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We’re studing momentum in my honors physics class, and I’m thinking back to all the fun we had last year designing a completely new unit for momentum, the Parcel of Momentum (POM).

I’ve spent the past few days trying to follow Kelly O’Shea’s great introduction to the Momentum Transfer Model (MTM) paradigm lab, but we had considerably more trouble than her class did. Ultimately, we got to the point where we were looking at a data table that looked something like this:

And we began to study this data looking for a pattern. Eventually, some students started to see that in some cases, the changes in velocity were exactly opposite one another, and these cases happened to be when the masses were equal. Later, they realized that in cases where the changes in velocity were not the same, the more massive cart had a smaller change in velocity than the less massive cart. And from there, students were able produce a nice graph showing that $m_1\Delta v_1=-m_2\Delta v_2$, that the carts seemed to be swapping something during collisions.

One student even said that it was like two people swapping money, and so this got me thinking, and I designed this with a little bit of free time today:

View this document on Scribd

So now I have a momentum currency for my class, and for a few minutes, I thought this would be cool for some sort of demo/activity in class. I’d give everyone a set amount of money, and then we’d simulate collisions where they would “transfer” momentum currency to one another. Finally, we’d tally all the individual transfers and see that momentum is conserved.

But then I got to thinking about this a bit more, and I’m not so sure this is a wise way to go. There are lots of ways that my momentum currency may confuse things more than I want. First, momentum is a vector, without creating some sort of perpendicular currency, I’m not sure that they will get that having more momentum doesn’t mean you can move in any direction you want. Second, objects end up with negative momentum, meaning they’re traveling in the negative direction. However, I have no way to track negative momentum, and so it would seem that this currency idea might mistakenly make students start to treat it like a scalar quantity, rather than a vector. Finally, I use the money metaphor a lot when dealing with energy, so I’m not sure we need a currency for both momentum and energy, and think that could get confusing fast.

So now I’m tempted to keep my POMs for myself, and not doing anything with them. But I’m curious if you have any suggestions about the usefulness of this activity or how to improve it.

So now

January 25, 2012 7:49 am

First, let me be clear: Momentum is king!

Ok, now that I’ve gotten that out of the way, let me actually put some thought into this. I agree with your concerns about the scalar trap. I would add that there might be too much focus on contact transfers in that activity. For me, the POM idea is great but really it’s meant to support the traditional Newton’s laws approach to solving problems. If we know that
3) things swap POMS
2) the swap rate is determined by interactions
1) if you don’t swap, you don’t change
as the foundations of Newton’s laws, there’s nothing wrong with using them in the traditional way.

As far as your activity, I suppose you could do it with bank accounts instead of physical dollars. However, there’s still the money confusion (momentum vs energy – though the latter is just a fancy way of doing momentum accounting), and you lose the notion of a true transfer. And, to deal with the vector part, as you say, you’d need 3 accounts per person.

When I’ve taught this way, I’ve had students solve problems the traditional way, but then asked them on occasion to explain the process from the momentum swap perspective. Sometimes the transfers are hard to pin down, but so are finding N3L pairs.

I don’t think I’m being too helpful here. I guess I’m saying that I see your struggles and I see why they’re happening. But I don’t really have a solution.

• January 26, 2012 2:13 pm

I like the 3 accounts idea, but I still think it might be too unclear and confusing when we get to the idea of thinking of energy as money. With IF charts, kids seem to pick up momentum conservation pretty easily, and they readily see that if something else transfers momentum into the system via a force, the momentum of the system will change. I think save my momentum play money and not put it to use in my class.

And of course, I love the 3 laws reframed in terms of the king.

2. January 28, 2012 1:59 pm

I think it’s a risky idea because students need to grasp momentum, mass, and velocity (not speed!) as three separate things. Perhaps if you drew a tall skinny rectangle (high mass, low velocity) and commented that has the same area as a fat short rectangle (low mass, high velocity) or a square (medium mass and velocity).

That’s a start, and it clearly shows that momentum is the product of two independent things they already understand, and not something opaque.

• January 28, 2012 8:02 pm

Absolutely. We use IF charts that help students see how both mass and velocity contribute to momentum, and the students love them.