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Unit 4: Balanced Forces Particle Model

The fourth unit introduces Forces. It takes about two and one-half weeks. It begins with a series of Bowling Ball Activities; e.g. make the ball speed up, slow down, turn 90^{\circ}, move in a circular arc. In the previous unit, a simplified “Interaction Diagram,” what many call a “System Schema.” As we begin to use this diagram, we see that multiple interactions are occurring.

Students are asked to make a quick sketch of momentum vs. time for the bowling ball starting from rest, being pushed by the broom, and then rolling at “constant” velocity. Most agree that it should be a horizontal line at p = 0, then a diagonal line as it is speeding up, and then a horizontal line at the final constant velocity.

In previous units, students saw the slopes are often important quantities, so they are asked to try to figure out what this slope of momentum vs. time represents. Usually, with little guidance, they can figure out that this slope represents the rate at which momentum is swapping, which we define as a “Force.” Thus, if an interaction is the swapping of momentum, it’s derivative is a Force.

From there we introduce the different types of interactions present during our activities. We identify three contact forces: push (Normal), pull (Tension), and slide (Friction). We also name one non-contact force, Gravity. From there, these types of interactions are added to the interaction diagram. Then show how this interaction diagram, can be used to make Force Diagrams.

We conclude the day by noticing that multiple interactions can balance out, thus multiple forces on a single particle or systems can balance out. We go on to notice that the system will only accelerate when the forces are unbalanced, which I mention is Newton’s 1st Law (when in an inertial frame of reference).

So the next step in the sequence is Worksheet 1 in which they practice making the Interaction Diagram with forces included and Force Diagrams. They are aided by a reading that help show in greater detail how to create Force Diagrams including equality marks.

From there, we do a lab to try to begin to understand the non-contact force of gravity by hanging various masses on a spring scale. Thus finding the relationship between mass and the force of gravity.

Once that’s complete we add this calculation to begin to add numerical values into Force Diagrams in worksheet 2. Along with a second reading, we end the unit with worksheet 3 as we add component forces into the mix.

The student goals for this unit are:

  1. can draw a properly labeled free body diagram of all the forces acting on an object including equality marks
  2. given one interaction between two objects, determine the direction of force exerted on each object
  3. determine the direction of acceleration of an object from a free body diagram
  4. determine whether or not the forces are balanced given information about the motion of the object
  5. determine the force of gravity on an object within a gravitational field

A Message to a Young Man

On October 25th, 2013, I was honored as the University of Notre Dame Alumni Association National Teacher of the Year. This was my way of saying thanks to everyone who helped me reach this milestone:

One of my first memories of Notre Dame was visiting my sister for Sophomore Sibs weekend. My sister is four years older than me, so we were both sophomores, her at ND, me in high school. While visiting, we went to Mass in my sister’s dorm. The overall message that the priest talked about in his homily was that we are all called to do something by God. Moreover, the Holy Spirit will act through friends and strangers to let you know what you’re called to do. If you’ll give me just a few moments, I’d like to tell you how the Holy Spirit has interceded to guide me through my life.

During a visit my junior year, my sister was taking my brother and I to a party in Grace Hall. What I remember most was on the walk to the dorm, we could hear music playing in various dorms nearby. All of a sudden, one of the parties started playing my favorite song growing up, Kermit the Frog’s “Rainbow Connection.” To me, that was the sign that ND is where I need to go to college.

Fast forward to the summer between my sophomore and junior years at ND. While working at a pizzeria in my home town, a repairman came and talked to me about how great it is to be a teacher. He went on and on about how we need good, intelligent teachers to shape the next generation of citizens. I honestly didn’t think much of it at the time; merely that this crazy stranger wouldn’t shut up about teaching for the 45 minutes he was working on the broken fridge.

During my junior year, during a class called Transport Phenomena, a two semester course on how fluids move through pipes, the class hit a sticking point. The professor, in his Italian accent, was going on and on about several simultaneous equations that describe a particular situation. Without going into the gory details, this final point was that the graph of all of the equations had a minimum in it. He proudly stated, “That is what engineers live for!” I honestly didn’t see the greatness of this, and this was the moment I started to think maybe engineering wasn’t for me.

