Lerner Physics

We worked on some more examples of fluid mechanics, but it wasn't that groundbreaking. I let them practice how they needed to practice, which, for most of them, was alone. 

We then moved on to the beginning of electricity. In previous years, I started with electrostatics, but I wanted to go right into electric circuits this year. I feel it's more understandable and there are many more labs for electricity. We started with a great lab based off of The Private Universe video, which was made by my science methods professor from grad school. I ask them two questions: "Why are there seasons?" and "Given a lightbulb, battery, and wire, draw how you'd light a light bulb." Then I have them try it with a lightbulb, a battery, and an unbent paperclip. Many hot paperclips ensue until everyone in the class can find all the ways you can light a lightbulb with just one wire and one battery.

My eleventh graders took the practice ACT today in school, which meant I had one, solitary senior in my class for half of today. The juniors unsurprisingly came to class in a combination of gosh-that-test-was-hard and I-can't-stop-speed-reading modes. Not much was accomplished. We went over a fluid flow problem that was assigned for homework. It took a long time to whiteboard, and I wasn't going to push it today. The problem seemed relatively straightforward until we got to part d. We hadn't done a projectile problem launched at an angle before, but it was great to see the students step up to the challenge. The first board I showed above nailed it, and the second board only had one problem in the quadratic which was fixed. (The acceleration due to gravity had to be negative.) We talked about the strengths and weaknesses of each method.

We added two more assumptions to our ideal fluid model: irrotational and non-viscous This allows to focus on only a few forms of energy with fluids, and these assumptions work well for the simple situations we look at in this class. We ended with three energies we need to track at different points of a fluid: gravitational, kinetic, and interaction energy. (I'm leaving that third type of energy a mystery, but if you think enough about the water that flows slowly under your house and then streams out fast from the tap on the second floor, you can understand that the water at your tap has more gravitational energy and more kinetic energy. Where did that energy come from? What type of energy did the water lose?)

After the test on the ideal gas model, we started talking about the four assumptions of our ideal gas model. We'll assume a steady state; we're not going to talk about pipes as they fill up with water. We'll also assume incompressibility, that we can't fit more fluid into a space by applying more pressure. This means the model, from now on, doesn't include gases, but that's OK. Now we can explain why, when water comes out the tap or oil pours from a bottle, the stream gets thinner as it falls. We came up with the concept of volume flow rate, which we'll practice tomorrow.

No picture today. Today felt luxurious. The first block of 50 minutes was spent whiteboarding four problems, along with a few demonstrations of Pascal's Principle (Pascal's Demonstrator has never worked better; I've learned, through experience now, to bring students close but not too close, and to fill the demonstrator up in a translucent tub full of water) and the pressure globe. 

The second half of class was spent on clicker questions. I haven't done clicker questions in a long time. The clicker presentation was made back in '08, the first year I taught AP Physics B. I remember how difficult the questions were, how the students struggled, and how I felt helpless to help them think like a physicist. This year was so much easier, probably mostly because my students are smarter, more engaged, and more interested in thinking, with a little help from me being able to help spark those qualities and answer their questions better.

We started today talking through questions about the pressure under the surface of the fluid. The problems started easy, with some simple computations. But then the questions got more conceptual. How does the pressure vary if the container isn't just a cylinder or a rectangle but has angled or curved walls? How does the pressure change if you submerge something in the water? So we ran some experiments:

We finished up talking about microstates and entropy which finished the ideal gas model. The class applauded. Then I asked the question, "how could we add gravity to our ideal gas model." Groans.

So many models build on the next. I'm telling a story. I'm trying to show logical connections between one idea and the next. And what a better way to extend the ideal gas model than to add gravity? How does the pressure relate to the depth of the fluid? And, since we can't really see differences in pressure that well with gases, why not look to liquids? Hence the lab.

We got very similar results, with slopes of 9200 pascals per meter. One group decided the slope would be negative, since we kept going deeper (and lower) to measure higher pressures. We figured out what the 9200 pascals per meter meant, and why it was smaller than theory would predict. We had a few minutes at the end of class to practice this new mathematical relationship.