Hugh Ross shared the slickest centripetal force lab I've seen that is really easy to do and is fairly cheap--I just need to get about 10 dual range force sensors. I really liked how we found the relationship between the net force and the radius and then with the mass non-quantitatively. After we figured out the relationships we then combined them to plot net force vs. m/r and guess what the slope was v^2! Very nice!
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After tonight's reading and today's discussion about our UCM lab tomorrow it caused me to remember something I wanted to do this past year but I didn't have the time to do it. The traditional rubber-stopper lab (hit-yourself in the head lab) always gives poor results. I can't afford the $300 sophisticated vernier equipment (spinning track). After asking if anyone had tried to do video analysis with the hit-yourself-in-the-head lab, Rob said that he had done it with his AP Physics class and although it gave good results for him he said that he wouldn't recommend doing it with first year physics students. How about doing video analysis with an air puck? I wonder if anyone has done that.
Questions I have: Would the vernier student force sensor work? Would the dual-range force sensor work? If I could measure the force how could I vary the mass of the puck to determine the relationship between force and mass? Yesterday we completed the Eel lab and Ek lab (using Ekmax = Eelmax). Today our task was too graphically and mathematically model the relationship between Eg and the variables height and mass.
The underlying concept like the Ek lab will be conservation of energy. However there are numerous ways to do this since we already have mathematical models for Eel and Ek. We chose to use a vertical spring to shoot a ball bearing into the air. The system our case was the ball, earth, and the spring. Our assumption was that energy storage right before the ball shot was Eel and the storage at the top of the ball’s path was Egmax. This gave a direct relationship between Eg and height. The slope of this graph was 0.32 N and the mass of the ball was 0.016-kg. This assumed that Eelmax was a trapezoidal region given by the product of the average force and the displacement of the spring. When the more traditional method of using Eel = ½ k∆x2 the Eg vs. height graph was linear with a slope of 0.27 N. Physics teachers know the slope should be the weight of the ball. Since the slope was significantly more than the weight this would imply that ball should have gone significantly higher than it did go. Since the ball did not go higher a significant amount of energy must have been stored as Eint when the ball was at its highest point. We do not have a mathematical model to determine this Eint so this method should be abandoned. This was my exact experience this past year. I even tried having the students let the cart explode upward from the backstop of an inclined dynamics track. First I had them let the cart roll down the ramp and then bounce off the backstop again ascending the inclined track. The cart didn’t go as far back up as it started. Students used this ratio to determine the percent initial Eel that was stored in Eg at the top of the cart’s motion as it exploded upward from the backstop. It worked but was very contrived and I feel that I lost a lot of students in the process. The thing that I learned from today’s activity is that students need to be directed to develop a lab that will minimize ∆Eint. I will illicit from students what are some ways in which you can cause a greater ∆Eint. Hopefully they will say to somehow increase the effects of friction or to cause some sort of radiative process (sound, light, etc.). I will then lead them to the point that they need to choose a procedure which “eliminates” these effects and suggest that they develop energy pie charts and play with their lab equipment to see if in fact these have been “eliminated”. I really wish I had flip cameras to open up the possibilities of quickly gathering data. I. What I like from Gregg Swackhammer's "Making Work Work":
1. Page 2: "Another difficulty common among students is the belief that work is done through any force on an object acting at least somewhat in the direction of its motion. For an example of a situation in which this belief is misleading consider a self-propelled object such as a jumping disk. The jumping disk is cocked into position and placed upon a table. No energy enters the jumping disk from the outside world as it pops up into the air. It does move upward, because the table exerts a force on it that causes it to accelerate. But there is no work done on the disk. There is simply a redistribution of energy within the disk itself. A careless application of W = F ∆x cos θ or the work-energy theorem (W = ∆KE) will lead students to the conclusion that there is work done on the disk. There is no work done on the disk because of the “jump.”" It reminds me of discussions I've had with other physics teachers who have maintained that the Normal force does positive work on a person as they ascend a flight of stairs. After reading several of Jewett's articles in the Physics Teacher I've become convinced that the Normal from the stair wasn't doing work and so the ∆Eg had to be explained in some other way (∆Echem). I remember this bothering me a lot in the beginning because a force must be causing this change in storage mechanisms and the most visible force is the Normal force. I no longer believe the macroscopic Normal force is involved in doing work. I now believe it is microscopic electrostatic repulsive forces that do the work. More specifically with regards to the first law of thermodynamics I believe that there is a change in internal energy (∆U) of the person which can be thought of as the sum of all the products of the microscopic electrostatic repulsive forces and their displacements. 