# Transitioning from Energy to Momentum

In my college level physics class we study Energy right before momentum. I really like this, particularly because we can begin our study of momentum as driven by the fact that a pattern emerges from data that is not explainable by Energy.

On the first day of my momentum unit I typically do a fun car crash activity to help students start thinking about how force and time are related in collisions. The next day we start building the momentum transfer model. (We’ll come back to force-time relationship at the end of this paradigm series) Last year, not having experience with Modeling Instruction, I just dove right in (chronicled starting with day 1 here). This year I wanted to utilize the discover, build, break cycle that Frank Noschese talked about in his TEDx talk. One of the tenants of modeling is that models are useful for certain cases and not for others. Thus I used an inelastic collision to springboard into momentum based on the fact that an energy analysis is not particularly useful for this situation.

When students walked in I showed them a scenario where a moving cart (A) collides with a stationary cart (B) of equal mass. I asked them to use the Energy Transfer Model (ETM) to predict the final velocity of the carts. A typical analysis looks something like this;

Assuming there is no conversion of energy to thermal energy, the kinetic energy of the first cart should end up as combined kinetic energy for both carts after the collision;

$\frac{1}{2}m_Av_{Ai}^2=\frac{1}{2}m_Av_{Af}^2+\frac{1}{2}m_Bv_{Bf}^2$

Noting that for this case $m_A=m_B$  and  $v_{Af}=v_{Bf}$,  the whole thing simplifies to

$v_{Ai}^2=2v_f^2$

Solving for the final velocity of the two carts together in terms of the initial velocity of the first one,

$v_f=\frac{v_{Ai}}{\sqrt{2}}$

Once we got to here I simply said “Go test it,” and they got to work in the lab.

Before I go on I want to comment on the lack of thermal energy in the above derivation. Many of my students correctly tried to include E_therm in their analysis. This is great, but I pointed out that today was a lab day and thus we need to be able to measure things. Me: “Can we easily measure E_therm?” Student:”Ummmm…no.” “Right, so let’s ignore it and see if the data upholds that assumption.” They almost always (correctly) want to include E_therm in every energy analysis, but we have done a couple situations in the lab where stored gravitational interaction energy transfers to kinetic energy for dynamics carts where assuming no changes in E_therm yielded good data. Thus students were primed for me to suggest that we could ignore E_therm. However, this is tempered with the fact that I do a demonstration showing that kinetic energy transfers to thermal energy in collisions (a couple weeks prior) and that they are used to me guiding towards ‘wrong’ answers. So I believe students went into lab cautiously optimistic that our the lab evidence would support the derived equation.

It doesn’t.

It only takes students 5-10 minutes to realize that the final velocities are closer to half the initial rather than the initial divided by the square root of two. Some of them try to justify the data (well, it seems kind of close to root two…), but after conferring with their classmates they give up and go with two. At that point I pulled them back up to the front of the room.

Me: So, did our equation work?
Students: Nope
M: But was their a pattern?
S: Yep. Final velocity is half the initial.
M: Wait, you mean that energy doesn’t predict the final velocity, but something else does?
S: Um…..

We had a quick discussion about how something must be going on that is different from energy. We also talked about how it makes sense that energy wouldn’t work; we expect some of the initial kinetic energy to convert to E_therm  after the collision.

From here I continued day 1 in pretty much the same way as last year. I found after a 45 minute period students were just about ready to talk about a relationship, just slightly behind where day 1 ended before adding the energy piece. My students are much more used to the idea of paradigm labs this year and are getting pretty good at looking for meaning in lab data, so I am not surprised that this addition didn’t significantly change the day one timeframe. Tomorrow we start with presenting the student derived relationships.

### 7 responses to “Transitioning from Energy to Momentum”

1. thommya

Ok, so this is so far over my head, I’m pretty sure I can look directly at Mars with the naked eye. WOW!

2. This is great, Casey. I’m interested in building mores of these “model breaking” activities into the curriculum to help build a stronger storyline. Want to work together on an outline that has a model building (aka paradigm lab) and model breaking exploration for each unit?

3. Nathan Zwierzynski

I’m intrigued by this approach.
I’m very interested in how you facilitate your students to question whether you’re feeding them good info or leading them to a contradiction between prediction and data. My initial impression would be that I’m worried about making the classroom high in uncertainty, but I think that is balanced out because these problems are demonstrated by real data that students have to reconcile. A problem back for lots of students is to make their lab interpretation match their equations and this lab rips up the use of that kind of intellectual dishonestly. I love the lab environment and approach that’s going on here.
I have to say that when I learned about momentum, I saw it as another approach to the same situations, but I was not confronted with a situation that showed me why we needed it. Your lesson seems specifically designed to give students an understanding of why they are learning it to give them a reason for learning about it. That’s awesome!

• Thanks for the kind words! I spend a lot of time all year purposefully making false arguments and waiting for kids to find and correct them, so this is nothing new. They realize very quickly that their data isn’t matching their prediction. In fact, early in the year their first lab report is an investigation into whether mass changes the acceleration of a cart down a ramp, which is their first experience, possibly for their entire school lives, of an experiment in science class that shows nothing happens. I hope that I’m teaching them to trust data. Additionally, Frank Noschese has really pushed the idea (within Modeling Instruction) of adding a “Break the Model” component. Most of what we teach in introductory physics is only useful under certain conditions; constant velocity breaks down when something accelerates, Newton’s 2nd Law breaks down with changing forces, energy is not conserved in most collisions…the list goes on. He embraces that and teaches students that we are using the simplest models possible to explain what we see, and often those models are limited. I like that approach a lot.