For the last couple of years, I’ve approach teaching energy from a conservation of energy perspective, deemphasized work, and focused on energy storage modes and transfer mechanisms. I think this has been very helpful for students, at least compared to starting with work and the work-energy theorem like I used to do. They understand the analogy as I pour water from the gravitational potential energy beaker into the kinetic energy beaker as the cart rolls down ramp. Students seem to more readily appreciate the idea that energy is always conserved, and, if a system doesn’t have as much energy as it used to have, we simply need to find to where it was transferred. It’s like a mystery.

This year, I’m trying to leverage as much of the modeling methodology as I possibly can which includes energy pie charts and bar charts. As usual, I started conceptually and avoid numbers. We drew energy pie charts for various scenarios. Here’s an example from the Modeling curriculum:

Students readily understood and easily created these visual models and seemed to appreciate that they could actually handle real-world aspects like friction. If an object was sliding across the floor, we would include the floor in our system so that the total energy in our system, and, therefore the size of the pie chart, would remain constant as energy is transferred from kinetic energy storage mode to the internal energy storage mode. No problems here.

We then moved to energy bar charts but continued to postpone introducing numbers in Joules calculated from equations. Students had little trouble with this visual representation. For the object sliding across the floor scenario, most groups continued to include the “surface” as part of their system such that the total energy in the system remained constant and no energy flowed out of their system. For a scenario where someone pushes a box up a ramp, some groups wanted to include the person in their system, but after a discussion of the complex energy transfers that occur within the human body, they decided to keep people out of the system and include energy flowing into the system.

We started having problems when we started calculating specific energies. Students continued to want to account for energy being transferred to the internal energy storage mode. So, for example, when asked to calculate “the average force exerted by a ball on a glove,” they would get stuck trying to calculate how much of the kinetic energy of the ball is transferred to the internal energy of the ball and how much is transferred out of the system by working. I felt like an idiot when my response was, “well, since we don’t have a model that can help us calculate how much energy is transferred to the internal energy of the ball and how much energy is transferred outside of the system, we’ll have to assume that all of the energy is transferred outside of the system.” The students looked at me with that expression of, “you have gotta to be kidding me; if that is the case, why have we been including internal energy all this time?”

Basically, we stopped including internal energy in our quantitative energy bar charts and always had energy be transferred out of the system. With the aid of this visual model, students would consistently solve relatively complicated roller coaster problems without making the typical common mistakes. I could honestly tell my classes, “those of you who drew the energy bar charts, solved this problem correctly, and those of you who didn’t bother, didn’t.” Despite this clear improvement over previous years, not having a clear rationale for why why we handled internal energy differently in the quantitative bar charts compared to the conceptual visual models was disappointing. I’m sure the students were confused by this.

Suggestions for next year?

geoffPost authorI posted an abbreviated version of this post to the Modeling List since a few more people read that list than my blog. I received a few helpful comments. I’m now believe that I’ve reconciled the disconnect between the qualitative and quantitative bar charts.

Next year, when solving problems quantitatively, we’ll quantify mechanical energy storage modes in our bar graphs and qualitatively represent internal energy for completeness. I’ll be able to rationalize this approach personally by keeping a multi-body system in mind and for my students with a careful definition of work. I’ll decouple the product of force and distance, which can be used to calculate the energy storage or transfer, from the concept of work, which is the energy transferred between the system and its environmnet. Sometimes the product of force and distance is work; sometimes not.

If you have participated in a Modeling Workshop and you’re not actively following the Modeling List, you’re missing out on some great stuff.

Jane JacksonGeoff, Thanks for referencing the Modeling Instruction website (http://modeling.asu.edu) and the Modeling listserv. (2300 teachers subscribe, most are high school physics teachers who have taken a Modeling Workshop). I will make a compilation with your post to the modeling listserv and the enlightening responses from Matt Greenwolfe and Gregg Swackhamer. I’ll post the compilation at http://modeling.asu.edu/listserv2.html . By the way, information about most of the upcoming Modeling Workshops nationwide is now posted, at http://modeling.asu.edu/MW_nation.html . Cheers, Jane Jackson, Co-Director, Modeling Instruction Program Department of Physics, Arizona State University, Tempe