Building the Energy Transfer Model

Hey guys, bring a pencil and a calculator next door. I want to show you something that’s been bothering me a lot.

Springs are strange

I’ve been thinking a lot about springs.

They’re sort of odd, you know? When you hold them like this [hold spring looped to one finger on each hand and stretched a bit] and then like this [same as before, but move hands a farther apart so the spring is stretched more], there’s definitely something different. Right? [Right.] But Newton’s Laws (great as they are) don’t seem to cover it completely. I mean, everything is at rest both times, so the forces are balanced both times. [Right.] But something is definitely different.

What’s different about the spring?

So I have an idea about how to visualize what is different when a spring is stretched more or less. I was thinking that we could attach the spring to a cart. The spring would pull the cart as it “unstretched” and make the cart speed up.

We could do the same thing to two carts at once and see the difference in the effect on each cart. So it would be a sort of cart race to compare the spring effects.

We could use the “special” box of springs from back in the balanced force unit. Remember when we found the spring constants for them (during the Fs lab)? It will be convenient to already know those values.

If you open up the new packets to the first inside page, you’ll see that I put in spring force (vs spring stretch) graphs based on the data from your experiments back in September for these two springs (the two different versions of the longer spring in that box).

[Hand the two springs to one kid.] So which one is spring 1? [After a couple seconds, the kid realizes that she can figure that out from how “stretchy” the springs are and identifies spring 1.]

Spring effect on carts

Great idea: we could use two different springs in our race. If we could get them to give the same spring effect to each cart, then we would have a foothold in identifying what it is that’s different about the springs when you stretch them more or less. [Kids seem to think this is at least a decent idea. A minus of this experiment is that I’m not setting them up to have the great ideas about what to set up, though they do get to have the great ideas about how to get the carts moving with the same speed.]

We need two people who are going to be very careful in making measurements. And each of them needs a backup person to watch what they are doing and double-check the measurements. [Eventually two kids will agree. Usually, though, everyone knows who the careful measurers are, so they pressure them into doing the job. I use the names of the kids a lot to help everyone keep track of which spring/cart we are discussing, so let’s name them Aaron and Bertie for the purposes of this post.]

Okay. The springs are hooked onto the carts at one end and onto paperclips tied to strings at the other end. I will hold the ends of the springs. Aaron and Bertie will move the carts so that the string is just barely taut. Then they will pull the carts back to stretch the springs. Make sure you look at the edge of the cart to measure the stretch, not the spring, because it will be easier to be precise in moving the cart.

Now we need an idea for how to stretch the springs so that they will give the carts the same effects.

[The first suggestion is almost always to give them the same stretch. Sometimes students will quickly dismiss that idea because the springs will have different forces. Even when they dismiss it at first (and then almost definitely decide to try the same force first), they usually then try the using the same stretch second (thinking maybe they were wrong that the different forces would matter since the same force didn’t work). Overall, there are four usual suggestions. All four of these usually get suggested (though not all at first).]

Same stretch (run on the graph)

Okay, good idea. So let’s have Aaron and Bertie both stretch their springs 10 centimeters. The backup person should watch what they are doing and make sure the stretch is really 10 centimeters.

Remember 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 careful at their motion relative to each other (not for which one reaches the end of the track first).

Ready? On the count of three… One, Two, Three!

Huh. That didn’t work? Let’s try that again. [When I say that, the kids often say something like, “Was it supposed to work?” They’re so used to verification labs, even at the end of the first semester (or close to the end of the year in my regular class) that some are already willing for you to just tell them what was “supposed” to happen. Yikes. I respond, “I’m not sure. Let’s try it again one or two times to make sure we keep seeing the same thing.”] Wow. Bertie’s cart wins every time? [At this point, someone will note that the forces are different so it isn’t really surprising that Bertie’s cart would win. That leads us to the next idea…]

Same force (rise on the graph)

That makes sense. So let’s keep Bertie’s spring stretched to 10 centimeters. How much should Aaron stretch his spring? [Give them a few minutes to sort that out with the graphs.] Okay, so Bertie is stretching her spring how much? [10 cm] And Aaron is stretching his spring how much? [20 cm] Okay, ready to try it? Backup people, make sure to watch them measure.

Huh. That didn’t work either? Let’s try that again. Last time, Bertie’s cart won. This time, Aaron’s cart wins. So, at least we know that there must be some way of making them equal in between those values. But neither the run nor the rise worked for making that happen.

Well, is there any other feature of a graph that we’ve found to be physically meaningful? [Almost every time, the first answer will be to make the slopes equal.]

Same slope

Great! We’ve definitely seen the slope of a graph represent physical quantities before. So how do we change the slope for the spring? [After a few seconds, they will realize that they already know what the slope represents and that they can’t change the spring constant without changing the spring. Back to the drawing board.]

Okay, so not the slope, then. Any other features of a graph that we’ve found meaningful this year? [It often takes a minute or two for them to think through this idea. They will usually either say area (yay) or displacement (boo… they think displacement is a word that means area on a graph, not a word that means change in position for an object).]

