This weekend I listened to the podcast of NPR's Talk of the Nation: Science Friday. It included an interview with James Kakalios, a Professor of Physics and Astronomy at the University of Minnesota. Professor Kakalios has a new book coming out called "The Physics of Superheroes".
I can say from experience that he's not the first to use a superhero to try and make the application of introductory physics a little more interesting than most textbook examples. After all, Spiderman is just easier to picture than an "idealized free body". I don't know that I've seen anyone take it as far as it seems Professor Kakalios has.
Here is my favorite line of reasoning from the interview (I'm skipping over the math and ballparking the numbers, so forgive the generalizations).
Superman is able, we're told, to leap tall buildings in a single bound. The original Superman story says that Superman has powers far beyond those of mortal men due to his race coming from Krypton, a planet with greater gravity than earth, and not, as later explained, due to the yellow sun of Earth versus the red sun of Krypton. Early comics specified he could leap 1/8th of a mile into the air. An often-used introductory physics equation asks how fast he needs to leave the surface of the earth in order to leap that high. The answer is something like 140 mph.
An application of Newton's second law (along with a couple of other assumptions) tells us that his legs must be able to apply about 6000 lbs of force on the ground in order to launch him at that speed. Assuming, then, that if his legs are able to supply that force, they are probably genetically coded to support about half of that weight in normal standing weight. In other words, his weight on Krypton was probably around 3000 lbs. Since we know his weight on earth is about 220 lbs, we can determine that the gravitational force on Krypton is about 15 times that of earth.
Knowing the gravitational force of Krypton, it's possible to imagine a model of how the planet of Krypton is constructed. In order to get that much gravity at the surface, you pretty much have to have a planet with a neutron star at its core. And thus (this is my favorite part), it becomes apparent why the planet Krypton exploded. The forces and stresses caused by such a core would make an planet unstable, at best.
Sounds like it might be a fun read.