for work being done on the cart).
    Now throw a ball into the air. The same kind of conversion happens, but now we say that kinetic energy of the ball is converted into potential energy…of the ball. By doing this I feel as though we are giving the earth/gravity a special place in our analysis that hasn’t been justified yet in the students view (even though most students would just copy/paste my behaviour and not ask the question, which is more comforting to them hehe).

    1. These are great questions. I usually have students practice LOLs in as many ways as they can. I encourage them to take different objects out of the system to see how they affect the way we would represent energy being stored and transferred. I think it’s totally okay to take the earth out of the system (it would then be doing work on the ball—negative work on the way up, then positive work on the way down). At some point, they will try taking the ball out of the system and see that they’ve broken their diagram at that point (and that helps them find the edges of the usefulness of the model, too, so it’s a good thing for them to try sometime).

      I’m not sure whether I’ve answered your question here. If I haven’t, can you say a little more about why it would be a problem to take the earth out of the system (and then I’ll try again)?

      1. Hi Kelly, I was trying out some variations on the situations you mentioned in your post to see if I understood the way the LOL diagram worked. Referring to the thought experiments I described earlier: I did it for the cart-spring system and then could easily take the spring out of the system. I got a bit stuck when I tried to do it with a ball thrown up and the earth outside the system. Maybe the easiest response would be to show me your LOLs for that situation.

        It has to do with the way we usually talk about energy (and that might be where I’m going wrong). When the cart is cruising along, it has kinetic energy. When it hits the spring, the kinetic energy of the cart is converted into potential energy of the spring. This works well with the spring inside or outside of the system, those LOLs make sense to me. We also have an easy time identifying the spring as a solid, concrete, real object.

        I can’t figure out a sensible LOL for a ball thrown up in the earths gravitational field, with the earth outside the system. As the gravitational field does negative work on the ball is loses kinetic energy and we say that THE BALL gains potential energy. In the spring-cart example, we attribute the potential energy to the spring, whether inside or outside of the system. With the ball-earth example, we attribute the potential energy to the ball. Maybe that phrase is only valid when tacitly assuming the earth is inside the system. Trying to draw a LOL with the earth outside the system, I find that when using the same phrasing I end up with unbalanced LOLs. The ball looses kinetic and gains the same amount in potential energy, which would seem twice the amount of work done by the gravitational field.

        I’m sure drawing this up would be much faster than trying to describe it…I hope you get my line of reasoning and can point me to where I’m going wrong with this.

  6. I’ve been trying to be a modeler for a few years, but there was quite a bit that we did in the workshops that I couldn’t get my head around the “why”, which meant that I did a reall Half….., well you know what kind of job, doing the activities…

    Now I know the WHY, and what the exercise is trying to do, that I am now going into the LOL charts full bore… THANK YOU!

  7. Thank you for the insightful blog post. I’m currently a learning assistant in an introductory physics course. Next week we will be introducing our students to LOL diagrams. I plan to use the advice you’ve given when showing students how to use this approach to solve conservation of energy problems.

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