In addition to traditional Ohm's law labs and equivalent resistance (parallel and series circuits). Rob Spencer suggested a P vs. V "dry" lab. I think it could be done though with a vanity bar???
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This was a challenge to connect the concepts of charges, e-fields, and potential. The group drew a charged capacitor, 2 light bulbs in series and an open switch. We were asked how we knew it was charged and what had to be done to do this and what exists in the capacitor.
We were talking about how the "charges pile up" right before the resistor/light bulb (I have a problem with this idea--all charge carriers in a circuit have the same drift speed--the volume flow rate must be constant--all circuit components with zero resistance in any particular branch need to have same KE of charge carrieres). We also talked about how the pressure before the resistor was higher than after. I am more comfortable with this approach. Need a small massed handle on generator (should use genecon generator or make of small motor with prop????). They use an LED to indicate the charging of the capacitor. I wonder if it would be a good idea for students to figure out for themselves that LED are unidirectional. Bi-directional LED's might be a good idea.
Bob presented how he does electric field mapping & equipotential surfaces mapping. He uses carbon paper and paints various conducting surfaces. Also hollow and solid objects are put in between. A probe is put at various locations and the coordinates are recorded with the potential. Bob recommends that you give each group different shapes to motivate them to get their data quickly (some nit picky take forever on one data point and there are a possible 500 data points--it takes a long time).
Then this data is put into excel and plotted 3-D to show the equipotential surfaces and to help students make the connection with gravity. Then they print out a 2-D black/white equipotential map and draw in their perpendicular E-field lines. A variation of this activity is to use a container of water over a grid and the water is the conductor. I like this way because students actually see this as "real". With the conductive paper students don't see the lines drawn on the paper as being a 3-D object like a plate. In their minds this isn't real. It might be a good idea to use LED's to show the directionality of the e-fields in the water container. I was thinking about justifications for the particle model of light besides the photo electric effect and started thinking about the Compton effect showing that light has momentum which a wave would not have since there is no net transfer of mass but I think its too complicated to explain let alone replicate in high school.
A physics question came to mind while thinking about the Compton effect. I understand why we relate frequency to energy since color is related to energy. Additionally, color and frequency are constant in refraction experiments whereas speed and wavelength change. However why do we relate photon momentum to wavelength. I understand that the wavelength changes for Compton scattering as does the momentum of the photon. However since the speed of light is constant the "color" of the light (frequency) also changes. A few possibilities that came to mind: a. Conservation of energy is a symmetry is time and conservation of momentum is a symmetry in space so it kind of makes sense that since frequency is related to time it would be associated with energy and since wavelength is related to space it would be associated with momentum. b. The Bohr atom indicates that angular momentum (not linear) is quantized. Usually this is shown as an electron exhibiting wavelike properties of a standing wave and thus not radiating and spiraling into the nucleus so it looks (based on diagrams) that the wavelength is important however without just the right frequency there wouldn't be a standing wave. c. Since frequency is related to energy perhaps it would be better not to associate it with momentum so by default wavelength is related to momentum. I know I missing something I just don't know what it is. After being presented with an electrostatics demonstration we were prompted to decide that the balanced force model should be applied. Further we were suppose to discover a relationship for this new force. We theorized that it was related to how much charge was on the objects and the distance between the two objects. We discussed ways in which we could theoretically know the amount of charge on one of the objects. However we noticed that the force seems to slowly change and we theorized that the charge must be leaking off and so we decided that we needed to work quickly to gather any data. Therefore we decided to only change the distance.
