The Problem:
We were solving some simple static equilibrium problems today. The first problem involved a 2m board (60 kg) spanning across two scales that supported the board on each end. A 70-kg person stands on the board 1.5 m from the left scale. The question was, “How much does each scale read?”
Student Solution:
The standard way to solve this problem would be to sum the forces and torques to zero, but here is how a student today approached the problem:
The board weighs 600N. If the person wasn’t on the board, each scale would have hold 300N of force, because it’s symmetric. When the person (weighing 700N) stands on the board, more of his weight will go on the right side, because he is closer to that side. More to the point, the person is 3/4th of the way down the board, so the right board will have to hold 3/4 of his weight (525 N). This leaves 175 N of his weight on the left scale. Taken together, the board’s weight and man’s weight, the left scale will read 475N and the right scale will read 825N.
My Instructional Move (real time decision vs post-hoc decision)
When I came around to talk with this student, what I did was spend some time making sense of what he did, but then I (regrettably) just basically told him that what he did gave the right answer, and encouraged him to approach the problem the using the more standard approach. In hindsight, I would have liked to have encourage him to assume that his numbers are correct, and to use those numbers to see if in fact the Forces and Torques sum to zero. If those numbers work out to balance both the forces and the torques, than the approach is sound; if not, it’s back to the drawing board. Instead, I encouraged him to start the problem again assuming he didn’t know the answer and see if he got the same answer using a different method. At the end of the day, I should have said, “Check to make sure your answer satisfies the conditions for static equilibrium”. This values his approach, while keeping our idea on the core physics ideas he needed to practice.
General Thoughts on “Starting from Basic Principles”:
The more and more I do this, I become less and less opposed to “guess and check” strategies in physics. This student wasn’t guessing, but the idea is the same. “Hey you have a hunch about how much of the weight gets distributed?” Cool, run with it, prove to me that it satisfies the the conditions for static equilibrium. Oh, you have a strategy that you think might work more generally, even better. Prove to me it works in all cases.”
I think this runs counter to the prevailing attitude that students should start problems from basic physics principles… We want students to start the problem by writing, “Fnet = 0” and “Tnet = 0″… or at least state that idea in words. While I agree the endpoint of learning needs to look something like that (seeing fundamental physics principles and using them to guide process), I’m definitely not convinced its a good starting point. For one, in my experience students don’t see why summing the torques will magically tell them about how the forces get distributed. Forcing them down that path is awkward, because it’s kind of “trust me, it’ll work out. It’s a good strategy. Let’s trust the physics”. But if the students have some guess (or strategies) for figuring out how the forces might distribute, that’s awesome, and I can press them to prove their solutions satisfies basic physics principles.
Teach. Brian. Teach. 
This is a really cool insight (accepting more “guess and check” approaches). What do you think about a simulator that would let them put in the assumptions for the scale forces and the appropriate down vectors for the weights to see if, when you “turned time on,” things moved? I think if you did something like that, they’d immediately see which way they got it wrong and it might graphically illustrate why summing torques etc is a good way to go. #NaBloCoMo #3.
I like the simulator idea… pull them toward seeing static situations in terms of attempts to cause turning.