Same area

Another good idea. Let’s keep Bertie’s spring stretched to 10 centimeters. What’s the area under her spring’s graph if the spring is stretched to 10 centimeters? [Give them a few minutes to figure that out.] Okay. So we need to figure out how much to stretch Aaron’s spring so that his graph will have the same area. [This is absolutely the toughest part. In Honors Physics, some to most of them will figure it out without much prompting. In regular Physics! class, they usually need a lot more guidance on how to set up that kind of calculation. I relate it back to kinematics problems where they knew the slope (acceleration) and area (displacement). They have solved many problems like that in the same graphical manner. I might also briefly mention the ACT science section and applying graph skills to new contexts to make that connection for them.]

[Check that each person knows how much to stretch the spring.] Should we try it? Alright!

Hey! That looked pretty good! Let’s try it again and make sure it really works. Cool! [And yes, they are pretty psyched that they’ve found a way to make the spring effects the same for both carts.]

So… do you think the area has a physical meaning?

What other graphs have we used this year that had areas with physical meanings? [velocity-vs-time graphs (change in position), acceleration-vs-time graphs (change in velocity), force-vs-time graphs (change in momentum)]

How about graphs that didn’t have physically meaningful areas? [A few will quickly mention position-vs-time graphs as they have tried to use that area for something before!]

So each of those areas has always shown us a change in something. Interesting.

Do you think the area on this type of graph has a physical meaning? [Well, yes.] Why? [The carts had the same speed when we made the areas the same.]

At this point, we’re coming around to the idea that the area on this graph (a force vs displacement graph) represents a change in something meaningful. Having cleverly read the front of the packet, they will always suggest to call it energy. The big idea here: the area on a force-vs-displacement graph represents the change in energy. Some smaller ideas (like energy being transferred to the cart by the spring) are starting to percolate. We’re about out of time for one day, though, so we’ll have to keep building this model next time.

Follow-Up Posts in the ETM series:

This post details the first day (about 40 minutes) of my energy unit. We have just started building the model. There are a few more steps to piecing this whole model together (building a common vocabulary about energy and two new representations), and I think they warrant separate posts. I will update this post with the links as the next few are written.

* Common types of energy (ETM Cheat Sheet)

* Drawing energy pie charts

* Drawing LOL charts (Energy Bar Graphs)

15 thoughts on “Building the Energy Transfer Model

  1. I have to say when I read your posts I always feel like I was cheated by my physics education. I /never/ had a class where we learned to solve problems graphically (using slopes & areas). They may have been mentioned but that was about it.

    Personally, I find it much easier to visualize what’s happening through the graphical approach rather than simply plugging in some numbers into equations. To be honest, when I wrote my post on Hooke’s Law (, I didn’t realize the area under the graph was the energy. I mean, it makes total sense, but I’d been “trained” to not think about things like that. As usual, good stuff. Looking forward to the rest of your series. :-)

  2. Mr. O’Shea-

    I am interested in implementing the modeling process into my physics class (maybe chemistry too). Do you have any books that you could recommend that I could read about the modeling process?


    1. Hi there!

      There are a lot of resources on the Modeling Instruction website. The site can be a bit of a maze, but it is worth the investment of time clicking around because there is a lot of great content in there.

      And let me know if you have other more specific questions that I could try to answer.

      Kelly. (who is a Ms., not a Mr., just by the way)

  3. Kelly,

    (Sorry, this is more of a general question) I have been a Modeler for about 8 years, and I am going to use sbar for the first time this fall. You or @fnoschese may have a post on this that I have not seen yet. As a modeler, I am wondering if anything has changed with whiteboarding homework when using sbar.

    Currently, we have the investigation and build the model. During model deployment activities, the students are whiteboarding the work they did the previous day/at home. There are many times when the questions are extensions of what we discussed in class. My expectation is that students will attempt the problems in order for them to participate in (or at least follow) the whiteboarding discussion. Ultimately, I see the homework as some practice, but also new learning as they work through the problems in their heads. The discussion then clarifies and solidifies the model they were unsure of when they first saw the questions.

    While there are always students who do not attempt the work, my concern is that I will have many more students choosing not to do the work that night. They will come to class expecting someone else to put the answers on the whiteboard for them, and they will then reap the rewards (in their minds) of getting the answers with little mental effort. I know that these students may not gain the understanding needed to demonstrate the standard, but wouldn’t this impact the level of involvement in the class discussions?

    I guess I am asking if you have seen any issue with this or if you have adjusted your review of the modeling activities away from the basic whiteboarding presentation we see in the the workshops.

    1. Hey Kris,

      Thanks for the great note!

      I actually am not very big on homework these days. I assign some problems from the packets during September so that I can wean them slowly off of assigned homework and because they aren’t yet ready to practice on their own. After that, the homework is more guided by what they need to do to become more proficient with each standard.

      Most days in class are spent working on problems and/or whiteboarding problems. I basically have them work in a sort of “individually together” manner at tables, then have groups whiteboard different problems once everyone has worked on all of them. So I basically have no problems with that at all.

