# Monthly Archives: May 2014

## AP Physics 2 Storyline

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.

## AP Physics 1 Storyline

As I prepare for the transition to the AP 1 course, I’ve taken this school year (2013-2014) to begin trying some things out. Based on what I’ve tried, here is the storyline I’m going to use with my AP 1 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.

We begin the year jumping right into the Constant Velocity Particle Model (CVPM). The students at my school come out of chemistry, and for the most part have decent skills when it comes to doing labs. Although we don’t use modeling in our other science classes, they have a majority of the basic skills. So I save a little time by skipping the Scientific Methods Unit.

Our second unit, then progresses to the Constant Acceleration Particle Model (CAPM). As I mentioned, I plan to give more detail later, but for those familiar with the materials provided, I’m not doing that much different from those documents.

The third unit is where I make my first big adjustment from the traditional modeling curriculum. After reading numerous posts from some of the bloggers I admire the most (read Momentum is King, Kelly O’Shea’s blog, and more recently Mazur’s Physics Textbook), I decided to try out teaching momentum before Newton’s Laws. During this third unit, Momentum Transfer Model (MTM), we focus on interaction diagrams and the swapping of momentum as the mechanism of physical interactions. We stress the choosing of a system, and that momentum swaps within the system, or swaps out of the system as an impulse. In the end, we are building the concept of Newton’s Third Law. In addition to what I call Interaction Diagrams (others call system schema), we also introduce the Momentum Diagrams (IF Charts). We hold off on discussing collsions in great detail until after impulses are further studied with unit 5.

The fourth unit, Balanced Forces Particle Model (BFPM), then begins to bring in the concept of forces as the rate of swapping momentum. Here we introduce the major contact forces: normal, tension, friction (name not equation) and the non-contact gravitational force. We also begin using force diagrams to determine if the forces are balanced or not. We stress one way of understanding Newton’s 1st Law as “Balanced Forces -> no acceleration, Unbalanced Forces -> acceleration.”

In the fifth unit, Unbalanced Forces Particle Model (UFPM), we now get into Newton’s 2nd Law in two ways. One the classic:

$a=\frac{F_{net}}{m}$

And two, we build the parallel between kinematics and Newton’s Laws. In kinematics, the slope of a position-time graph gives velocity-time, the slope of velocity-time gives the acceleration-time. Finding the area allows us to go the other way. The same is then true of momentum and forces. The slope of a momentum-time graph gives Force vs. time, while the area under a Force vs. time graph give the change in momentum (impulse). For those students going on to calculus based physics, this helps lay the ground work. For the rest, it shows a nice connection between these different models. With this new information, we can now add a Force vs. time graph into the momentum graphs and make “IFF” graphs. Other features of the unit are the building of the equation for friction in relation to the normal force, and the independence of components by looking at 2D projectile motion problems.

We then wrap up the first semester with our 6th unit, Energy Transfer Model (ETM). After building the concept of energy storage through Energy Diagrams (LOL Diagrams). We discover that Energy storage is a “cheat” to help us solve more complex problems, since it is a second conserved quantity. We come back to collisions and find that, in elastic collisions, we can now build a second conservation equation: 1. momentum (IF charts) and, 2. energy (LOL diagrams).

As a review of the first semester, the students will then have to build a paper car that will hold an egg inside. They will have two tests: 1) a speed test to see who has the fastest car and, 2) a crash test to see who has the safest car. During the design, they must make use of all the models we have built this semester.

To start the second semester, we begin studying the Central Force Particle Model (CFPM), or what most people would call uniform circular motion. In this unit we also add in building the concepts of Newton’s Universal Gravitation and satellite motion.

In unit 8 we now move onto full rotational motion, the Rotating Bodies Model (RBM).  To be honest, I may try to split this up into two units, as it’s got a lot of stuff going on here. In short, within this unit we retrace units 1-6, but in the rotating or polar frame of reference. We begin with rotational kinematics ($\theta$  vs. t, $\omega$  vs. t, and $\alpha$ vs. t). Afterwords, we build in dynamics with angular momentum, torque, and rotational energy storage.

In unit 9, we move on to harmonic motion with the Oscillating Particle Model (OPM). Overall, we stay pretty true to the model materials here. We start with looking at a bouncing mass hanging by a spring. We later bring in pendulum motion.

In unit 10, we then move on to the Mechanical Wave Model (MWM) in which we build a mental model of coupled oscillators. From what I can tell AP-1 only focuses on one dimensional waves, so we looked at boundary effects: reflection (open/fixed) and refraction. We also build in wave superposition. We begin looking at sound waves and doppler shifts as further examples of waves. At least so far, I don’t build in diffraction through “narrow” slits or 2D interference patterns.

In the last unit, we then look at circuits in what I call the Charge Flow Model (CFM). We begin by looking at sticky tape activities to introduce the electric force and electric energy. During that discussion we bring in the concept of gravitational potential ($gh$), to help understand the concept of electric potential ($V$). From there, we have them build simple circuits with lightbulbs, then move onto simple circuits with fixed resistors while measuring the current (flowrate of charge). We eventually get to adding multiple resistors in series and in parallel and try to create a model that explains how the resistors add in these two different ways.

To review the entire year, we then do a video analysis project in which the students must analyze movie, tv, or internet videos and determine how feasible those scenes actually are. Here is an example from which I got my idea: