Wednesday, January 04, 2006

Faster than a speeding bullet

I'm a few chapters into The Physics of Superheroes by James Kakalios. Go read it. It's good for the non-physicist who wants to learn some physics while exploring superpowers, the physicist who enjoys wacky back-of-the envelope calculations, and the physics teacher who wants ideas for exciting examples to use in class. After a historical introduction to comic books and superheroes, the chapters are arranged like a physics textbook, with sections for mechanics, thermodynamics, electricity & magnetism, and "modern physics", with the relevant superheroes introduced at each point.

Kakalios begins with an astute observation about physics education:

The real world is a complicated place. In order to provide illustrations in a physics lesson that emphasize only a single concept, such as Newton's Second Law of Motion or the principle of Conservation of Energy, over the decades physics teachers have developed an arsenal of overly stylized scenarios involving projectile motion, weights on pulleys, or oscillating masses on springs. These situations seem so artificial that students inevitably lament, "When am I ever going to use this stuff in my real life?"

One trick I've hit upon in teaching physics involves using examples culled from superhero comic books that correctly illustrate various applications of physics principles. Interestingly enough, whenever I cite examples from superhero comic books in a lecture, my students never wonder when they will use this information in "real life." Apparently they all have plans, post-graduation, that involve Spandex and protecting the City from all threats.

So true. The irrelevant details in the example problems make such a difference for student engagement. So instead of the standard weight on a pulley, when I'm teaching I'll often change it to a monkey on a pulley; it doesn't cost any extra. Lots of imaginary monkeys get harmed, but the students pay more attention, so it's all worth it. Some textbooks understand this and others don't. The Halliday/Resnick/Walker book that we use for AP Physics C is much better in this regard than the Walker book (not the same Walker) that for some reason we use for Regents physics. Where Walker has a box sliding down an incline, Halliday/Resnick/Walker has a box of cheese, because why the hell not? One memorable problem in H/R/W involves a box of dirty money and a box of laundered money. Walker tries to be hip by asking questions about movies... and the movies are The Rocketeer and Robin Hood: Prince of Thieves, both of which came out the year my freshmen were born! I saw them in the theater when I was in junior high, but I'm not taking the class. And it's not like those were left in from some hoary previous edition; these movie-based questions are new to the 2003 edition. Now you see what I have to deal with every day.

Meanwhile, I am convinced that the Regents physics exam is a conspiracy to get students not to be interested in physics. A student wants to measure the speed of a 2.0-kilogram object, blah blah blah. Could the questions be any duller? So when I put together the January final, I based most of the questions on old Regents questions, but changed the student to Batman and changed the moving object to the Batmobile or a mutant frog or whatever. The "ph" in physics stands for phun!

Back to Kakalios and superheroes. I don't know much about comic books, except what I know from The Amazing Adventures of Kavalier and Clay and Megillat Esther and the odd Batman or Spider-Man movie here and there. So I've learned lots of comic book history so far, e.g. the original Superman couldn't fly! And the differences between the Golden Age (1940s) and Silver Age (late '50s and '60s); the latter had much more science, thanks to the Sputnik effect and fighting against the idea that comics are a corrupting influence on the youth. As for the physics, I already know all the basic physics discussed (as one would certainly hope from someone who does this for a living), but it was inspiring to see the back-of-the-envelope calculation for the acceleration due to gravity on the planet Krypton, and the density thereof. I hope this book is successful in bringing physics principles to a general audience. I feel it apologizes too much for using math, playing into the popular conception that math is scary and that it is socially acceptable to be innumerate. (If you have TimesSelect, see Kristof's column from December 6, 2005: "In the U.S. and most of the Western world, it's considered barbaric in educated circles to be unfamiliar with Plato or Monet or Dickens, but quite natural to be oblivious of quarks and chi-squares. A century ago, Einstein published his first paper on relativity -- making 1905 as important a milestone for world history as 1066 or 1789 -- but relativity has yet to filter into the consciousness of otherwise educated people.") But it goes on and uses the math anyway, so maybe a few apologies here and there are what it takes.

Now is the time on Sprockets when we nitpick. That's right, I don't only nitpick pop-physics books by rabbis; pop-physics books by physicists should be held to an even higher standard.

First of all, it's confusing the way he switches back and forth between different units -- between the miles and pounds that the lay American audience is more familiar with, and the SI units that make it easier to do the physics calculations. And then there's "the density of neutron star material is one hundred thousand billion grams per cubic centimeter", apparently because people are afraid of scientific notation, but I find it much simpler than "hundred thousand billion". But that's just a question of taste.

More objectively, the explanation of Newton's Third Law made me sad. As far as I can tell, it was eventually used correctly to explain how (Golden Age, pre-flying) Superman jumps. But before that, we have:

You can only support yourself by leaning on the wall if the wall resists you -- that is, pushes back with an equal and opposite force. If the force were not exactly equal and in the opposite direction, then there would be a net nonzero force, which would lead to an acceleration and you crashing into the wall.

No no no no no!!!!! Yes, it's true that the wall exerts a force on you, preventing you from crashing through the wall. But this has nothing to do with Newton's Third Law. The "action" and "reaction" forces never cancel each other out, because they're acting on different objects. A exerts a force on B, and B exerts an equal and opposite force on A. When you draw a free-body diagram for an object, you only consider the forces acting on that object. The sum of the forces acting on an object equals the mass of that object times the acceleration of that object. (Yes, if you're considering all the forces acting on a system of objects, then the action and reaction forces cancel each other out, from which we can derive conservation of momentum for a closed isolated system. But that tells you nothing about whether any individual object in the system is in equilibrium.) I've started to explicitly teach "Newton's Zeroth Law", to help avert this misconception. The wall does exert a normal force on you... well, forget the wall for now, let's keep it simple and make it the floor. The floor exerts an upward normal force on you, and this cancels out the downward force that the earth's gravity exerts on you, so you're in equilibrium. These two forces are equal and opposite, but they are not a Third-Law action-reaction pair, because they're acting on the same object (you). [The two relevant Third-Law pairs here are: 1) the floor pushes you up, and you push the floor down; 2) the Earth pulls you down, and you pull the Earth up.] If anything, this is an example of Newton's First Law: the sum of the forces on an object is zero iff the object is not accelerating.

But anyway, I look forward to reading the rest of the book! For great justice!

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