      My regular classes would probably go a little faster if I assigned homework (but I would also lose a few students who would never do any work outside of class and would therefore get little out of our class time). My honors classes wouldn’t actually go much faster if I gave them homework (based on my experimenting with/without). If you can get them really into using the class time well, not assigning homework doesn’t seem to slow the class down.


      1. Hi Kelly,
        I am leaning this way as well, as far as homework goes. I only have one physics class and the students who take the class have a very wide range of abilities as well as homework habits. So, I have made the decision to have very little homework and have them spend their time learning the skills in class.

        The big move this year is toward standards based grading. The problem, I really haven’t sat down and studied it enough to feel comfortable using it. The plan is that I am going to sketch it out on paper, type it up and then run it by several people before I put it in my classroom.

        Thanks for your help!

        JoAnn Flejszar

  4. I did not look through all of your packets of materials, but it looks like you have reduced the amount of problems from the modeling material by choosing more representative samples of the problems. When the students need extra work, do you typically make up some problems, have them make them up, grab some out of a book, or just have additional ones made and waiting for the need?

    I think that working the problems in class would be the best way to further student understanding right away. A relationship more like the coach than teacher, which is what we are trying to create. Unfortunately, I only have 53 minutes in a class period and up to 38 students (12 groups) which is enough time to assign and go over a set of whiteboards. It would take two days to work and go over one set of problems if I kept the same type of situation. However, I can see that if they are worked in class, we would probably only need to present and discuss a handful of problems from each set. (thinking out loud here) I feel like I would still provide 3-5 problems for practice at night that can be discussed the next day even if many of them do not do them. It may not be a class discussion, but more of an individual one or small group one as they are working on whiteboards.

    Thanks for your comments. You have provided so many great thoughts and resources for teachers looking to make the switch to modeling, SBG, or both!

    1. I think I have a modified set of problems (stolen from a lot of places, including Matt Greenwolfe and Mark Schober, plus books, and my own brain), but not really a smaller set of problems. I don’t have the same set of worksheets that the official materials do, that’s for sure. I just try things out, see what helps guide them along the path of building and understanding each model, then refine a bit each year. There are some extra problems on our class website (with answers, but not solutions, provided). They mostly ignore those until they realize that they really need to test on some particular standard, then they usually go and print them out and work on those. I’ve talked more about how I handle “homework” in the not assigned sense elsewhere, though I probably need to make a more specific post that really talks about how that has worked in my classes the past year and a half.

      In the packets, I don’t think of the problems for each unit as sets or as fitting into particular class meetings. It’s more of a continuous thing that we work through.

      But anyway, back to you—I can imagine a couple of scenarios that might fit what you’re trying to do. Here are the first couple that came to mind:

      1) Split the problems you want to use into in-class and out-of-class problems. Make sure the in-class ones hit all of the most important parts of the story because some kids will only do those (for various reasons, including just making poor teenager-type choices about when/how to work—which they should be allowed to make and still have space to recover later). At some point during a class after homework has been assigned (probably doesn’t need to be every day, right?), let’s say at the start of class for this hypothetical—students come in and know that they should go to one spot or another in the classroom depending on whether they’ve worked each problem in the homework or not. At both spots, the answers (not solutions) are available. They have maybe 7 or 10 minutes (or something that makes sense) to either work on a problem (if they haven’t done them) or discuss problems with their classmates (if they have done them). Since the answers will be available right there, they know where to focus the short discussion. Then move back to normal places in the classroom and on to the next part of class.

      2) Give a set of recommended problems for each unit that can be worked outside of class (or in class, on days when they have finished ahead of their peers, if they want). The homework is optional, but if they work on it, they can turn it in to you for feedback. They can work together with classmates (or anyone else) if they want, but they can only get feedback on problems that they worked on their own. They can come and see you (assuming there’s some easy office hours-type time for that to happen) to talk about problems that they didn’t work on their own, but you only give feedback on their completely individual work. They can submit as many of the problems as they’d like. They can even submit them after a test on that unit (which is helpful in SBG since they will need to test again on skills they haven’t mastered). I did something like this my first year with SBG, and it worked really well. A few kids did the “homework” before the test (back when I was giving unit tests, which I don’t anymore). A large number of kids did the homework after the test and before they wanted another chance at the standards. This method doesn’t take up class time, and it gives the kids more control over their homework. It might even get some to see the value of practicing before testing… eventually!

      Probably a few other ways to make that work. I know Matt Greenwolfe has separate in-class and out-of-class problems (if you look at his materials, he’s split them into “whiteboard” worksheets and homework worksheets).

  5. Hi Kelly,
    I’m excited to try this set-up for energy…springs are such a good way to start! Do you have any specific info you could pass on about the Fs spring lab you allude to doing during the BFM unit? I’m curious how you set that up but didn’t find any write-up in the modelling packet. Thanks for your advice.

    1. I’ll have to write up a blog post at some point that outlines the Fg and Fs labs that my students do during the BFPM unit. Here’s the super short version:

      In a very circular/hand-wavey way that bothers me but does not bother them, they basically stretch various springs horizontally with spring scales and graph the spring force vs the spring stretch (not length).

      Does that help? Or too short? :)

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