The purpose of the Day 1 activity is for students to learn how to operate the camera, take and analyze data, and most importantly how to think through an investigative experiment where you make decisions on what to do next based on looking at your data.

• Students will want their first video of the water drop to be “good”. They will worry about whether or not they have the “right” frame rate, is the drop the “right” distance from the camera, etc. A major teaching point of this lab is that you can only answer these questions by taking some quick preliminary data, analyzing it and thinking about what you are seeing. So they really should be taking a quick video with out fussing too much over it, do the analysis and then make decisions on what to do next based on what they learn from that process.
• Building on the above bullet point… the wiki talks about, and we know that they will need to take multiple videos of the pinch off process at different frame rates and maybe magnifications. Students will want to just take a higher frame rate video at higher magnification, because the wiki mentions it. So you will get questions about what frame rates should the use, how do they get more magnification, etc. A teaching point here is that we want to teach them how to use the data from their first video to decide if and where to follow up with different operating parameters. The point is you don't simply take “all” of the data and then sort it out later. This is an investigation into a phenomena where the assumption is no one knows what data to take because no one has figured out what to do yet. So when the students ask about taking a second video, they should be able to point to something in the video and data from their first recording that suggests there might be something to gain by doing a second one. Some examples include:
  • Noticing that early on in the process the drop is shaped like an hour glass, near the end of the process it looks more like two spheres connected by a cylinder. This suggests something has changed in terms of the physics driving the process.
  • Noticing in their data that close to the end of the process their error bars are really big because the minimum neck radius was down to a few pixels making it difficult to measure. So higher magnification would help for that part of the process.
  • Noticing that the pinch off process starts off slow, and accelerates as you approach the moment of pinch off, and is going so fast at the end that the data points are far enough apart in time that it appears something significant may have happened between the last two frames. Thus, raising the frame rate by a factor of 10 and looking at the end of the process would fill in that gap.
• This is an exploratory lab. The assumption is that there is no known power law or model to compare their results to. Instead we have used very big picture and vague reasoning to come up with three functional forms that might reasonably be expected to describe the observed behavior. The goal is to see if any portions of the data appear to follow power law behavior that is consistent with any of the forms. This is a subtle distinction, but it has to be emphasized to the students. There are no right answers. The process is what is important.

• The day 1 activities in particular are intended to give students a chance to figure out what is going on, and probably make some mistakes, take sub-optimal data, etc., without the pressure of losing points on their grade as a result. Everything on the day 1 analysis should be graded in this context.
• Things that students should NOT lose credit for, but should be heavily commented on, include:
  • Videos that are too zoomed out, poorly focused, too dark, too low a frame rate, that miss part of the process, etc.
  • Misconceptions about what they are fitting, and how they are supposed to think about their results.
  • Misinterpreting parts of the data.
• Things that they should lose credit for include:
  • Sig figs.
  • Poorly done plots with unreadable fonts, bad axis labels, too much clutter, etc.
  • Poor explanations of what they did, what motivated their decisions to change camera parameters, not doing any fits to the data, etc.

In the past we have had students plot their data on a log-log plot, then select regions which showed power law behavior, and fit those regions to the functional form of a power law with the exponent being a free parameter. Then they compared the best fit power to the three forms developed from the dimensional analysis to see if any of the agreed.

This process however makes it seem to the students as if they are supposed to find power law exponents in their data which “agree” with one of the “models”. They then interpret the point of doing the experiment as confirming the theory, which as described above is not the point of the lab.

This time we are having the students plot and fit their data as before, but with the exponent of the power law fixed so that the only free parameter is the pre-factor. They should do this three times, using each of the three exponents (0.5, 0.67, & 1.0) for each region of the data that appears to show power law behavior. They then overlay the lines representing these fits with the data, and it becomes pretty obvious visually when one of the exponents is consistent with the data. Although in principle interpreting the fits this way is not really different from what we used to do, the procedure is different enough that it may jar the students out of automatically thinking they are rigorously fitting the data to precise theoretical models.

The plot below shows data I collected for the pinchoff process of water. I took two videos at different frame rates.

A couple things to note about this video.

• The overlap between the two videos, obviously taken for different drops, merge together almost “perfectly”. This is an impressive demonstration that the pinch off process is very repeatable, meaning the evolution of the shape of the neck is precisely defined by the physical processes which are driving it.
• The magnification was the same for both videos. The reason the error bars for the measured neck radii are smaller for the higher speed video, is because the higher frame rate reduced the effect of motion blur which made it possible to more precisely define the edges of the neck.
• The low frame rate video was recorded first. Note that the measurement closest to the moment of pinch off appears to be falling off the trend exhibited by the preceding data. While the error bars are too big for this to be considered more than a suggestion that something interesting is happening here, it is enough to motivate taking higher frame rate data between to fill in the rather large gap, the hope being that if some new behavior is emerging it will become more apparent.