Yesterday, Will sent me over a curious article, Hockey Puck Math. It’s one of those Yahoo! answers pages. Apparently, someone had some physics homework and they decided just to ask online, “A hockey puck is hit on a frozen lake and starts moving with a speed of 13.7 m/s. Five seconds later, its speed is 6.80 m/s. What is its average acceleration? What is the average value of the coefficient of kinetic friction between puck and ice? How far does the puck travel during the 5.00 s interval?” You can click over to the link if you want the solution.
What struck me was that the approach to the problem was all wrong. It looked at the problem the way students normally look at this kind of problem: by seeing what equations are around and then plugging them in. Of course, given the question, this is exactly what the student was expected to do. I mean, who would care what the average acceleration was? It’s such an incredibly boring way of looking at the problem.
The nature of the problem is energy balance. There are two kinds of energy: the kinetic energy of the puck and the heat energy of the friction. When I used to work with graduate students, I would throw in potential energy as well and have them do the problem with energy and force and show that they were the same. The point of such problems should be to understand the nature of physical phenomena, so math shouldn’t be of much concern.
When I taught undergraduate physics, I would often hear from my students that they understood the physics but were just having trouble with the math. Well, that wasn’t true. In fact, they were very often doing just fine with the math and it was the physics where they were hopeless. But it did make me see that surprisingly little physics was being taught in physics classes. And I worked to take as much math out of my classes as possible. Math should generally be the thing the student introduces late into the process of solving problems — not at the beginning.
Let’s look at our problem here. The essence of the problem is this:
In this “ke” is the kinetic energy (½m×v2) of the puck at the beginning and the end. And “heat” the energy lost to friction that happens to be equal to μ×m×g×x. I would give 80% credit for that much because the concept we are dealing with is the conservation of energy. But the whole solution requires understand how objects move under constant acceleration. It’s just that it isn’t all that important.
Sadly, most teachers would not grade this problem in this way. They know that it is a conservation of energy problem, but in grading it, they get lost in the details of the problem’s solution. And you see this in questions. There is not even any mention of energy or force. This is why people leave physics courses thinking that the subject has no relevance to their regular lives. I can’t wait at a bus stop without doing a little physics to find the best place to stand. Physics is life. And most physics teachers do not help people to see that.