Amazingly enough, as I was walking in my dorm later that day, a flier for the Alliance for Catholic Education popped up. I remembered my sister talking about ACE and started thinking about looking into it. I also remembered that crazy repairman I and thought maybe I should think about teaching.

Amazingly enough, one of my roommates got a new girlfriend. As we started getting to know her, she told us that her cousin was the director of the ACE program and that he was always asking her to bring friends over to his house to try to convince them to apply. After doing just that a few weeks later, I was excited to apply. I’m grateful to say that I was accepted, and soon learned that I would be heading to Jacksonville FL and teaching chemistry at Bishop Kenny High School. Throughout my experience in the ACE program, I encountered the best teachers I ever had. They still inspire me to this day.

During my first year at BK, the volleyball coaches, one of whom was my housemate, asked for some help with the volleyball team. I was already helping with the soccer team, but after some arm twisting, I was convinced to help that team too. A few years later, a few of the volleyball team moms found out I was single, and took it upon themselves to find me a significant other. For the most part I humored them, and just went about my life. At the end of that season, one of those moms was very adamant that she knew “the one.”

It turns out, she was right. Stephanie and I hit it off right away, and 10 months later I was lucky enough to be engaged, and a year after that, I was married to the most amazing woman I’ve ever met. That same year I was to be married, my principal asked me if I would be interested in taking over the physics program at BK. Part of my fear of teaching physics, which I’ve never told anyone, was that I would be teaching the same subject as my favorite ACE teacher, and I wasn’t sure if I could live up to his standards. However, after talking to my department chair about it, I accepted.

During our discussion, she recommended I look into a new lab based curriculum developed at MIT. Since I was the only physics teacher, I only had to convince my admin to adopted her recommendation. Not an impossible process, just a necessary step BK has to ensure our students receive a good education.

A year or so later, a few students asked me about adding an AP physics class. While discussing the possibility with one of the academic deans, she recommended I look into what other teachers do for their AP classes. In my searches, I stumbled on a few blogs talking about Modeling Instruction.

At about the same time, we had a workshop day where teachers shared some of their best practices. One of those mini-workshops was on how that teacher uses twitter to find lesson plan ideas. With his help, and a little searching, I found a great group of physics teachers that blew me away with what they were doing in their classes. For the first time, I had other physics teachers to bounce ideas off of and even have weekly meetings online. Many were also singing the praises of Modeling, so I decided to look into going to a workshop.

While at the workshop, not only was I fully convinced of the power of teaching through Modeling, I also had a fellow participant share a news story about what would become one if my favorite books, “The Last Lecture” about Randy Pauch celebrating his life as he was dying of cancer. Those three weeks proved to be a very transformational time for me.

When I returned to school the next year, I set about trying to convince my admin to switch to that way of teaching my classes. Just about the time I received their ok, my wife and I found out we were going to be parents. As we were to begin preplanning that next year, Dillon, you overachieving son of mine, decided to come early. So instead of me starting the year as planned, I had a sub with no experience teaching physics, trying to introduce my students to this new way of learning. After returning to the classroom, I set about trying to recover from that crazy start while balancing the joys of fatherhood.

For the most part, that brings us to this award I’m being honored with tonight. I think it’s important for you to know all these steps throughout my life to share how I think the Holy Spirit has guided me to this amazing award. To me, humility isn’t hiding your accomplishments, but rather celebrating them as gifts God has given you. I can’t begin to thank all the people that have helped me get to this point, but what I can say is this: Dillon, when you’re old enough to read this letter, I can only hope that you realize that God has a plan for you too. Have the courage to be open to the amazing people that enter your life, so they, with the help of the Holy Spirit, can help guide you along your path. Most importantly, take time to enjoy the steps along the way, as I’m sure God has a plan for you to experience your own amazing ride.

Momentum is King!