We wanted to plot the F vs. r however we noticed that based upon the free-body diagram and the triangle formed from the suspended pith ball as a charged balloon is brought near were similar. Therefore all we had to measure is the horizontal displacement from the vertical for the pith ball, d, as well as the center to center distance, r, between the charged pith ball and balloon and plot d vs. r. We tried to take data by hand measuring but it took to long and we only got three data points. Therefore we decided to videotape the lab and use Tracker to obtain the measurements. This meant that the data acquisition was complete in only about 30 seconds. The linearized best fit was an inverse square relationship. Hugh Ross suggested that we try his Fun Fly stick since it was more of a "point" charge. When we analyzed this data we got an inverse relationship. We couldn't figure out what we were doing wrong. Well it was a fortunate mistake. When the fly stick approached the pith it did so line an infinite line charge. The relationship in this case would not be inverse square but in fact would be an inverse relationship. Totally Cool! Last year in AP Physics we just simulated line charges with a Feinmann suggested lab of using a line of light from a computer screen. It worked but its a simulation and this is so much better since they already do the Coulomb lab. We theorized if we brought a plane charge (thick and rather large styrofoam board) we would get a constant relationship. We didn't try this since we lack the styrofoam but evidently Rob Spencer says that there is a video on line. He says that he has tried this but that it didn't come out well (its problematic). Since the pith ball has to be far from the edge of the "infinite" plane of charge and the pith ball is hanging from string, I can see how it would be problematic because the "infinite sheet might start to hit the suspension string of the pith ball and so it would have to be lowered (pith ball now closer to top edge of plane). Maybe it would be a better idea to give the pith ball the opposite charge so that it is attracted to the plane and so the plane would never approach the suspension string. Additionally the pith ball should start near the plane and move away and students need to mass the pith ball and using the free-body actually plot Fe vs. r as opposed to d vs. r. As the pith ball moves outward the angle should remain the same. Now that I think about it I think when I have my AP kids do this lab I will have them try having the pith ball oppositely charged (attracting) and not let them plot d vs. r for any. After this lab students would do several deployment activities (practice worksheets) then they would be introduced to E-fields. The way this occurs is that they are given the same charge magnitudes (positive) and a negative central charge is located some distance away. Students are asked to calculate the magnitude of the Coulomb force and they are asked to come up to the board and draw in their force vectors on the board. After noticing that the force is greater nearer the central charge and after some discussion as to what happens if the charges are doubled (vectors longer but those same distance are the same length), students are asked to create a table of forces for charges that are multiples of their test charge but located at the same location. Then they are asked to plot Fe vs. q. Students are asked what the physical significance of the slope of their graph is and they are asked to explain why their slope is different compared to other in the class. After analyzing the units of the slope students are asked to compare Coulomb's law to the universal law of gravitation (g = GM/r^2). They are then asked what the slope repres A lot of concepts in the lab and there are many new terms just handed to the kids (insulator, conductor, electrons, negative and positive charges). I think that there are good things here but it moves too quickly for a novice. I think it would be better if it would be broken up and cover one new concept at a time (sticky tape = likes repel and opposites attract). I don't know if there are any simulations of triboelectric phenomena or not but I think this might be a good idea before presenting the idea of positive/negative. I guess I would like to know what the reason was historically for those terms why not electric/anti-electric or amber/silk or yellow/white???? Then students can be introduced to the terms conductor/insulator. Josie shared an idea of having the students form a human circle circuit with an "insulator" or a "conductor" so students see the effects and therefore define these themselves. Then I would might have the students expand upon the introductory sticky tape lab to investigate how to remove charges, which is positive/negative, and the difference between induction and polarization.
My group decided to present how the modeling program presents the photon model of light. The modeling materials suggest that a demo is presents showing an electroscope being discharged by UV light but not regular light. Then the materials use this as a spring-board to the photo-electric to show the limitations of the wave model of light.
