When Models Fail: Gravity

This post is written to imply the tone and hand gestures of Shannon McLaughlin, a badass teacher in the Des Moines metro, who was probably Green Beret, MI6, and a union roofer all at the same time.

Today a student and I tried to energy-pie-chart out the journey of Apollo 11 from launchpad to the Moon. It quickly devolved into a confusing and awesome conversation about what gravity does when it steals energy from you.

We often call this “potential” energy in science class, and lately I’ve been questioning the pedagogy surrounding the whole thing. Don’t get me wrong, obviously potentials are important, but most students have the following misconceptions:

  • Potential energy is stored in an object as some kind of glowing liquid thought up by Stan Lee.
  • Potential energy will ALWAYS become kinetic energy.
  • Gravitational potential energy is a function of the time that gravity has to act on you (as in, a projectile on the way down has more potential energy because it has been in ‘gravity’ longer than when it was on the way up)

At the root of all of this is the pedagogical decision to introduce students to the standard gravitational potential energy early on:

[latex size=3]PE=mgh[/latex]

This equation makes sense for the regime in which we use it, and plenty of physics worksheets, exams, and detritus contain all sorts of qualifying bull shit like “…near Earth…”, which makes us all feel great about our physics degrees, but most students don’t see why we waste the ink.

That’s a problem.

A huge effing problem.

If you really believe in Modeling, then you have to make a huge freaking deal about the limitations of models, almost to the point of caring more about limitations than actual implementations of the models in the first place.

PE=mgh fails for a lot of reasons. I made the following illustration to help my students through this, and I’m wondering what you all think I should add. This is an intentionally flawed infographic designed to get students to reject the linear model of gravitational potential energy.

Getting to the Moon. The Earth is green, the moon is grey (small, click to embiggen), the distances and radii are all to scale. Redness indicates influence of the Earth (as m/r). Blueness indicates predominant influence of the moon (as m/r) Scale = 300.78 km/px. The graphic is intentionally flawed, because I like breaking models more than using them
Here’s a raw version with 1/r potentials mapped. The moon, Earth, and distances are to scale. Again, red=earth influence; blue=moon influence) I built this pixel-by-pixel in Processing (Processing.org). Email me if you want the code.

Here’s the deal: If you use the traditional model of potential energy, then there must be an appreciable amount of potential energy from the moon when you’re on the launch pad (first pie chart).

That’s insane.

I mean, what the hell, then, does the wedge from Andromeda look like? Jupiter? The Sun?

That’s a conversation I want to have before dropping the following:

[latex size=3]F_g=\frac{Gm_1m_2}{r^2}[/latex]

[latex size=3]U=-\frac{Gm_1m_2}{r}[/latex]

I hope you grock why I’m writing this. It has nothing to do with knowing physics, and everything to do with how students think.

Help me make this even more mentally uncomfortable.

Oh, and this is SO AWESOME (evidently xkcd is my whole curriculum)