One idea that has been gnawing away at me is Andy Rundquist’s awesome notion that, “Momentum is King.” One quick link to see some of his ideas in greater detail is here. My issue is how exactly to make that stick in a modeling class, or stated another way, how does the storyline for mechanics change? The main issue I’m going back and forth over is if you teach momentum before forces, when and how exactly do you introduce the concept/term force?

Here are my thoughts so far:

I’m planning to progress though Constant Velocity Particle Model and Constant Acceleration Model as set up by the modeling content. (As a brief aside, if your not familiar with Kelly O’Sheas blog on modeling, go there ASAP!) From there, I’m planning to use a modified version of the Momentum Transfer Unit (Impulsive Force Model). After that is where I’m stuck, but here’s what I’m roughly thinking:

1) Jump to Balanced Forces, and don’t make the explicit connection between momentum transfer and forces. Basically begin creating a second parallel concept. Progress through the modeling materials for balanced forces (Free Particle Model is the official name) as designed and wait until unbalanced forces (Constant Force Model) to make the connection.

2) Recast the balanced forces model as multiple transfers model and remove the discussion of forces. Continue to reinforce the idea of momentum swaps, but now discuss the fact that the swaps can balance out. Focus on the system schema and stress that if there is not net momentum swap, the momentum must stay constant. Instead of hammering home “no net force, no acceleration; net force, acceleration” recast it through momentum. Then introduce the concept of force in the next unit, Unbalanced Forces Particle Model (which may or may not need/get a new name)

3) Jump to Unbalanced forces first and show the connection between impulse and Force. Begin by showing that a force is the rate of momentum change and that the area of a F vs t graph.  You could build the IF bar graphs in the momentum unit into IFF bar graphs. In the process focus on how each object has the same momentum swap, but different accelerations; that the forces are the same, but the effects may be different. (I’m looking at you bug on windshield problems!). Once complete, go to balanced forces and show that you can have multiple, simultaneous interactions, which can balance out. Now bring in things like system schemas and force diagrams.

My quick $0.02:

1) If I’m making the effort to put momentum first, it doesn’t seem right to then ignore it when introducing the concept of forces.

2) Seems to flow a little better than (1), but when do you build in force diagrams? Adding them in the unbalanced forces unit make that unit really big, but I’m not sure I would feel right calling them momentum swap diagrams (especially if no other physicists do so).

3) Part of me is really drawn to this storyline, but in the end, that means I’m teaching Newton’s Law in the reverse order (3rd -> 2nd -> 1st). There is probably a good reason why no textbook or the modeling materials do it that way.

I’d love to hear feedback, if you’ve got any.

Modeling the NGSS Physics Course

As this year draws to a conclusion, and I look ahead to the coming changes in physics education (yes I’m looking at you college board and NGSS), I’m beginning to look ahead to how I might change what I’ve done to meet these new standards. Please note, I’ve only taught with Modeling Instruction for one year now, but maybe my fresh eyes will be beneficial in bridging the between the traditional modeling curriculum and what will be needed in the future courses.

Over the next few weeks, I’m hoping to add more posts to fill in more details, but here’s what I’m thinking so far the what I can put together for a physics class (assuming there is still such a thing) from the NGSS:

Unit I: Scientific Methods/Intro to Modeling/Constant Velocity Particle Model

Paradigm Lab: Buggy Lab

Objective: to determine the graphical and mathematical relationship between position and time for a toy buggy.

Unit II: Constant Acceleration Particle Model

Paradigm Lab: Cart on incline plane

Objective: to determine the graphical and mathematical relationship between position and time for a cart moving down a ramp.

Here’s where I possible get a little crazy. In an effort to break up two big projects I think I’ll need to do for NGSS, I’m splitting momentum from energy. The two big projects are an Egg Car project and a Rude Goldberg project. I’m thinking by doing this, I’ll have 1 project each quarter instead of two very close together. I’m not definite about this, but figured I’d throw it out there and see if I can get any feedback positive or negative from more experienced modelers.

 

Unit III: Momentum Transfer Model

Paradigm Lab: Cart Explosion

Objective: to determine the graphical and mathematical relationship between the ratio of velocities to the ratio of masses when two carts explode apart.

