As I prepare for the transition to the AP 2 course, here is the story-line of how I’m planning to teach my AP 2 students next year. Before I get into the details, I do plan to use Modeling Instruction throughout the course. If you haven’t had the chance to take a workshop, do yourself a favor and find one. Also, I plan to make future posts providing more detail for each unit.
For those that have drilled deep into the materials provided by the Modeling Community, you may have found the resources provided for topics such as fluids and ideal gas law. Within those materials, there is a recommendation to use computer programming to bridge the gap between systems with only a few particles (read: AP1 events) to systems with many, many particles (read: fluids and/or thermodynamics). With that in mind, I plan to begin the year with a unit on Computer Modeling. I hope to accomplish two things: 1) Review some of the major concepts from AP1, and AP2) Prepare the students so they can see how analysis of fluids, the Ideal Gas Law/Kinetic Molecular Theory all come out of the models we build in AP1.
From there, we move to a unit on Ideal Gases, which I call the Ideal System of Particles Model (ISPM). Within this model we will recreate some of the various classic gas experiments (Boyle’s, Charles’, etc.) to build a model for monatonic ideal gases. We will connect what we see in the lab, with what our computer models predict. We will also begin to look at what happens to that gas when changes occur such as a compression or an expansion. In so doing, we will enhance our model so that it can predict what happens to the energy within our gas with those various changes (read: thermodynamics).
After building a model for gases, we move on to a unit on fluids which I’ll call the System Flow Model (SFM). Again, I plan to use the modeling materials provided. For those that haven’t seen them, they in essence begin by looking at what is happen to a small volume of water. In so doing, we build the continuity equation and the energy density equation (Bernoulli’s Equation). We also look at the pressure at different depths, and how those with effect that small volume (buoyancy).
In unit four, we begin the a second major concept of the year, electrical interactions. We again will make use of the 4 units developed by the modeling community. First up for this concept, a model for an Electrically Charged Particle, which I will call the Charged Particle Interaction Model (CPIM). We build parallels to the other non-contact force studied in AP1, namely gravity. We develop a field equation and a universal equation (Coulomb’s Law), just as we did with gravity.
In unit five, we build upon that model to describe the energy changes that can occur, what I call the Electrical Energy Transfer Model (EETM). After quickly developing a model for the energy storage in electrical fields, we create a short-hand way of tracking energy changes by looking only at the product of the field with the distance through which it moved (electric potential).
In unit six, we now develop a model for the movement of charged particles through circuits, what I call the Charge Flow Model (CFM). We begin by tying this model back to the third unit on flowing particles. Along the way, we also develop Ohm’s Law, and Kirchhoff’s Laws. We also develop a means to predict the power dissipated by a resistor.
In unit seven, we begin by looking at a weird side effect of moving charges, namely, their interaction with other moving charged particles, the Magnetic Interaction Particle Model (MIPM). We show how this force a different interaction than the electric force, but also show how they are both based on the same fundamental quantity of charge. Along the way we build up a third type of force field, and look at the quantities that effect it and interact with it.
In unit eight, we begin our third major topic of the year, the study of light. In this unit we build a Particle Model of Light (PLM) to describe reflection of light. We look at both smooth and rough surfaces. Also study flat and curved surfaces.
In unit nine, we see the limitation of a particle model of light in understanding how lenses, diffraction gratings, and thin films. In the process we develop a new Wave Model of Light (WML). Along the way we develop a set of equations: one that relates the focal distance, image distance, and object distance; and a second that related the heights of the object and image with the distances of the object and image. We also develop ways of understanding total internal reflection, double slit or diffraction gratings, and the effects of thin films.
In unit 10, we encounter some events in which the wave model breaks down: photoelectric effect, atomic emission/adsorption of light. In the process we build a new hybrid “Photon” or “Quantum” Model (QM). By no means are we building the actual Quantum Mechanical Model through things like the Schrodinger’s Equation, but we are building the concept of photons and discrete energy levels within an atom which are further along than just the Bohr’s Model.
In the final unit, we will again do a mild “hand waving” to try to take our “Quantum” model and use it to explain radioactive events. Along the way we will develop our “Standard” Model (SM). Again, not the actual Standard Model developed of the last 5o years, but a rudimentary look into particle physics to study nuclear decays, Compton Scattering, and a very cursory look at the Strong and Weak Nuclear Forces.
As you can see, if you’ve made it this far, this course is not as completely developed at this point. I’ve taught some aspects of this. I plan to make use of as much of the advanced modeling materials as I can, but I’m guessing I’ll be creating some of the materials as I go. To end the year, I plan to have students do a second Video Project in which they must try to analyze videos using models from these second year models to begin reviewing and getting ready for the AP2 exam.