# 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.