Unit IV: Balanced Forces Particle Model                         (w/ universal gravitation)

Activities: bowling ball games, Universal Gravity Simulation

Paradigm Lab: Gravitational Field Lab

Objective: to determine the graphical and mathematical relationship between mass of an object and its weight.

Unit V: Unbalanced Forces Particle Model

Activity: Ball toss

Paradigm Lab: Modified Atwood Machine

Objective: to determine the graphical and mathematical relationship between Force, mass, and acceleration

Unit VI: Energy Transfer Model

Paradigm Lab: Cart “Launch”

Objective: to determine the graphical and mathematical relationship between compression of a spring, maximum velocity, and maximum height of a cart launched up an inclined plane.

Unit VII: Oscillating Particle Model

Paradigm Lab: Bouncing mass on spring

Objective: to determine the graphical and mathematical relationship between amplitude, mass, and spring constant with period.

Unit VIII: Mechanical Wave Model

Paradigm Lab: Snakey Lab

Objective: to determine the graphical and mathematical relationship between pulse length, pulse amplitude, and tension with wavespeed in a snakey spring.

Activities: water tray waves, speaker interference

Unit IX: Electrically Charge Particle Model

Activities: Sticky Tape

Paradigm Lab: Balloon Lab

Objective: to determine the graphical and mathematical relationship between charge, distance, and electric force

Unit X: Magnetic Particle Model

Paradigm Lab: Field cause by a current carrying wire

Objective: to determine the graphical and mathematical relationship between current, distance from the wire, and magnetic field for a wire carrying a direct current

Activities: Mapping the magnetic field of a bar magnet

Unit XI: ElectroMagnetic Wave/Particle Model

Paradigm Lab: ????

So far, I’m stuck. I’m not sure what lab to do. From what I can tell, NGSS doesn’t have any focus on optics, rather on using EM waves to transmit information. In the end, to me this unit needs to show that we need both a particle and a wave model to show different aspects of EM behavior, but other than specifying interference, diffraction, and the photoelectric effect, all other standards are about information.

Modeling the AP-2 Course

As this year draws to a conclusion, and I look ahead to the coming changes in physics education (yes I’m looking at you college board and NGSS), I’m beginning to look ahead to how I might change what I’ve done to meet these new standards. Please note, I’ve only taught with Modeling Instruction for one year now, but maybe my fresh eyes will be beneficial in bridging the between the traditional modeling curriculum and what will be needed in the future courses.

Over the next few weeks, I’m hoping to add more posts to fill in more details, but here’s what I’m thinking so far the AP-2 Course:

Unit I: Computer Modeling

Students will be introduce to the vPython programing language, and will work through a series of situations as they try to build a computer model that matches the given situation. The situations will review most of the major concepts from mechanics as they build up a computer model. The end product will be a program that models multiple equal-mass balls moving inside a box that show elastic collisions with the boundary and each other. They will use this program to predict the results of the gas law experiments.

Unit II: Thermodynamics/Ideal Gas Particle Model

Paradigm Lab: Gas Laws labs

Objective: to determine the graphical and mathematical relationship between pressure, volume, number of particles and temperature

Unit III: Fluids

Paradigm Lab: Pipe Lab

Objective: to determine the graphical and mathematical relationship height of fluid above opening, pipe radius, hole radius, flow rate, and exit velocity

Unit IV: Electric Charge/Field

Paradigm Lab: Balloon Lab

Objective: to determine the graphical and mathematical relationship between charge, distance, and electric force

Unit V: Electric Potential

Paradigm Lab: Mapping the electric field and equipotential lines

Objective: to determine the graphical and mathematical relationship between position and potential between two charged plates

Unit VI: Electric Circuits

Paradigm Lab: RC Circuit

Objective: to determine the graphical and mathematical relationship between potential and time for the charging and discharging of an RC circuit.

