## Day 11: Expanding Our Idea of Objects, Systems, and Situations

We talked about how which forces are internal and which are external change when you change the system boundary. We saw how the many forces of gravity become just one when we make the system larger. We defined the mass of the system and the position of the system (the center of mass). And then we tried our model on two air pucks that were previously filmed. We saw no obvious external forces, but the position-time graph wasn't a straight line; the velocity-time graph was. Turns out the system was on a hill, and we need to explore a new type of motion.

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## Day 10: Interaction Diagrams for Different Objects of Interest

After going over homework on force pairs and forces at angles, I divided the class into six groups and had each group draw an interaction diagram and a free-body diagram using the situation pictured above. Here's what they came up with:

The interaction diagrams looked different because the objects for the FBDs were different. Each group had a different system of interest, so each group saw the situation differently. This insight allowed us to quickly define internal, external, and negligible forces.

Then we investigated what point should we track on video analysis to see CVPM for various systems. I'm working with some great friends and colleagues I met at the Ohio Modeling Workshops in Columbus, Ohio, and we're working on a manuscript for the Physics Teacher, so I don't want to go into too much detail here. (I'm already thinking of little tweaks for next time.) But my colleagues and I are trying to develop systems thinking in physics, and so far, so good. My first try with students worked well today.

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## Day 9: Forces at Angles and Interaction Diagrams

Today was all about how to deal with forces at angles. I had them, for the most part, come up with numerical ways to deal with components and vector addition diagrams, and then I summarized their methods in a chart. Then we tried some problems in class. I modified some classic Modeling Instruction questions to be only in variables to get them ready for what they'll see on the AP exam.

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## Day 8: Forces at Angles

Today was all about forces at angles. We worked on two problems. The first was on a force table. One force was at 0°; the other at 90°. Students knew what the picture should look like, but they figured out how to do the math in their groups without me teaching it. The last picture is their homework assignment. What can they figure out about this situation?

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## Day 7: Forces at Angles and Trying to Quantify Forces

We had a long discussion about how to analyze forces at angles. When a person pushes a table at an angle, should we call that a normal force? A normal and a friction force? We decided that perhaps an applied force would be a way to sidestep this debate. We also debated which direction friction point. This even required, after I thought the discussion was done, a student call up another student to go through question 2 (pictured) after I thought we came to a class consensus. Hey, if I'm wrong, feel free to call someone else up!

Then I introduced two ways we can look at forces at angles--as components and through vector addition diagrams. I lamented we had a no way to quantify forces. So it was off to lab to figure out some quantitative relationship involving the force of gravity. We were creative about what objects we used as test masses.
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## Day 6: The Mistake Game

After they took their test, we did our first mistake game (Thanks, Kelly O'Shea! Your blog is great!) on the whiteboards. For most of the questions, only one of the students was supposed to make a mistake. On the last question, I told all the students to make a mistake. We had the best discussion when everyone made a mistake.
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## Day 5: Starting BFPM

We started today by trying to figure out when constant velocity happens in the real world. We weren't sure, as a class, if we had two fans of unequal strength, if the cart sped up to a certain constant speed or was always speeding up. We had to take the cart off the track and put it on the floor to check.

Then I talked about the four major types of interactions (gravity, normal, friction, and tension) and about how to make an interaction diagram. Then we practiced making interaction diagrams and free-body diagrams.

My students don't know yet how important interaction diagrams are. Wait until they see how we use them in MTM and ETM.

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