You hang weights on a steel wire, one kilogram at a time, and read its stretch to a hundredth of a millimetre. So far this looks like any other experiment — except this is the first one where the formula itself stops being true partway through, and nothing outside the experiment tells you where.
What makes this one different
In the viscosity experiment you saw a formula give a wrong answer outside its range — but there we told you where the range ended. Here nobody does. Below the elastic limit the wire returns to exactly its original length when you take the weights off, and Hooke’s law holds. Above it, part of the stretch becomes permanent and the wire is no longer the wire you started with. The trouble is that the curve past that point is a gentle convex bend, not an obvious break — on the plot nothing looks wrong.
So how do you find it? With the one thing you can do from inside the experiment: take every weight off and re-zero the scale. If the wire came back, everything up to that load was valid. If it did not, you crossed the boundary somewhere along the way and the points above it have to be thrown away. That test adds no number to your answer; its only job is to establish which of your data you are entitled to use — which is a new kind of measurement.
The second lesson hides inside the formula: E = 4L/(πd²m). Look at the square on the diameter. A one per cent error in d becomes a two per cent error in E. The page shows the diameter’s share and the slope’s share side by side, and the diameter almost always wins — which is not where you would look first, since the extension is the quantity you sweat over and the diameter seems like a single easy number. The wire is also not uniform, so one micrometer reading is not enough even with a perfect micrometer.
The Python section finds the same boundary without lifting a single weight: it fits a line to the first few points, then asks each later point whether it was predicted. The first point that says no is the elastic limit. Two completely independent routes, one boundary.