Hanging Slinky Analysis 1: Sums to Integrals

Hanging Slinky

Last time, we (re-)introduced the Hanging Slinky problem, designed a few years back as a physics lab but suitable for a math class, say Algebra II or beyond. We looked at the length of the hanging slinky as a function of the number of slinks that hang down, and it looked seriously quadratic.

I claim that knowing that the real-world data is quadratic will help you explain  why the data has that shape. That is, “answer analysis” will guide your calculations.

I beg you to work this out for yourself as much as you can before reading this. I made many many many wrong turns in what is supposed to be an easy analysis, and do not want to deprive you of that—and the learning that comes with it.

HangingSlinkyWithParabola Continue reading Hanging Slinky Analysis 1: Sums to Integrals

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Strom’s Credibility Criterion

Long ago, way back when Dark Matter had not yet been inferred, I attended UC Berkeley. One day, a fellow astronomy grad student mentioned Strom’s Credibility Criterion in a (possibly beer-fueled) conversation—attributed to astronomer Stephen Strom, who was at U Mass Amherst at the time.

It went something like this:

Don’t believe any set of data unless at least one data point deviates dramatically from the model.

The principle has stuck with me over the years, bubbling in the background. It rose to the surface in a recent trip to the mysterious east (Maine) to visit a physics classroom field-testing materials from a project I advise called InquirySpace.

Background

There is a great deal to say about this trip, including some really great experiences using vague questions and prediction in the classroom, but this incident is about precision, data, and habits of mind. To get there, you need some background.

Students were investigating the motion of hanging springs with weights attached. (Vague question: how fast will the spring go up and down? Answer: it depends. Follow-up: depends on what? Answers: many, including weight and ‘how far you pull it,’ i.e., amplitude.)

So we make better definitions and better questions, get the equipment, and measure. In one phase of this multi-day investigation, students studied how the amplitude affected the period of this vertical spring thing.

If you remember your high-school physics, you may recall that amplitude has no (first-order) effect (just as weight has no effect in a pendulum). So it was interesting to have students make a pre-measurement prediction (often, that the relationship would be linear and increasing) and then turn them loose to discover that there is no effect and to try to explain why.

Enter Strom, after a fashion

Let us leave the issue of how the students measured period for another post. But one very capable and conscientious group found the following periods, in seconds, for four different amplitudes:

0.8, 0.8, 0.8, 0.8

Many of my colleagues in the project were happy with this result. The students found out—and commented—that their prediction had been wrong. So the main point of the lesson was achieved. But as a data guy, I heard the echo of Stephen Strom.

Continue reading Strom’s Credibility Criterion