Day 8: Mathematical Model for Pressure in a Fluid

AP Physics 2 started class sharing their mathematical models for pressure vs. depth below the surface of a fluid. In general, students struggled a surprising amount getting the equation for the best-fit line correct and handling unit conversions. One student shared that they needed a week to get back in the swing of things (it is the eighth day of class), and another shared that them struggling with this was “kind of sad.” Once we got the mathematical models captured in the Google Doc correctly, I was surprised at the range of values for the slope.

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We discussed potential sources of major systematic error such as losing the seal between the glass tube and the plastic tube or heating up the air trapped in the plastic tube by holding it tightly throughout the experiment. I need to investigate calibrating the pressure sensors and seeing if the experimental technique can be improved to gather higher quality data.

After discussion the lab, we derived the general form of the equation through application of the balanced force particle model on a cylinder of water at rest within a beaker of water. It was good to reinforce a basic model from last year.

  ##paradigmlab ##setbacks ##expdesign ##fluids  

Day 7: Fluids Paradigm Lab Continued

Today in AP Physics 2, groups shared their results from yesterday’s fluid paradigm lab. The groups investigating pressure vs. volume of fluid above a point or pressure vs. depth in fluid were confident that the pressure at a point depended on the depth below the surface of the fluid and not on the volume of fluid above that point. They had sufficient data that they were also confident that there was a linear relationship between pressure and depth. The groups that investigated pressure vs. fluid density at constant depth/volume had inconclusive results. The pressure they measured varied by less than 1% between the three types of fluids. This provided an opportunity to discuss how the experimental technique can affect the uncertainty of the measurement. We discussed that with the new understanding of the relationship between pressure and depth, these groups could gather several measurements at various depths in each of the three fluids and compare the slopes of the resulting graphs to see if density has an effect. While we were discussing measurement uncertainty, we also discussed how the depth is defined not by the position of the bottom of the glass tube, but the water level within the glass tube. While the groups investigating the effect of fluid density on pressure applied their new experimental technique, the rest of the groups repeated gathering pressure vs. depth data while carefully examining the fluid level in the glass tube.

For homework yesterday, I posted a link to the four-step Plotly tutorial on linear fits. All students were able to create graphs in Plotly. However, what confused several groups was that Plotly reports the equation of the line of best fit as y = a + bx, and these groups assumed the coefficients were in the form of y = ax + b. That lead to some confusing results at first.

Some groups are still finalizing their analysis, but three groups in one class reported their findings for the mathematical model of pressure vs. depth for tap water. We need to work on units (check out the units on the vertical intercept) and investigate the cause of the error in the third equation (at least they have the proper units for their intercept).

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  ##paradigmlab ##fluids ##chromebooks ##plotly  

Day 6: Fluids Paradigm Lab

Today we started the AP Physics 2 fluids unit watching this video of a can being crushed as it descends in a lake. Like any paradigm lab, students made observations and enumerated variables that may be related to the crushing of the can. We determined which we could control and measure in the lab, and defined the purpose:

To graphically and mathematically model the relationship between pressure, volume of fluid above, depth below surface of fluid, and type of fluid (density).

We divided these various experiments among the lab groups, and groups started designing their particular experiment.

One group investigated if fluids of different densities result in different pressures at the same depth:

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Another group investigated the affect on depth below the surface on the pressure.

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Tomorrow, groups will share their qualitative results and then we will focus on refining our procedures to build the model while minimizing uncertainty. I love how students often surprise you in a paradigm lab when they focus on the characteristic that doesn’t affect the dependent variable. I can’t wait for the discussion after the group who measured the pressure in various sized containers with the same volume of water above the probe (which results in different depths for different containers) presents.

This paradigm lab was inspired by the article Pressure Beneath the Surface of a Fluid: Measuring the Correct Depth in The Physics Teacher.

  ##fluids ##paradigmlab  

Day 5: Exams with Canvas

I started AP Physics 2 today with the following on the screen.

xkcd: Scantron

I explained that we can’t afford to lose any more TAs as casualties of Scantron exams. So, we will be taking parts of our exams on our Chromebooks using Canvas quizzes. Everything went smooth. The new features related to specify when and how often students can see their responses and the answers will make it easier to keep control of the questions and yet review them in class.

  ##tech ##chromebooks ##canvas  

Day 4: Peer Instruction, InfuseLearing, Chromebooks

Today, I introduced peer instruction, the rationale and research behind it, and feedback from previous students. This year, with every student having a Chromebook, I’m trying InfuseLearning to gather student’s choices. I like the flexibility of the answer types supported by InfuseLearning, the ease with which students connect (just a room id), and the flexibility to pose answer choices on the fly. I miss having an on-screen timer to encourage students to submit their answer in a timely fashion. I also found it someone inefficient to switch between the questions I projected and the graph of student responses. Perhaps I’ll find a way to optimize this as I gain experience. The InfuseLearning site worked well most of the time, but I had to disconnect and reconnect once during each class period. It appeared that I was still connected, but all the students were told to wait for the next question even though I had already started it.

Groups of students are discussing a special relativity conceptual question and trying to reach a consensus.

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  ##tech ##peerinstruction ##chromebooks  

Day 3: Chromebook Deployment

My AP Physics 2 classes are part of a district-wide Digital Learning Initiative. My two sections are testing Chromebooks and the Google ecosystem. @anna_kraftson, our Technology Integration Specialist, led the deployment and walked the students through broader topics like their digital footprint and net-etiquitte. We then walked students through connecting their Google Drive with Canvas and forwarding their existing Office365 student e-mail to their new Gmail. We ran into a couple of surprises, but managed to work around them and get every student to where we wanted them to be by the end of class.

Two students were absent on a field trip. Their Chromebooks are waiting for them.

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Day 2: Special Relativity and Classroom Improvements

Today in AP Physics 2, we started discussing special relativity. I like starting with this topic for several reasons. It is a great example of breaking a model and defining a new one. In addition, it requires students to rigorously apply logic in order to uncover the implications of Einstein’s postulates of special relativity. Finally, deriving the time dilation equation with simple geometry and algebra removes the mystery that encompasses special relativity.

I don’t have a photo of us discussing special relativity; so, I took a couple of photos of some summer additions to the classroom. I hung a cool clock that I received as a gift last year. I also now have my walk and don’t walk signs on display. I was going to use them to tell students if they should pick up handouts on the way in the door. With Chromebooks, I hope to have very few handouts; so, I’m not sure how I’ll use the signs.

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