## Building meaning for momentum from discussions, definitions, and data.

Today we started our next unit in physics with a ‘next time question’ from Paul Hewitt:

My reason for giving this was specifically because of the fact that we haven’t learned anything about it. I wanted the students to speak purely from their intuition. I asked them the following:

We aren’t quite ready to answer this by calculation, but I do want you to make a guess.

Will they move together faster than, slower than, or with the same speed as the ball?

Would your answer change if the ball bounced off Jocko instead of him catching it?

Student responses included:

• We need to know if he bends backwards when he catches it, because that will affect it.
• No matter how he does catch it, he will move slower. The larger mass will result in a smaller acceleration.
• The clown has a non-conservative force, so the kinetic energy will decrease.

Interesting responses. We talked a bit about collisions and throws and catches of objects and what they ‘felt’ doing this with different objects. I introduced the idea that it might be nice to have a physics quantity that contains the direction and rate information of velocity, as well as the mass.  I told them that physicists did, in fact, have such a quantity called momentum. They responded with a few non-physics related ways they had heard the term and described what it meant.

To figure things out about how momentum relates to collisions, I then had them analyze the three air track collision videos from the Doane Physics video library using Tracker. Their tasks were as follows:

• Find the momentum of each cart before and after the collision for the video you are assigned. Calibration information is contained in the first frame of each video.
• Find the total momentum of the system before and after the collision.
• Find the total kinetic energy of the system before and after the collision.
• What is thechange of the momentum of the system during the collision?
• What is the change of the kinetic energy of the system during the collision?
• Talk to your classmates and compare your answers for the three different videos.

It was pretty cool to see them jump in with Tracker and know how to analyze things without too much trouble. Fairly soon afterwards, we had some initial velocities and final velocities, and changes in momentum to compare.

I was, of course, leading them toward something with the change calculations.
We calculated the changes in momentum, which were non-zero. Were the magnitudes significant? A student suggested looking at the percent change compared to the initial momentum. For the first two videos, the loss was less than 1%, though for the third it was around 20%.
A student proposed the possibility that the change should be zero if no momentum is lost during the transfer. Comments were made about how that made sense in the context of our previous unit on energy – things feeling right when all of a quantity can be accounted for.
I then did a little pushing (since we were almost out of time) about what this might mean about total initial momentum and total final momentum.  I also gave them definitions for elastic and inelastic collisions. I then assigned them a couple simple questions that I wanted them to figure out if we can say that the change in total momentum before and after is zero:
Then it was time for Calculus.
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I don’t usually like giving students information. I don’t like giving it away without some sense of where it comes from. I also like when students can discover quantities without equation definitions. Sometimes though, the simplicity of an idea like momentum and its power can come from taking the calculation itself as a tool that can be used to analyze a situation.
In previous classes, I have given the definition, shown situations in which momentum is conserved, and then asked students to use this idea of momentum conservation with their math skills to find unknown quantities. I really liked this alternate approach today of using momentum itself to analyze a situation and then have the idea of conservation come out of discussion. I think its potential for ‘stickiness’ in the minds of students is much greater this way.

## Testing physics models using videos & Tracker

I’ve gotten really jealous reading about how some really great teachers have stepped up and used programming as learning tools in their classes. John Burk’s work on using vPython to do computational modeling with his students is a great way to put together a virtual lab for students to test their theories and understand the balanced force model. I also like Shawn Cornally’s progression of tasks using programming in Calculus to ultimately enable his students to really understand concepts and algorithms once they get the basic mechanics.

I’ve been looking for ways to integrate simple programming tasks into my Algebra 2 class, and I think I’m sold on Python. Many of my students run Chrome on their laptops, and the Python Shell app is easily installed on their computers through the app store. It would be easy enough to ask them to enter code I post on the wiki and then modify it as a challenge at the end of beginning of class.. It’s not a formal programming course at all, but the only way I really got interested in programming was when I was using it to do something with a clear application. I’m just learning Python now myself, so I’m going to need a bit more work on my own before I’ll feel comfortable troubleshooting student programs. I want to do it, but I also need some more time to figure out exactly how I want to do it.

In short, I am not ready to make programming more than just a snack in my classes so far. I have, however, been a Tracker fan for a really long time since I first saw it being used in a lab at the NASA Glenn Research Center ten years ago. Back then, it was a simple program that allowed you to import a video, click frame by frame on the location of objects, and export a table of the position values together with numerically differentiated velocity and acceleration. The built-in features have grown considerably since then, but numerical differentiation being what it is, it’s really hard to get excellent velocity or acceleration data from position data. I had my students create their own investigations a month ago and was quite pleased with how the students ran with it and made it their own. They came to this same conclusion though – noisy data does not a happy physics student make.

I wanted to take the virtual laboratory concept of John’s vPython work (such as the activities described here) for my students, but not have to invest the time in developing my students’ Python ability because, as I mentioned, I barely qualify myself as a Python novice. My students spent a fair amount of time with Tracker on the previous assignment and were comfortable with the interface. It was at this point that I really decided to look into one of the most powerful capabilities of the current version of Tracker: the dynamic particle model.