While the discharge of an electroscope is a neat demo the students haven't been presented with any electrostatics or electrodynamics yet. Also the students have not constructed a relationship between color and frequency yet (could be wavelength too). Students haven't constructed the relationship between potential (voltage) and energy nor have they determined the charge of an electron. Additionally due to the cost of the photo-electric experiment equipment it is doubtful that there would be enough for multiple groups of students to perform the experiment. The simulation that the materials suggest plot all of the data automatically for the students and one of the graphs uses E instead of V in the plot versus frequency. I believe that the photon model should be included after the Bohr model. However if I do include it in the light unit as a capstone class lab I think I could be successful in a modeling approach if Vcutoff vs. Intensity and Vcutoff vs. frequency can be plotted. The following is how I would do it: 1. Present a solar cell powered toy, calculator, etc. and ask students what is happening here in terms of energy (encourage energy pie charts). Students might mislabel the energy storage mechanism for light don't worry about this but hopefully they would say something like Elight which is later stored as Eelect, Ek and Edis. 2. If students haven't already developed the idea that the energy of a wave is related to it amplitude this should be done now (multiple speakers quiet in and of themselves sound loud together--thus lots of energy--which can be shown to have larger amplitude on an oscilloscope, swinging pendulum shows that larger amplitude has more energy). Additionally students need to see that brighter sources have more energy and are said to be of greater intensity (show bathroom light bar with one light, two, etc. all of equal bright intensity but together greater intensity = more energy). 3. Students need to accept that this new term Voltage is related to energy. This could be done by having students note the effects of increased voltage on a light bulb (greater voltage = greater brightness and thus more energy). 4. Ask students to predict which characteristics of a wave might effect the voltage (Eelect) of the circuit. Anticipated answers Intensity, wavelength, and frequency. Help students to see that since wavelength and frequency are related to the speed of light which is a constant then we only need to test one of these. Further help them see that the different light sources are different colors and remind them of the connection between color and frequency. Recommend that students plot Vcutoff vs. frequency first. 5. The mathematical model found from Vcutoff vs. frequency indicates that the wave model is justified. 6. Have students come back and whiteboard their preliminary results indicating the wave nature of light and then ask them to predict the relationship they will get for Vcutoff vs. Intensity for a particular frequency of light that gives a non-zero voltage. This prediction should be direct. 7. Now have students go back into lab and have them plot Vcutoff vs. intensity. 8. Have students come back and whiteboard their results (no relationship) and ask them what this implies about the wave-model of light. Ask them to suggest another model for light and hopefully they will suggest the particle model again. 9. Given that only one particle of light can interact at a time what does it mean to have a more or less intense light source. They should suggest more particles per second (not faster just more). If they are having trouble with this have the students sketch the photo-electric effect equipment set-up and have them sketch in particles coming from the light. Now ask them to predict what the Vcutoff vs. intensity graph would look like again given that only one particle can interact at a given time. Hopefully they will suggest a digital square-wave looking graph with the maximum being a cutoff. Each square represents a particle of light's amount of energy being stored as Eelect then it would drop back to zero. As the intensity increases the density of these squares would increase maintaining a constant Vcutoff. 10. Recap for student what the graph Vcutoff vs. f suggests about the nature of light and what Vcutoff vs. Intensity suggests about the nature of light. In other words when light interacts with matter we need to use the particle model of light we call these particles photons and otherwise we need to use the wave model of light. This is known as the photon model of light which we need to use from now on. After reading the modeling teacher notes on curved mirror reflections my partner (Mike Thomas) and I felt that they were lacking a strong conceptual foundation and jumped to quickly into definitions and calculations so we decided to supplement the notes.
Now that we have demonstrated that energy is transported in a wave I think a natural question would be what storage mechanism is manifested here? The wave has a constant speed so the first thought would be Ek. But the displacement of the mass is zero. I believe that it is 50 % Ee and 50% Ek but I'm not sure.
Additionally since the transport of energy in the wave is at a constant speed another natural thought would be that the balanced force model should be applied. Should it? I don't think so because the oscillating medium is not in equilibrium. One last thought. We watching the videos of waves pulses interacting with interfaces between media it reminds me of collisions and conservation of momentum. I wonder if this should be addressed at all? |
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