2. I like the idea of not using the word "Potential". I'm sure I will screw that up a lot and correct my self repeatedly. I'm kind of afraid that students will be thrown though when they hear those terms in college. Hmmmm. Maybe it will be good that I screw up from time to time. 3. I like energy pie charts, energy bar graphs and the way he does flow diagrams. I did the flow diagrams wrong last year. II. What I don't like from Gregg Swackhammer's "Making Work Work": 1. Page 2 (friction is taboo): "Work done by agents exerting frictional forces cannot be calculated by W = F ∆x cos θ. Despite this fact, many textbooks actually assert that it can be calculated this way. The problem here is our limited knowledge. We do not know the actual magnitudes of the forces being exerted on the microscopic level at the points of contact, nor do we know the distances over which those forces are exerted. Textbooks often use the net frictional force and the center of mass displacement ∆xcm as though they are the appropriate variables to insert into W = F ∆x cos θ. They are not. Therefore students end up with misleading results as they use W = F ∆x cos θ to solve friction problems . . ." I have some major objections to abandoning the notion that students should be able to calculate the work done by friction with W = F ∆x cos θ. I understand what Swackhammer is saying however here are my objections 1) everyone else is doing it that way and 2) some way cool discussion won't happen. I know what you are thinking #1 is lame. Hey I want my kids to be able to compete with everyone else when they take that college physics course or on that AP Physics test. Telling the kid, "I'm not teaching this material because it is pedagogically unsound and you should tell your professor I said so!"--just won't cut it. With regards to #2 I really like the conversations we have when students solve problems like: A 0.25-kg cube slides down a 0.5 m, 30 degree frictionless incline and onto a horizontal rough 0.1 m long surface (μk = 0.15) before striking a horizontal spring (k = 30 N/m). What is the maximum compression of the spring? I think Swackhammer is saying this can't be done using the definition for work using the net frictional force and ∆xcm--this isn't really work but some quasi-work-thing. That is what Jewett says too. I get that but I don't think that either one would argue that the quasi-work-thing equation gives an answer that can be tested in a lab and that it would probably give an accurate prediction. So if it models a real-life testable occurrence why not use it especially if students don't find it confusing in the least. In fact students often are the ones who would suggest that the work done by sliding friction is W = F ∆x cos θ. It "works" nicely and adds richness to the discussion. Page 10, full paragraph 3--whoa so I can't use the work-kinetic energy idea to explain different skid lengths being proportional to the square of the velocity. Of course you can because there is a well known relationship. Granted it might not be quite as straight forward as we present to our students or what is presented in textbooks but most models have their imperfections and when a person is ready to move on they do so. Again I feel like this makes something harder and we are losing some great conversations by "throwing the baby out with the bath water." While I agree that very little energy flows to the road, the friction between the wheels and the road is necessary to couple the translational kinetic energy to the rotational kinetic energy. This is why the proportional relationship between skid length and speed squared exists but I don't think it is necessary to get into that depth with students. Nor do I think it is justified to not teach it. 2. Internal Energy On page 5, section 3.2.1 paragraph two, Swackhammer reasons that "Therefore the work done on the box must be greater than zero." O.k. I feel you Gregg, but then lets go back up to your jumping disk. Does it warm when it jumps? If so is there work done on it after all (even if it isn't equal to the ∆Eg)? It definitely warms when it collides with the ground. Is there work being done on it then? If so what is doing the work? It can't be the Normal force because it isn't displaced. If you say work isn't being done in both of these instances then you have some 'splaining to do, Lucy. (I'm tired). Page 10, last full paragraph, Swackhammer says, "The energy flow diagram makes it easy to see why there is no work associated with this system, because no energy enters or leaves it." So does this mean that internal forces are incapable of doing work? Example: An extended system (a blob of gas) is heated and thus expands (internal forces). Is work done? III. What I don't understand from Gregg Swackhammer's "Making Work Work": On page 4 Swackhammer says, "The stronger the gravitational field, the less gravitational energy it possesses! The enormous gravitational field of a black hole is the symptom of an enormous loss of gravitational energy." I don't get this at all. I thought gravitational energy at a point is meaningless . . . its the change in gravitational energy that matters in going from one point to another. I don't see how you can say that a strong field has less energy than a weak field . . . don't get it. Aaaarrgh. I've posted my data for the KE lab in this posting. This lab is contrived such that we are able to ignore the Edisp by having the dynamics track slope gently to compensate for friction slowing the cart. We then can assume that the Eel max = KE max. KE (Eel trapezoid) vs. v is plotted and so is KE (Eel triangle) vs. v. Both were top-opening parabolas. The linearized graphs and generalized mathematical models are displayed below for the cart by itself. Both correlations are similar. However the general mathematical model for the case where I set Eel = 1/2*k*∆x^2 was closer to the acceptable mathematical model for KE (1/2*m*v^2). We increase the mass and repeated the experiment. In the image below you can see that the correlation for the KE (trapezoid) vs. v^2 was much better this time than the KE (triangle) vs. v^2. That said the general mathematical model was no better than the KE (triangle) vs. v^2 graph. I don't think this settles the debate we had in our modeling session today of whether the rectangular area of the Eel vs. ∆x graph of a spring is usable or not but my personal opinion is that it isn't usable.