My students have been working with Newton’s laws for the past month. After discovering the power of the dynamic model in Tracker, I thought about whether it could be something that would make sense to introduce earlier in the development of forces, but I now don’t think it makes sense to do so. It does nothing for the notion of balanced forces. Additionally, some level of intuition about how a net force affects an object is important for adjusting a model to fit observations. I’m not saying you couldn’t design an inquiry lab that would develop these ideas, but I think hands-on and actual “let me feel the physics happening in front of me” style investigation is important in developing the models – this is the whole point of modeling instruction. Once students have developed their own model for how unbalanced forces work, then handing them this powerful tool to apply their understanding might be more meaningful.

The idea behind using the dynamic particle model in Tracker is this: any object being analyzed in video can be reduced to analyzing the movement of a particle in response to forces. The free body diagram is the fundamental tool used to analyze these forces and relate them to Newton’s laws. The dynamic particle model is just a mathematical way to combine the forces acting on the particle with Newton’s second law. Numerical integration of acceleration then produces velocity and positions of the particle as functions of time. Tracker superimposes these calculated positions of the particle onto the video frames so the model and reality can be compared.

This is such a powerful way for students to see if their understanding of the physics of a situation is correct. Instead of asking students to check order of magnitude or ask about the vague question “is it reasonable”, you instead ask them whether the model stops in the same point in the video as the object being modeled. Today, I actually didn’t even need to ask this question – the students knew not only that they had to change something, but they figured out which aspect of the model (initial velocity or force magnitude) they needed to change.

It’s actually a pretty interesting  progression of things to do and discuss with students.

• Draw a system schema for the objects shown in the video.
• Identify the object(s) that you want to model from the video. Draw a free body diagram.
• Decide which forces from the diagram you CAN model. Forces you know are constant (even if you don’t know the magnitude) are easy to model. If there are other forces, you don’t have to say “ignore them” arbitrarily as the teacher because you know they aren’t important. Instead, you encourage students start with a simple model and adjust the parameters to match the video.
• If the model cannot be made to match the video, no matter what the parameter values, then they understand why the model might need to be adjusted.  If the simple model is a close enough match, the discussion is over. This way we can stop having our students say “my data is wrong because…” and instead have them really think about whether the fault is with the data collection or with the model they have constructed!
• Repeat this process of comparing and adjusting the model to match the observations until the two agree within a reasonable amount.

Isn’t the habit of comparing our mental models to reality the sort of thing we want our students to develop and possess long after they have left our gradebook?

It’s so exciting to be able to hand students this new tool, give them a quick demo on how to make it work, and then set them off to model what they observe. The feedback is immediate. There’s some frustration, but it’s the kind of frustration that builds intuition for other situations. I was glad to be there to witness so we could troubleshoot together rather than over-plan and structure the activity too much.

Here is the lab I gave my students: Tracker Lab – Construction of Numerical models If you are interested in an editable version, let me know. I have also posted the other files at the wiki page. Feel free to use anything if you want to use it with your students.

I am curious about the falling tissue video and what students find – I purposely did not do that part myself. Took a lot of will-power to not even try. How often do we ask students to answer questions we don’t know the answer to? Aren’t those the most interesting ones?

I promise I won’t break down and analyze it myself. I’ve got some Python to learn.

## Modeling anyone? Fans on carts edition.

After reading a lot about the success that others have had with teaching physics using the modeling method, I’m giving it a shot as I start Newton’s laws with my physics class. When I taught this with my AP physics previously, I did a traditional development of Newton’s laws describing (I admit it – lecturing) about Newton’s understanding of what caused acceleration. We talked about acceleration being proportional to net force and inversely proportional to mass, and then went from there exploring what it meant for net force to be zero through a series of problems involving net forces, components, etc.

What I did seemed to work in so far as students were able to solve the problems I gave them. The undying assumption of course is that what I did was efficient and made me feel that I had got across the material to students, but along the way I wasted an opportunity for students to SEE the principles in action and try to figure things out on their own. Since my students this year are not taking the course at the AP level, I see no reason not to try this and see how it compares in the long run to student understanding and enjoyment of the exploration of physics concepts. It is the sort of thing that I can see doing even in the Physics B curriculum, as dense as it is, given the fact that students really need a chance to play to connect the mathematics of the equations to the fact that physics describes the real world, not just idealized situations.

Here’s where I’d love to get some input though – I am giving my students a test in the first half of the 85 minute period tomorrow, and then my plan is to let them spend the rest of the time watching some videos that I took this afternoon of toy fans attached to cars on an air track. The students will get to play with the actual air track, but I want to introduce to the way I want them to play by seeing these videos that I created.

I have posted the series of videos here at my wiki site. The general instructions for what I want them to do are there, but I might as well run through them here as well.

First, I want them just to watch all the videos. No physics, just observation. After they have done this, I’ve posted a number of questions I want them to use to classify, analyze, and predict based on constant velocity and non-uniform velocity cases. I plan to have them sketch what effect a single fan would have on the motion of the cart. My plan in the end is to have them construct a situation with the fans that results in a given scenario. For example: arrange the fans on the cart so that The cart has zero initial velocity and an acceleration to the left. Draw position, velocity, and acceleration graphs, and then use Tracker to confirm/refute what their models suggest will happen.

Let me know your thoughts either here or through Twitter (@emwdx) – I am excited to try this, and excited to give the students a chance to get some first hand experience testing their own ideas. I had a blast playing with it this afternoon, and while I do have a different standard for what is ‘fun’ at times, I don’t think this is one of those times.