Tuesday, July 2, 2024

BDA Diagrams (Before, During, After) on Desmos, with vectors!

This post is a follow-up to the earlier BDA Diagram post, which was itself a follow-up to an earlier version of that post. All of which is to say that a number of years have passed, I still like tinkering with Desmos, and BDA diagrams have become an integral part of my curriculum. So I'll have more to post on that topic. Oh, and there was a pandemic in there, too.

In addition to tinkering with my Desmos BDA project as part of aligning it more closely with my curriculum, I decided that it would be nice if the interacting objects at the bottom of the graph also had attached vectors representing momentum and change in momentum. I did finally do it, but I had no idea how difficult it would be. Each adjustment to the initial values of the simulation required whole new representations of vectors that I did not anticipate. The first tricky part was, how do you draw a programmable arrow in Desmos? There is no built-in arrow symbol with programmable dimensions. How do you make sure that an arrow is pointing in the right direction? How do you make sure the arrow is the right length? And for the "during" part of the graph, how do you make arrows that grow and shrink and switch direction? And where do I place the moving labels? I had no idea how happy I would be to work in only one dimension.

For reference, please check out the earlier posting: BDA Diagrams (Before, During, After) on Desmos.

I still have the switch that toggles between a 3-axis and 6-axis view, but now the default is the more elegant 3-axis view. When I have students first draw these graphs by hand, I start with drawing each object on its own 2-dimensional graph (momentum vs. time). As they get used to the concept, I switch over to both objects sharing a single 2-dimensional graph. This corresponds to the 3-axis view of the Desmos graph, where the two objects are sharing each of the three graphed quantities (P, V, and F). For the sake of simplicity the two objects at the bottom still remain circles as they collide. I've color-coded them and the vector arrows to match the P graph colors.

There are two options for displaying the vector arrows. In the default option the vectors show both momenta p1 and p2 during the entire interaction. Toggle to the second option and the vectors show both momenta p1 and p2 but only before and after the interaction. During the interaction, the vectors show Δp1 and Δp2 instead.

Otherwise the new graph functions like the old graph. I've added a lot more documentation to the side panel and have added and reorganized folders. Here's the link to the project: https://www.desmos.com/calculator/raf2oblffa

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