# Day 86: a vs v or v^2?

Today we started by plotting a vs. v from the spinny chair experiment.  For most groups the data either looked non-linear or they had crazy negative intercepts. I took time to go to each group to ask questions about those aspects, and guided them toward linearizing their graph as a result, since it’s been a long time since we last linearized and we only did it once. The data ended up great after linearizing by squaring v, and it became clear to the students through the discussion that the slope was smaller for groups with higher radii. That plus a unit analysis of the slope led to the conclusion that $a=\frac{v^2}{r}$. A couple other graphs below.

# Day 20: CAPM Paradigm Lab Discussions

I stole a chapter from Kelly, again, and started day 2 of the paradigm lab for CAPM by having a discussion about the different ways we can make a cart move by itself on a ramp using the beauty of “save latest run” on LoggerPro. Then I did something different for each class, because I had a number of different ideas how to run the discussion part after this and I wanted to try them all. Stupid scientist in me, I guess.

The one I settled on was actually going back to a board meeting, where students make a circle and each group presents their data on a whiteboard in front of them. Students make observations and claims, which I record, and they try to come to a consensus about what the graphs tell them. The class that proceeded this way only took 10 minutes to nail down that slope is acceleration (which we defined more precisely as the rate of change of velocity) and that the intercept is the initial velocity, IF the data is time adjusted so that t=0 is when the cart is released from the hand.

We had some time left so we discussed what acceleration means (for now, the amount of velocity added or subtracted each second), and looked at the fact that a cart slowing down can have both positive and negative accelerations (we did the same trial, pushing the cart up from the bottom and stopping it near the top, both with the motion detector at the top of the ramp and at the bottom).

Oh, I almost forgot. In each class we discussed the graphs above in different ways, but in one I did something I really liked; I had each group pick one and sketch it on their desk, then list observations or claims. Then I had groups rotate to evaluate those observations and claims or to add their own. We rotated twice then went back to our original spots and re-evaluated the original work. Here’s some pics of what kids wrote for this.

Finally, I saw the best v vs. t graph ever, sketched by a student today.