We arrived in Steamboat Springs on Friday afternoon, happy to see some family and thrilled to have a place to settle for a few nights. This was the most vacation-like part of our entire trip, with lots of swimming, hiking, swimming some more, and sitting on the deck reading. For all the amazing things we’d seen and done over the last month, it still felt great to take a break from our travels. I had no plans to do anything math or science oriented during our stay, which was foolish. I should have known that I’d see something at some point that sparked my curiosity, and on the fourth day of our stay that’s exactly what happened.
By chance, we were given the opportunity to take a lesson on stand-up paddle boarding, something none of us had ever done but had seen plenty of when we went to the beach. I’m not a big fan of water-based activities, so I volunteered to stay on shore with our youngest child while my wife and the other two kids took the lesson. They had a great time, and our son loved it so much that he wanted to go out again the next day. Watching their lesson was intriguing enough, and it looked pretty straight forward, so I agreed to take him.
As I was paddling around the lake and just kind of playing around, it occurred to me that I was putting Newton’s Third Law to work. Newton’s Third Law states that for every action (force) exerted by one object on another, the second object exerts a force that is equal in size but opposite in direction. Thus, when I dipped my paddle in the water at the front of the board and rowed towards the back, the water responded by pushing my paddle forward, and since the paddle, me, and the board were all connected, the effect was to propel the board forward through the water.
We don’t usually think about these kinds of actions in these terms, and certainly not to this level of detail, when we’re doing them. I happened to find it quite comforting to think that way, and it gave me a framework for experimenting: what I rowed sideways? what if I didn’t paralllel to the board? etc. It also gave me an idea.
The description I gave above about how the forces are interacting is the kind of thing we might ask our physics students to write when solving a problem or doing a lab. The problem with this is that the situations are usually a little contrived in order to highlight the desired relationship. Students learn how to analyze these situations in the lab, and they learn how to analyze similar theoretical situations in problems, but they aren’t often able to appply the same analysis principles to something outside of the lab, like being on a paddle board. What if we put students in a situation, asked them to do something, and then asked them to analyze what they did? Rather than describing a person kicking a soccer ball, let the the students go kick a soccer ball. Rather than calculating the work required to push a box, let them push the box. By putting the students in the situation, they should have a better context for analyzing it, and ultimately for developing long-term understanding of the concepts. That way, if they’re ever stuck on a paddle board on a lake, they’ll be able to figure out what to do.