Matter & Interactions I, Week 7Posted: September 30, 2016
I will edit this post at a later date to include diagrams.
This was a pretty good week. Students are beginning to ask deeper, more insightful questions and that tells me they’re engaging in the material more than before. We formally began chapter 2 on the momentum principle, but I did something quite different from the textbook.
I took the opportunity to introduce system schemas (I’ll add a link later). I think system schemas are important because they allow for some foundational physics reasoning to happen without the burden of geometry contained in free body diagrams. System schemas allow students to think about systems and interactions that cross system boundaries, and this is important because the momentum principle and (all?) other physical principles apply to systems.
I introduced one slight change to the schema. Sometimes, an interaction only exists for a brief duration when analyzing a problem. As an example, chapter 2 presents the problem of two students running down the hallway toward each other, and they eventually collide. There is a contact interaction between them, but it only exists while they’re in contact with each other and not before. Several years ago, a student of mine and I decided to indicate such “temporary” interactions with a dotted line rather than a solid line.
I also introduced free body diagrams. These of course contain the geometry in a given problem, but I had an insight this week that to my knowledge had never occurred to me before. Free body diagrams are coordinate free. One can draw such a diagram for a given physical situation without introducing a coordinate system. Why? Because vectors are coordinate free. So draw a free body diagram to reflect the physics. Then to solve the problem in the traditional ways, project that diagram onto any convenient coordinate basis. We did this in class for a particularly simple situation: a block at rest on a surface. Let the system consist of only the block. There are only two interactions with the block: one shared with Earth (a gravitational interaction) and one shared with the surface (a contact interaction). We can project this situation onto an orthogonal coordinate basis that is rotated with respect to the standard basis (+x to the right of this page, +y to the top of this page, +z out of this page) and when we do, we introduce components that weren’t necessarily there before, but they’re there now and they always null each other out (think of the block sitting motionless on an inclined plane tilted from upper left to lower right).
But now the class has a mystery to figure out. In the rotated basis, the components are easily understood as gravitational (the components of the force due to Earth parallel to, and perpendicular to, the surface), contact (the component of the force due to the surface perpendicular to the surface…the normal force), and friction (the component of the force due to the surface parallel to the surface). The normal force and friction force are components of the force due to the surface. But where do these components go when the surface is horizontal?
We ended the week with a computational problem from chapter 2.
As always questions, comments, and constructive criticism are welcome.