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.
Below is the force addition and free body diagrams for a group before we whiteboarded.
Here is the corrected version. I love whiteboarding!
We have a cool program that some teachers started where students are encouraged during homeroom each month to write notes to their teachers. This is this month’s stash that came to me. So nice to feel appreciated!
Today we collected centripetal acceleration vs. speed data using spinny chairs, Labquest accelerometers, and lots of masking tape. Tomorrow we analyze data.
Today we played on spinny chairs to investigate centripetal acceleration. We first went through setting up the Labquests, learning the basics of how an accelerometer measures acceleration, and identifying the direction of +x and +y. Then I had them predict what they thought the x and y accelerations would look like, informally. Some student sketches below.
First note: we really need to work on correctly labeling our graphs. At any rate, is is rare for students to correctly predict that they will see a negative y acceleration and zero x acceleration. After predictions, I had them spin (as fast as possible and with arms as outstretched as possible, and keeping the Labquest as level as possible) and we had a conversation about what they found. (Note: I found that we actually get better results just standing and spinning…not near as fun, but far less noisy of data)
I am continually amazed at how students learn. These whiteboards are for the same problem, a boat traveling directly upstream. Since we had done a relative velocity problem where the resultant formed the hypotenuse of a triangle, the group generalized that and thought they should do it for every problem. I saw this multiple times throughout the day. Kids need a chance to flesh out their thoughts, not just try to generalize what we tell them to think.