Another interesting discussion came up in modeling. Assume we have a spring that isn't very stiff but it requires a very large initial force to stretch it any measurable amount. In this case you would get a graphical model like that shown above. The question is does the rectangular region represent usable energy . . . could it be stored as other types of energy KE, PEg, etc. What do you think and why?
Interesting side topic today in the modeling workshop. I love these things. "If a wound up bunny moves up a hill where is the gravitational potential energy stored?"
a. In the bunny b. In the gravitational field of the earth c. In the gravitational field of the bunny d. In the gravitational field of the system The conversation became somewhat sematical (is that a word). One could argue that the bunny stores the energy in the earth's gravitational field. Or could they? If a single mass occupies an otherwise massless universe does it have a gravitational field? Likewise if a positive point charge occupies an otherwise chargeless universe does it have an electric field? Electric field lines help us to conceptualize the electric field and they are defined to begin on a positive charge and end on a negative charge. If a lone positive charge were to have electric field lines emanating from it they would be spherically symmetric. However where are the lines going? They either go somewhere or they don't. If they go somewhere then the somewhere is negative but we just said that there is no other charges in the universe. Hmmm then I guess they go nowhere and they don't come from the charge and therefore we don't even know the charge is positive. In a like manner if there are no other masses in this otherwise massless universe (except for one point mass) then there must not be any gravitational fields associated with the mass and therefore there would be no mass associated with this lone "mass". Hmmmm. So where does General Relativity come in here? There would still have to be some effect of the lone object's mass on space-time. So is there still a gravitational field here? Would there still be an electric field for the lone "charge"? Too many questions . . . too few answers. Just began my two-week modeling workshop held at Guerrin HS being presented by Hugh Ross and Rob Spencer. Rob and I have been discussing SBG and how it would work within Modeling. He clued me into Kelly O'Shea's blog.
He and I talked further about whiteboarding. I shared with him some of my concerns about students not preparing for the day's whiteboarding because they didn't do their homework (no attempt). He had many suggestions: time limits, two grades (first is just attempt, 2nd is how much learned), assessment. I like the idea of using a count down timer and some sort of concluding formative assessment to keep students on task and invested in the learning event. Need to look into rubrics for these. Back to the workshop . . . I just found out that beginning in the 2011-2012 academic year Indiana science teachers will be responsible for teaching literacy standards in addition to the state standards in their discipline. The Indiana DOE science specialist, Jenny Hicks, provides this explanatory video. While I think these standards will be easy enough to accomplish I’m wondering when we were going to be informed, August 15th?
Additionally the DOE suggests some resources to help teachers in this set of four videos. Here is the summary of the resources: Emphasizing Informational Text: 1. Inspire.com (biographical information, science information) 2. Project Gutenberg Literacy Standards for All Content Areas: 1. Reading in the Disciplines (pp. 4-6) 2. Dr. Shanahan’s Disciplinary Literacy Blog with videos, ppt’s, graphic organizers, etc. 3. DOE’s Literacy Standards for Science & Exemplar Texts Text Complexity: 1. Lexile analyzer 2. Lexile of a known book The Special Place of Argument: 1. Purdue OWL rhetorical writing 2. ProCon.org As I was investigating the Common Core Literacy Standards for science I ran across an unrelated initiative to re-write the national science education standards. Education Week’s Erik W. Robelen states there are three goals: 1) decrease the number of core standards, 2) embrace the view that science students should continually build on and revise their knowledge and abilities over many years, and 3) emphasize that learning science means using scientific knowledge and the tools of scientific inquiry.
The draft was released last year and the Conceptual Framework for New Science Education Standards are due out this summer. I have always been frustrated with our “mile wide and inch deep” curriculum in physics here in Indiana. Eight years ago I sent out emails to physics professors all throughout the state trying to start up a conversation about this topic. I was disheartened by the feedback I received. Everybody had their own little pet topics that they wanted to be able to cover. Most agreed that doing everything actually accomplished nothing–just as the research stated. I was so dissollusioned in fact that last year at a Modeling Workshop where we had the ear of the state science curriculum specialist I chose not to get on the “less is more” bandwagon because I “knew” that it would go no where and just fall on deaf ears. Its nice to know that someone with more power might just force our state to move in the right direction. I know that once the framework is completed none of the states will be compelled to adopt them. However, now that we have the common core standards being adopted for Math and English and the Literacy standards for the other courses it seems like the next logical step would be to adopt the science framework. I’m pretty excited about this. I think all three goals fit nicely with the Modeling approach. More information about developing the next generation of science standards can be found here. |
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