Unit VII: Magnetism

Paradigm Lab: Field cause by a current carrying wire

Objective: to determine the graphical and mathematical relationship between current, distance from the wire, and magnetic field for a wire carrying a direct current

Activities: Mapping the magnetic field of a bar magnet, Force on a current carrying wire in a magnetic field

Unit VIII: Particle of Light Model

Activities: Image in a flat mirror, image in a curved mirror

Paradigm Lab: Intensity of Light

Objective: to determine the graphical and mathematical relationship between distance to the screen and area of shadow

Unit IX: Wave Model of Light

Activities: Diffraction Grating

Paradigm Lab: Lens Lab

Objectives:

  • to determine the graphical and mathematical relationship between object distance and image distance.
  • to determine the graphical and mathematical relationship between the ratio of image distance to object distance with the ratio of image height to object height.

Unit X: “Quantum” Model

Paradigm Lab: Photoelectric Effect Simulation

Objective: to determine the graphical and mathematical relationship between intensity of light, color of light, incident metal, and stopping voltage

Activities: Determining the Rydberg Constant for Hydrogen Emission

Unit XI: “Standard” Model

Paradigm Lab: Compton Scattering Simulation

Objective: to determine the graphical and mathematical relationship between incident wavelength, reflected wavelength, angle, and momentum of scattered electron

Modeling the AP-1 Course

As this year draws to a conclusion, and I look ahead to the coming changes in physics education (yes I’m looking at you college board and NGSS), I’m beginning to look ahead to how I might change what I’ve done to meet these new standards. Please note, I’ve only taught with Modeling Instruction for one year now, but maybe my fresh eyes will be beneficial in bridging the between the traditional modeling curriculum and what will be needed in the future courses.

Over the next few weeks, I’m hoping to add more posts to fill in more details, but here’s what I’m thinking so far the AP-1 Course:

Unit I: Scientific Methods/Intro to Modeling/Constant Velocity Particle Model

Paradigm Lab: Buggy Lab

Objective: to determine the graphical and mathematical relationship between position and time for a toy buggy.

Unit II: Constant Acceleration Particle Model

Paradigm Lab: Cart on incline plane

Objective: to determine the graphical and mathematical relationship between position and time for a cart moving down a ramp.

Unit III: Balanced Forces Particle Model

Paradigm Lab: Gravitational Field Lab

Objective: to determine the graphical and mathematical relationship between mass of an object and its weight

Unit IV: Unbalanced Forces Particle Model

Paradigm Lab: Modified Atwood Machine

Objective: to determine the graphical and mathematical relationship between Force, mass, and acceleration

Unit V: 2D Particle Model

Paradigm Lab: Ball Toss

Objective: to determine the graphical and mathematical relationship between horizontal position, vertical position, and time for a ball tossed through the air.

Unit VI: Energy Transfer Model

Paradigm Lab: Cart “Launch”

Objective: to determine the graphical and mathematical relationship between compression of a spring, maximum velocity, and maximum height of a cart launched up an inclined plane.

Unit VII: Momentum Transfer Model

Paradigm Lab: Cart Explosion

Objective: to determine the graphical and mathematical relationship between the ratio of velocities to the ratio of masses when two carts explode apart.

Unit VIII: Central Force Particle Model

Paradigm Lab: Orbiting Rubber Stopper

Objective: to determine the graphical and mathematical relationship between mass, radius, period, and tension.

Unit IX: Rotating Particle Model

Paradigm Lab: Atwood Machine with attached spinner bar

Objective: to determine the graphical and mathematical relationship between the torque caused by a falling object, mass on bar, the location (radius) of the masses on the bar, and the angular acceleration.

Unit X: Oscillating Particle Model

Paradigm Lab: Bouncing mass on spring

Objective: to determine the graphical and mathematical relationship between amplitude, mass, and spring constant with period.

Unit XI: Mechanical Wave Model (1D & 2D)

Paradigm Lab: Snakey Lab

Objective: to determine the graphical and mathematical relationship between pulse length, pulse amplitude, and tension with wavespeed in a snakey spring.

Unit XII: Charged Particle Model

Activities: Sticky Tape, build a circuit

Paradigm Lab: Dimmer Switch Lab

Objective: to determine the graphical and mathematical relationship between voltage drop and current for a light bulb and for a fixed resistor, each in a series circuit with a potentiometer.

