paradigm lab

Days 87-91: Pendulums & Conservation of Momentum

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AP Physics: Pendulums

This week we started simple harmonic motion. We started by using a video on Pivot Interactives that has a pendulum, a glider on a spring, and a spinning disk that all go through simple harmonic motion with identical periods and amplitudes. Students plotted position vs. time and velocity vs. time graphs. When we shared the results, the students in calculus made some great connections to derivatives. We then moved into a lab to find the factors that affect the period of a pendulum. This is one of the labs where I felt like the hard work learning how to do an experiment really paid off as students worked pretty independently and got great results.

Physics: Conservation of Momentum

This week students worked on practicing conservation of momentum problems. One of their tasks was to figure out an unknown mass using results from a collision. One thing that has been tricky every time we do this practical is students sketch bar charts for what they want the collision will be, such as having both carts come to rest after a collision, but have trouble adjusting if their bar charts don’t match the actual collision. I think this comes down to many aren’t thinking of momentum bar charts as something that describe a physical event. I wonder if it would be helpful to do an activity where students do various collisions between pairs of carts, but focus only on representing those collisions with bar charts.

Days 64-67: Kinetic Energy & Newton’s 2nd Law

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This week was a little goofy. Tuesday was our first day back from break, then a big winter storm meant we had to close schools on Wednesday. We used up our regular snowdays in December, so Wednesday was an emergency e-learning day, which means students completed asynchronous assignments.

AP Physics 1: Kinetic Energy

Our first task back from break was to find the relationship between velocity and kinetic energy. I waffle every year whether to do this with tracks and probeware, which as the advantage of being firmly rooted in the real world for students, or use Pivot Interactives, which has the advantage of measurements that are easier to make. With the weather forecast, I opted for Pivot. I had students complete the first section that takes them through making measurements and modeling the energy transfers with energy bar charts individually, then complete the remaining sections in groups. It’s been a little while since we linearized a graph or developed a mathematical model from data, but I was really pleased with how they did.

Physics: Newton’s 2nd Law

Our big goal this week as a paradigm lab for Newton’s 2nd Law. In some conversations last year, Kelly O’Shea suggested using carts on ramps as an alternative to the more standard modified Atwoods machine. Students used a force sensor to measure how much force it took to hold the cart in place. Next, we used some vector addition diagrams to reason out the force they’d measured is the same as the net force when the cart is released. Students used the motion encoder carts to determine the acceleration, then changed the angle of the ramp and repeated their measurements. I really like that this is conceptually much simpler than the modified Atwood, so students can focus on making sense of the data, and this approach makes a really clear conceptual link between balanced forces and unbalanced forces. For the e-learning day, we had students do some reasoning with vector addition diagrams of balanced forces to help review those skills to support the lab.

Days 61-63: Energy Bar Charts & Newton’s 2nd Law

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This was supposed to be a four-day week, but an impending winter storm means we will be starting our winter break a day early.

AP Physics 1: Energy Bar Charts

This week I introduced students to energy bar charts and we spent a lot of time working and whiteboarding problems. Since we had two rounds of whiteboarding in a 3-day week, I asked students if they wanted to change it up from mistakes whiteboarding, but they were adamant that mistakes whiteboarding helps them learn. I was more concerned about whether they would be up for engaging in that much mistakes whiteboarding than whether it would be useful, so happily went along. I am really glad that they are seeing the value in making, analyzing, and discussing mistakes for their learning. I also had some great conversations with students this week where they talked about the growth they feel like they are making in this class, which is fantastic. That is a great note to go into winter break on.

Physics: Newton’s 2nd Law

This week felt more awkward with this course. We had a quiz on Monday that had been pushed from last week due to a snow day. Then the plan was to start the lab we’ll be doing on Newton’s 2nd Law. We are planning to use the motion encoder tracks, but students haven’t had any hands-on experience with them yet and haven’t used any velocity vs. time graphs in a few weeks. To address those issues, I put together an activity where students reviewed position vs. time and velocity vs. time graphs using the motion encoder tracks. That seemed to really help students feel comfortable with the equipment and set up what they’ll need to remember to find acceleration in the lab. That left us with today to start the lab. I dragged my feet on the introductory discussion rather than starting data collection, then picking it back up after two weeks off. We’ll see what I think of that decision when we come back from break!

Days 27-31: Balanced Force Practical & Newton’s 2nd Law Model-Building

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This week we wrapped up balanced forces with a practical. I used some magnetic hooks to attach spring scales to the whiteboard and let students measure the forces and any angles they wanted. Even though I only had two setups and five groups, different groups ended up taking different approaches, which was great for students to see in some discussion after the practical. We also had some good discussion about uncertainty when we measured the actual mass and students were initially disappointed with how far their calculations were off before, which lead to the realization they’d actually been pretty on target!

After the practical, we started Newton’s 2nd Law with a paradigm lab using the standard modified Atwood’s machine. There was some messiness in the value of the slope that students got, which is pretty typical from when I’ve done this lab. One of these days I’ll figure out how to coach students to really high-quality results! Students did really well at translating the equations for their line of best fit into something that had units and variables that matched the experiment and did a nice job in the board meeting making sense of their slope and intercept.

