One section of Honors Physics came up with an expression of conservation of momentum today. We finished taking some data, then broke into groups to do some thinking about how we could represent it to highlight a pattern. After about 15 minutes, we came back together for a board meeting to talk about strategy. We had some graphical representations, some ratios, and a lot of consensus about how difficult it was to think about how to represent 6 variables at once. I gave a small nudge by saying that bar charts might be a different graphical way to represent the data. I didn’t say anything more than that (nothing about what the height should be, how to show each trial, just nothing at all beyond “you might think about bar charts”).
Some groups took the nudge. One group quickly decided that they could fit more variables into the chart if they made both the height and the width of the bars meaningful. They made the height the initial velocity, the width the mass, then wrote the final velocity inside of the bar. The width as mass idea spread to a couple of other groups, and a lot of bar charts emerged. By the end of the next 15 minute work session, the bar charts were in progress, but hadn’t resulted in a pattern just yet.
On the other hand, one group stayed with their initial graph. They had made a scatter plot that showed the change in velocity for a cart vs its mass. I suggested at the previous meeting that they have a way to denote which two points were from the same trial. They returned with symbols around the points, and they had also noticed that if you found the area of the rectangle created by the origin of the graph and the data point, the two points carved out areas that were the same size (though one was always positive and one was always negative).
The ratio group had continued with the ratios. They had made a huge table of every ratio they could think to calculate (initial and final velocities, masses, basically every permutation of the 6 variables, plus other ideas). In the end, they had noticed a correlation between the ratio of the changes in velocity and the ratios of the masses. In short, those two ratios were always equal, but opposite. They wrote an equation to state it. When they talked about it, we also noticed that they had basically be interpreting their scatter plot as a bar chart. The areas they were talking about were of the bars.
Two really cool ways of approaching the representation of the data. Also, two ways that I had not yet seen students do. I love how open this experiment is and how ready they are to try new representations of the data. So much room for creativity and tough thinking.
After that, we spent about 10 or 15 minutes pulling things together from the theoretical side and realizing that we get the same results as both of those groups had determined experimentally. Next class (Thursday), I’ll help them pull together an IFF chart for the first time, then we’ll finally get to practice a bit. Pretty exciting!
The regular physics class that met this morning found the relationship between mass and weight.
Next class (Wednesday), we will do the spring force experiment, then move into quantitative problem solving. Also pretty exciting!