I started Universal Gravitation today (we do CFPM earlier and then come back to this, I like to spiral concepts when possible and I like revisiting CFPM after energy to address that no work is done by centripetal forces), and this is how I started. I liked it a lot. I was amazed at how entrenched the misconceptions are….students really wanted the force on the sun to be smaller than on the earth.
Today we worked on problem solving with the Central Force Particle Model (CFPM). I really, really like force vector addition diagrams (FADs) here, as after a week of qualitative analysis kids understand that if the motion is uniform, then the net force should be towards the center, so the FAD helps them get the direction of the force(s) causing the centripetal force correct. Also, I have really been enjoying doing mini-board meetings for problem solving whiteboarding, as this group is doing.
Today I used the typical spinning stopper situation as a goal-less problem, I enjoyed seeing what kids came up with.
I posted previously about how I designed a new worksheet to directly address the problem where normal force changes directions depending on speed for vertical circles, and today I saw the fruit of that worksheet. I had two groups whiteboard each section and then present together. These groups assumed normal force was in different directions for part c, and the answers came out the same with opposite signs. The worksheet forced them to address the direction of normal force, and reconciled it at the end by finding the speed of the coaster if normal force is zero. Most of the material I use I’ve stolen from the normal modeling materials and Kelly O’Shea, but this is one I’m really proud of because of the great thinking and discussion that resulted. The worksheet can be found in my CFPM packet.
As we go through conceptual aspects of circular motion, students are starting to confront their misconceptions with what they think should be true based on what we’ve studied. This group was a fascinating example; they ‘knew’ that the net force should be toward the center of the circle in the yoyo problem (Problem 4 of Practice 1 in this packet, the descending part), so they tried to make the tension at an angle. They got up and in front of the class and immediately addressed their conflict, that if they draw tension sideways the net force is angled, which they didn’t think could be correct, but that it didn’t seem to make sense to have the tension angled. Discussion helped them and the rest of the class realize that centripetal force can be a component of the overall net force if the circular motion is non-uniform.
We’re doing circular motion whiteboarding, and students still really want the force to be unbalanced upward at the top of the loop. We’re making progress though, it helps that students can directly confront their misconceptions through dialogue.
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 couple other graphs below.