Days 20-23: Mathematical Force Models

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This was a short week due to a PD day on Friday.

This week, we focused on building mathematical models for the force of gravity and spring force. My students have taken very nicely to writing equations for lines of best fit in “physics” where they add units to their slope and intercepts as well as use variables that match their experiment. My students are also taking nicely to using “for every” statements like “the force goes up 10 N for every 1 kg of mass” to think conceptually about the meaning of their slopes. Students have also done really well with turning their intercept into statements like “the intercept is the size of the force when the mass is 0 kg” to think about what kind of intercept makes sense.

With the spring force experiment, I had students stretch their springs both vertically and horizontally to see the graph had the same slope in both directions. This usually seems to help address conceptions about the role of gravity in the behavior springs that come up when we get to energy and simple harmonic motion.

Days 10-14: Building CAPM

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This week, students did a lab with ramps to start building the constant acceleration of a particle model. Students used Vernier Video Analysis to get their graphs, and I really love how the video analysis tracks set up motion maps for constant acceleration. Students seemed to feel pretty good about some of the math-y skills in this lab, including linearization and “translating” their line of best fit into a version that has variables that match the experiment and units on the slope and intercept. We then did some mistakes whiteboarding with problems translating between different representations of constant acceleration, which my students continued to do fantastic with.

One thing I think is worth thinking about it it feels like because this is our first experience with linearization, the later days of this lab feel very focused on the math. Then, it feels like we set the heavy math aside while working on translating between representations, only to circle back once we are ready to start doing problems. I wonder if there is a way to structure the constant acceleration unit differently to make it feel more coherent. We have the Vernier motion encoder carts, so I wonder if one option could be to start by having students more or less play with carts on ramps to focus on the shape of graphs, then work on translating representations. Then once students are solid on the representations, do the more standard ramp lab to bring in mathematical representations.

Days 123-127: Kinetic Energy & Centripetal Force

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Physics: Kinetic Energy

The biggest task this week was a lab to determine the equation for kinetic energy. On some recent labs, students have struggled to get good data. I think part of the issue is many don’t buy into the idea that knowledge should come from the labs they do, so they don’t invest the effort or attention into getting good data, which makes it hard to see how it leads to physics concepts or equations and becomes a self-reinforcing cycle I wanted to interrupt with this lab. We talked a little about what I observed and my hypothesis, then I re-did the gravitational potential energy lab as a demo and made a point of discussing the things I was doing to get good measurements and check the quality of my data as I went. When we were getting ready to whiteboard, I also checked in with groups to make sure they had quantities on the correct axis and were seeing that they needed to linearize. The result was data that really nicely showed the quadratic relationship between kinetic energy and velocity and most graphs even had slopes very close to half the mass of the carts students used! A lot of students were really proud of their results, which was great to see and I’m hoping will encourage them to continue those good data collection practices.

AP Physics 1: Centripetal Force

I like to ignore the College Board’s recommendation to do centripetal force as unit 3 because it is such a nice opportunity for built-in review of a lot of ideas about forces. We started by spinning some rubber stoppers on strings to talk qualitatively about how we could change the force in the string before moving over to Pivot Interactives to collect quantitative data (disclaimer: I am a content writer for Pivot Interactives). Next, we used an activity I originally got from Lucas Walker using exoplanet data to find the law of universal gravitation. Students are making the connections I want them to, but I can tell they are starting to feel some fatigue. I typically rely a lot on Pivot Interactives for this topic since we don’t have much equipment, but students got pretty into the brief hands-on activities we did this week, so I think I should make sure to keep working those in to help my students stay engaged these next few weeks.

Days 72-74: Unbalanced Forces & Kinetic Energy

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We had a short 3-day week to lead us into break.

Physics: Unbalanced Forces

We wrapped up unbalanced forces this week with a lab practical. I put a cart on a ramp, held in place by a string attached to a force sensor. Students had to first predict the tension in the string and next predict the time it would take the cart to travel between two photogates on the track once I cut the string. It was trickier than I expected for students to recognize that the tension in the string would be the same as the net force on the cart once the string was cut. Since that was an important idea in the paradigm lab we did this year, I left students to figure out that point on their own, but I think it would have been worthwhile to give students some questions or other structure to think through that aspect of the practical. We haven’t revisited velocity vs. time graphs lately, so I was very excited to see how well they did annotating their graphs and setting up equations to find the time.

A cart on a track with two photogates. The cart is tied with a piece of string to a force sensor and is held in place just before the first photogate.

AP Physics 1: Kinetic Energy

Students used Pivot Interactives for a lab to find the mathematical model for kinetic energy. Their data came out beautiful, but the introductory section of the activity didn’t do as much as I’d hoped to prepare students to collect data. This fits with a larger pattern I’ve noticed this year where students in both my courses don’t seem to make a clear connection between the pre-lab discussion (which the introductory section was similar to) and the actual lab. I think I haven’t helped students make a clear connection between the experimental design thinking we do in those discussions and what they will actually need to do in the lab. I’m giving some thought to how I can do a better job of showing how those discussions lead naturally to what students will be doing in the lab.

A silicone puck is levitating over a curved magnetic track. The puck is held in place near the top of the track by a small block of wood.