Collisions

As a much delayed followup to my presentation on sound, today I gave a presentation on how math fits in to football. I worked on the presentation quite a bit which included several videos, an accompanying worksheet, and two live demonstrations. Molly and I discussed having the presentation run for the entire class which is the reason for the ambitious composition. I practiced the talk with some less physics-inclined friends and went to class feeling like there was some chance the subject would go over better than previous ones. Of course, everyone knows what's said about the best laid plans...

 If you'd like to see the presentation and worksheet, they're available at the following two links:

Football Presentation
Football Worksheet

Let's start our playback of today's presentation by stating that I probably bit off more than I could chew. I knew there would be problems getting students to concentrate on a single subject for more than 20 minutes (see previous talks and the field trip tours), but thought that the variety in the presentation would be enough to keep them under my thumb. Turns out that I was wrong about that. I did not get through the talk with the first class, and after some last minute changes, only eked through the second. Part of the reason for this was the prevalence of troublesome students another is that there was too much material. I got so worried about having enough material to cover the lecture that the opposite happened.

The Presentation
Whenever discussing physics or other science subjects I always hear the question, "but what does this have to do with math?" Well, usually it's not a question and is worded a bit more aggressively, but you get the point. I tried to short-circuit this sentiment by explaining that physics was simply how we use math to model the world around us. A bit general, but at least some of the students nodded their heads. To drive the point home, I described a couple of famous equations that described physical phenomena. From here I transitioned to some of the important kinematic equations that physics students first learn. I defined what each term meant and provided a written description on the back of their worksheets. We went over examples of potential and kinetic energy. Finally, I asked them to write examples of how kinematics could be related to football and then presented four examples of my own that would be the body of my talk.

The first question (one football player tackling another) was a chance to explain the conservation of moment. I began by showing them a head-on collision of two steam engines. Like all of the later video clips, it was one of the more popular parts of the talk. I made an analogy between the trains and two colliding football players, but indicated that the mass and velocities of the players would not necessarily be the same. In the first class, I attempted to lead them through the process of solving how fast one player must be going to stop another (in one dimension). In the second class, I skipped this section in an effort to save time and address the more important points of the talk. After the situation was presented, I showed them a clip of two such players colliding and asked them to make connections between the math and reality.

We next talked about conservation of energy, in the form of a car colliding with a concrete wall. I pointed out that the car had energy before the collision and asked the students to discuss and describe where that energy went afterward. At this point I ran out of time with the first class. In the second class, I continued on to described how the kinetic energy of two colliding football players could cause one to clip into the air. I had planned on calculating a specific height however, as before, the numerical part was skipped for time and clarity. Again, I included a video of a real football player getting flipped into the air.

Next up was a question on how one could throw a football as far as possible for a given amount of effort. Here, I wanted to show that while the math could be very difficult, we could use a simple experiment to approximate the result. To begin, I showed them the result of the actual derivation for range as a function of angle. This was followed by a discussion on how to model how a football player throws a ball. Eventually, with the help of several students I used a ball launcher to create a plot of range versus angle. I then showed them a plot of the functional relation derived earlier so that they could see the differences and similarities between the experiment and model.

As the talk progressed, I allowed the material to become progressively qualitative so that more advanced concepts could be addressed. I ended by trying to explain to them why spin on a football is important. Several of the students knew that a football would wobble or tumble if thrown without spin, but didn't know why it occurred. I gave a phenomenological explanation of angular momentum and some common examples. I had several students help me conduct the common demonstration of this by using a spinning bicycle wheel.

I ended by emphasizing some of the points that I thought were the most important and intentionally focused more on the basic concepts than the specific use of math or algebra.

Commentary
Talking, texting, dice throwing, and other thrown objects were a handful of all the distractions that ran throughout the talk. One student even thought it was appropriate to say "this is boring," on the start of every single slide. Molly and I did our best to contain these problems, but I tried to push on with the talk in order to cover each individual topic. On one hand, having to stop the presentation every three minutes to reprimand a student is not useful at all, but on the other if they're permitted to continue talking or doing whatever else it interrupts everyone anyway. I have some other thoughts about this issue that I'll put in a separate post, but it was a significant problem.

While I thought that the slide on the relation between physics and math would be useful, several students obviously did not pay attention or did not pay attention. I was asked about how any of the presentation was related to math on several later occasions, which was quite disappointing to hear. I tried to reiterate my initial point and while the students cared enough to comment on it, they did not care enough to hear my response.

The part addressing kinetic and potential energy went much better than I had hoped and most of the students participated readily. There was some confusion between the two, but in this case the students were mostly self-correcting. Momentum was a little less successful and I spent less time than I should have giving them a physical explanation of it. On the worksheet, I gave an example of 1 newton second being about as much "power" in a tennis ball traveling 40 miles per hour, but no one bothered to read it. I also cheated a bit by not explaining the difference between speed and velocity which I thought might have confused the issue more than it was already. The kinematic equations were accepted and the students did recognize the standard rate equation.

Most of the examples of kinematics in football were ones that the students recognized on their own. At this point, everyone was still on the same page and things were moving relatively smoothly. Conserving momentum was a little bit more difficult to get across, again because I do not think many of the students had a feel for what it is. The example dragged along painfully in the first class, especially the part about using algebra to calculate the required speed of one football player to stop another. As is good practice, I carried my variables through to the end of the calculation, but the students found it prohibitively hard to follow them. Among other problems, the students began to argue some of my points from experience. I did not have enough time to convince them that when they "dig in" they are describing a situation that's different from the model. I did try to explain that physicists use models of the world that aren't always accurate in every way so that they can first understand the principles of the system.

Conservation of energy went a little bit better, but I was still recovering from the bad experience with the momentum slides. I was relatively brief, and the topic wasn't as interesting without calculating how high a player would flip. For those looking at the slides, I included a fudge factor of 1/5 in the calculations on the slide. This is to account for other energy losses and the fact that I didn't run through an actual conservation of momentum, otherwise the returner would be flipped 20-some feet into the air.

The prelude to the best throwing angle went alright. Although, I was a bit annoyed when one student loudly accused me of showboating by displaying the derivation. The experiment was one of the highlights of the morning as several students were able to participate and almost every student was paying attention. Not only that, but the data matched my predictions quite well which provided me the opportunity to discuss modeling. The spin slides went fine and response to the demo was lukewarm. Everyone appeared to be tired by this point and I admit I was ready to be done as well.

Conclusion
I prepared too much material and glossed over some finer points in kinematics that should have been explained with more depth. I'm not sure if it is the way I present the material or if certain students lack the ability to be respectful and pay attention, but the number and magnitude of interruptions clearly aggravated confusion may have made much of what I said worthless. The students were extremely receptive to the live demonstration, but shut down soon afterward. Even now I'm frustrated with the challenge of teaching some of the students, but there were still bright spots and students that conducted themselves well.