I taught a one-semester Advanced Physics class that cumulated in the AP Physics B exam my first five years of teaching. For the past two years, I taught an official AP Physics B course. Both of these courses were packed with content. Despite being a proponent of [Modeling Instruction](http://modelinginstruction.org) and incorporating it into other courses, I never felt I could make it fit in these courses.

This year, I’m teaching the new AP Physics 2 course. The focus on inquiry, deep understanding of physcs, and science practices (and less content) aligns wonderfully with Modeling Instruction.

We just started the first major unit, fluids. I guided my students through a paradigm lab to model the pressure vs. depth in a fluid. We started by watching [this video](https://www.youtube.com/watch?v=fqWL5FsQXRI) of a can being crushed as it descends in a lake. I was worried students would find the phenomenon demonstrate too simple, but that definitely wasn’t the case. Like any paradigm lab, we started by making observations:

* the can gets crushed

* the can gets crushed more as it gets deeper

* the top of the can appears to be sealed

* the can must be empty (student commented that if full, it wouldn’t be crushed)

Students then enumerated variables that may be related to the crushing of the can:

* water pressure

* volume of water above the can

* strength of can

* air pressure inside of can

* gravitational field strength (student said “gravity” and I went on a tangent about fields…)

* temperature of water

* atmospheric pressure

* type (density) of fluid

* water depth

* speed of decent

* dimensions, surface area, shape of can

* motion of water

Students readily agreed that it was the water pressure that crushed the can and it is the dependent variable. In hindsight, I could have better focused the discussion by directing students to focus on the water pressure rather than the can itself. They had a lot of good ideas about what properties of the can would affect it being crushed, which I didn’t expect. I had to admit that I didn’t have any cans and we would have to focus on the fluid instead…. I was amazed that no one in my first class proposed that the depth of the fluid would play a role. Everyone in that class phrased it as the volume of the fluid in the container above the can was a variable to measure. This was fascinating to me and led to a surprising result for the students as the experiment was conducted. I think this illustrates the power of the modeling cycle and guided inquiry labs.

We next determined which of the above variables we could control (independent variables) and measure in the lab given the resources available at the moment:

* volume of water above the can

* type (density) of fluid

* water depth

* speed of decent

The materials we planned on using were Vernier LabQuest 2 interfaces, pressure sensors with glass tube attachments, three different sized beakers (for the volume variable), graduated cylinders, fluids (water, canola oil, saturated salt water).

We then defined the purpose of our experiment:

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

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

At the start of class the next day, groups shared their results. I was particularly impressed with the groups investigating pressure vs. volume of fluid above a point. While they measured a relationship between pressure and volume, their experimental design was sufficiently robust that they also noticed that the same volume above the measurement point resulted in different pressures in different beakers! That is, the pressure with 400 mL of water above the sensor in the 600 mL beaker is different than in the 1000 mL beaker and different again from that in the 2000 mL beaker. After further investigation they concluded that the relationship was based on depth, not volume.

The groups investigating pressure vs. depth in fluid were confident that the pressure at a point depended on the depth below the surface of the fluid, and 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. I learned of this important experimental technique in the article “[Pressure Beneath the Surface of a Fluid: Measuring the Correct Depth](http://scitation.aip.org/content/aapt/journal/tpt/51/5/10.1119/1.4801356)” in The Physics Teacher. 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.

After a second day of measurements, students confirmed the linear relationship between pressure and depth. In addition, with the improved experimental design, students confirmed a relationship between pressure and fluid density. The results were not as accurate as I had expected. We identified a couple of additional errors that may have contributed. One, a couple of groups lost the seal between the glass tube and the plastic tube connected to the pressure sensor when the glass tube was in the fluid. This results in the fluid filling the glass tube and future measurements are incorrect if the glass tube is reconnected without removing it from the fluid.

I asked my TA to minimize the known sources of measurement uncertainty, perform the experiment, and determine how accurately pressure vs. depth could be measured. The slope of his pressure vs. depth graph was within 3.16% of the expected value. This is quite a reasonable result. If we used a taller graduated cylinder, I expect the error could be reduced further.

I’ll definitely do this paradigm lab again next year!