Light Reflection, Refraction, & Diffraction

I hope it’s not getting old, but I would like to say that for those that have never attended a modeling workshop, although I hope this series of blogs peaks your interest, in no way should they be viewed as a replacement. Compared to the first set of workshop, I will not be posting links to the materials used as ASU and the AMTA have chosen to keep them under lock and key. If you are offended by that, I’m sorry, but they have chosen to restrict some materials, and I am in no place to challenge them. The basic thought process is that there research has shown that one best learns through doing, not through being told.  Therefore, the best way to learn how to implement modeling is to experience modeling for yourself, not to read about it.  In short, if you just read how to model, try to use it and find it ineffective, it could very well be you implemented it incorrectly.  Go to the workshop, you’ll thank me.  For those readers that have attended the Mechanics workshop, this may help you sort through the materials to which you have access, but again, you might want to try to get to one of these if you can.

2-D Wave Motion

We begin this portion of the unit by putting together ripple tanks.  Although these contraptions clearly show the behavior of water, I think there is a much cheaper solution.  By no means do I want to go full scale $2 whiteboard here (I mean no disrespect by that comment, I think that blogpost might be one of the greatest I’ve ever read), but I don’t see why you need that much complexity.  Why not just use a cafeteria tray, your finger and/or a ruler as a wave generator, and some simple objects (or even the edges of the tray) to show boundary interactions?  The time it takes to setup just doesn’t seem to justify the fact that you can see everything with a simple tray you’ve taken borrowed from your school cafeteria.

Anyway, mini-rant over, in using the ripple tank we are to look at how the waves react when a boundary is placed in the water.  Lo and behold, the waves reflect just like we saw with light!  We then try to look at refraction.  This part was very problematic.  The teacher notes say to put a thin piece of plastic in the water to change the water level.  For us, we did see a change in wavelength, however, we were never able to create a scenario in which the direction changed.  I think that side of things needs a little more refining (it has to be the procedure, it couldn’t be your humble blogger).

After a circle meeting to share the behaviors we saw, we worked on the second worksheet which brings in a new way of showing the behavior of waves: wave-front motion maps.  In some sense, just imagine a ray diagram with lines added to show the wave fronts (I’ll try to add pictures at some point, but the server here is way to slow).

One thing that we noticed in discussing this worksheet is that we needed to build the relationship between index of refraction “n,”  the speed of light in a vacuum, and the speed of light in a given medium.  I’m not sure if that jump to light is needed here, rather I think this might be better served taught separately as just mechanical waves (more on this to come in a later blogpost).

From there, we started a lab to show the diffraction of light.  The group set up a flashlight with a screen (open 3-ring binder) casting a shadow on a wall.  They then asked us, if a laser is placed under the flashlight and just touches the edge of the binder, where will the laser dot hit the wall in relation to the edge of the shadow?  We said that it should hit right at the edge of the shadow.  Once they set it up, we saw that the laser hit a few inches away, on the light side of the shadow’s edge.  I think care needs to be taken when setting this up to make sure that the students see that the laser is directly underneath the flashlight, and that the flashlight is small.  Several “students” (myself included) think that big of a shift seems unlikely to be due just to diffraction.

From there we move into a new behavior of light, that being diffraction.  By placing two boundaries in the water, we could look at what happens as the wave front passes between a small opening.  We were encouraged by the “teachers” to look at how the size of the opening effected the resulting diffraction pattern as well as how adjusting the frequency of the source on the diffraction pattern.

We finished up by working on worksheet 3: Diffraction to apply some of the concepts just developed.  One thing I really like was at the end of the worksheet.  The students are asked to predict what should happen if there are two openings.  After a good discussion, I left thinking, whatever the kids think here, as long as they can defend it using the wave model, is ok.  We now have a natural tie-in to a behavior of light not yet studied.  I’m ok leaving the question without a definite solution, as they’ll get it in the very next step of the unit, but that’s for the next blogpost.

{The Wave Model, brought to you by FIU, CHEPRO and the National Science Foundation}