Theory v. Experiment

Ah, it’s an age old debate in physics departments – theory or experiment? When I was in college, it became clear to me that you needed to stake your claim as either a theorist or an experimental physicist. While both camps utilize tools of the other, they clearly each have preferred means of investigating and learning about the world. Usually, we ask our students to engage in both activities equally. First, they write up the background in their lab report, then perform some experiment, and then draw conclusions. This week, I decided to purposefully split the class into these two camps, each utilizing only half of the tools they typically have at their disposal.

The problem at hand was a classic conservation of energy problem involving a pendulum released from a height equal to its length. The pendulum swings down, encounters a peg directly beneath its support point, and then swings in a smaller arc around this peg. There’s a nice visual here. The AP Physics Lab Guide calls this the Turning Point lab and asks how high the peg can be placed so that the rope remains taut as the object swings up and over the peg. My students had this as a homework problem, so they’d had a chance to familiarize themselves with it prior to class.

I started class by explaining the theory/experiment divide amongst physicists and then splitting them along those lines. The theory group was essentially limited by not being able to make measurements. Whiteboards, diagrams, and equations were their tools. They split into smaller work groups, each trying a different approach. As they became stuck, they consulted with one another and ultimately wound up working together on a large whiteboard at one end of the room, ending up with the following results:

The experimentalists were forced to rely only on measurements. Searching the room, they found materials to build a pendulum which they began to modify. First, they overcame the trouble with the pendulum running into the string by releasing it off center. They then requested my phone so that they could level all of the components. Each time I thought they were going to get caught by some bit of uncertainty, they found a way to minimize it. Their procedure amounted to finding a lower bound where the string was definitely taut and an upper bound where it wasn’t, and then narrowing that range with multiple measurements. They used the camera on my phone to record the swings so that they could review them. Here is the apparatus that they devised:

After each group had worked through their individual methods, I had them choose a spokesperson who then presented the group’s results to the class. I gave them instructions that if asked questions, they could (and should) share the load of answering them with their group members. I found that I was able to ask some pointed questions of the group that was listening as a means to keep them engaged and responsible for understanding the work of their classmates. At the end of it, the experimentalists determined that the location of the peg was 28.5 ± 0.5 cm as measured from the support pole while the theorists found that it should be placed at 3/5L, with L being the length of the pendulum. For this particular setup, that gave a result of 27.9 cm. Success!

Some thoughts on this activity

Pros

    It’s fun and a different way to approach a lab. Rather than reading through a bunch of identical lab reports myself, the class was able to quickly (2 periods for the entire process) develop an understanding of how to solve the problem in two different ways.
    I like that it put some focus back on good lab technique. This is an AP physics class and the folks that write the AP test have made a recent push to ask questions about experimental design. In the report out, students were able to probe sources of uncertainty in the experimental design and hear about different sources of uncertainty that they may not have considered if they had written their own report.
    The more I try pulling problems off of the page, the more I like doing it. If I can keep these to two periods, they would make a great way to really investigate some of the classic physics examples that we see in texts. These can become quick lab practicums and be graded or just done for the joy of learning. (I didn’t grade this.)
    The collaboration was great even with girls being pushed outside of their comfort zone. Given the choice, many of my girls would self select into the theory group, but this forced some of them to think about ideas and work on skills they might ignore if given the choice.

Cons

    Group size. I have my biggest class of AP physics ever this year at 13. With one student absent, I had two groups of six. And while everyone was engaged, I would want to shrink the groups to perhaps four. I’m not sure how well this would scale to a larger class of say 25 or 30. I think decreasing group size would also lead to more voices. In this instance, half the class already agreed with one another when it came time to present, so it was really only two voices that we needed to hear from.
    I’m a bit worried that not every problem will have the right blend of theory and experiment. This one seemed to work well as both groups were finishing around the same time. I’m not sure how many problems will strike that balance as well as this one seemed to. What do you do with half the class if they are done in 15 minutes?

I’m looking forward to giving this a try again when I find the right problem to investigate.

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7 comments

  1. This is really awesome – I’ve had students try to reenact physics problems to investigate them before, but have never had two competing camps work simultaneously toward the same end. Nice work!

  2. This is really great, Brian. It reminds me of a couple of things.
    1) When I was in grad school, I worked with a guy who was really a whiz at building and maintaining the laser. When we’d work on experiments, quite often I would run to the computer to simulate something to find out the best place in the parameter space to be, while he would just go to the laser and start tweaking. Most of the time I lost in the race to find the signal.
    2) I encourage my students to develop computer models of their experiments because, once working, the computer model can explore vast swaths of the parameter space, including portions we might not be able to do in the lab with the equipment on hand. I want them to do that to refine both our equipment purchasing and the experiment itself.

  3. I really like this idea. I did something simimlar earlier in the year (also AP Physics) with projectiles. Students had to find the angle of lauch (given distance and initial velocity) that would result in an impact against the wall at the greatest possible height. Students had three choices- solve the problem by recording a series of launches, use equations and excel to simulate the result of launching, or use calculus to take the derivative of the trajectory function. The calculus group finished much faster, and I simply had to have some extra problems for them to practice with while waiting for others to finish.
    Did you allow students to choose their own group for your task? Can you tell us a bit more about what whether next time you would assign them to a group, use a random selection method, or let them pick?

    1. David,

      I like that projectile practicum. In the past, we’ve tried to do “hit the target” variations and they always fail due to inconsistent launches. I think this one could be modified to work well. What type of launch apparatus do you use.
      As for your questions, I initially allowed the students to choose between theory and experiment, but only two spoke up. I then assigned the rest randomly. In the future, I would use a mix of random and specific assignments so that I could target girls who needed more work on a particular skill set.
      I did a second run at this using a conical pendulum in which they were tasked with determining an expression for/measurement of the period of the system. This time I used smaller groups of three that were assigned randomly. The theory group tended to finish quicker than the experimental group for this activity, but with reporting out we still managed to finish in a single period.

      Thanks for the comments.

      1. Our class has 2 Pasco short range launchers and 2 Pasco minilaunchers. Early in the year I ask groups of students to determine which launchers have more consistency and to measure the initial velocity of them. When I asked students to pick their own group, a little over half the class was waiting to see where the “smart kids” would go or just wanted to work with a friend. Since then I do most of my grouping either randomly or teacher assigned.

  4. This is great! I gave a variation of this problem to my honors kids last year, and this would be a perfect experiment to do with them next year in AP. Thanks for sharing. I do wonder how many problems we could do this sort of thing with. I like how you spilt it up into two camps, i would have absolutely chosen the theory camp myself as a student. 🙂

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