stephanie_pegg once recalled a time when she was taken off some or other project and asked to help her boss’s child with some or other school assignment. Well, recently the opposite happened to me: I was taken off some or other project to help set a school assignment for physics. I didn’t quite get to grips with whether it was bursary equivalent or only sixth form.
My task was to prepare first-principals workings and notes for a single degree of freedom oscillator without damping. As you can imagine, this was pretty straightforward for me, as I am used to rather more complex problems of oscillators with damping and so on. Although we don’t usually actually get to grips with the governing equations directly, for various reasons.
Anyway, having produced the kind of working and notes that could probably have been ripped straight from most first-year physics text books, I asked for a copy of the actual assignment to have a look. And I was a bit annoyed, actually, at the problem they’d set their students.
The situation described in the frippery as being the physical situation to model was the motion of a traffic light on an extension out over the road. This is a pretty common sight, and I think the teacher must have latched on to it on that basis. There was then a bunch of more technical stuff asking the student to attach a weight to a steel ruler and do some experiments on the position of the weight and the resultant “natural” frequency. This was to approximate the back-and-forth motion of the lights themselves if struck a glancing blow by a passing truck. Their model was appropriately simple: but not remotely similar to the real-world application they were supposed to have in the background of their minds!
My main beef is that the problem is not a 1 dimensional problem (which the spring-with-mass that I was asked to produce calculations for is), nor even a 2 dimensional problem (which the model they built is.) It’s a 3-D problem. The period of vibration will depend on the torsional strength of the pole and the bending stiffness of the arm. You can only start to solve the problem they ask for if you seriously neglect a lot of relatively important factors (the most important of which is neglecting the torsional stiffness of the pole, considering it infinitely stiff.)
Any child presented this problem, or indeed, presented any “real world” problem really needs to just chuck out the whole context they’re given and simply look at the material they have been taught and try to find something that looks applicable. In real life, that’s a dangerous game to play. I’ve been involved in peer-reviewing several jobs where an older engineer has simply made a bunch of approximations to squash their problem into the right shape for a solution they’ve been using for 40 years, and frankly, those solutions were just not good enough. A first-principals approach and appreciation of the complexity of the situation would have served them far better, if they’d been up to it.
What, in other words, was this round of experimentation supposed to actually teach them? That you’ve already got the answer, provided you can deem anything complex to be irrelevant? Is that the mode of thinking we should encourage? When I am instructing the technicians in various matters, I always try to break down my solutions into simple-enough parts, but I always pay special attention to why I am neglecting whatever features are irrelevant. These poor kids would just have had to guess.