If you’ve ever thought that the bubbles in your beer rose faster as they neared the top of your glass, it wasn’t the alcohol affecting your judgment. The bubbly drink is supersaturated with carbon dioxide (that’s what also gives soda pop its fizz), which means that the pressure of the carbon dioxide gas forced into the liquid is greater than atmospheric pressure. When the top is popped on a carbonated beverage, there is a popping or hissing noise, due to some of the excess gas under pressure rapidly exiting the container. There is still additional carbon dioxide in the liquid, which collects into bubbles near small imperfections in the glass and then, being lighter than the surrounding fluid, rises to the top. The buoyancy force lifting the bubble is directly related to its spherical volume, which depends on the cube of the bubble’s radius. The drag resistance force slowing down the bubble depends on its surface area (the bigger the area, the more beverage that has to be pushed out of the way of the rising bubble), which in turn grows by the square of the bubble’s radius. As the bubble moves through the drink, it sweeps up additional carbon-dioxide molecules dispersed throughout the liquid, becoming bigger in the process. There is thus a net excess force raising the bubble. If there’s a force, there is an acceleration (Newton’s second law holds even inside a glass of beer) and the bubble will rise faster and faster.
If I had an infinitely tall glass, would the bubbles accelerate to the speed of light? No; in Chapter 4 we noted that the drag resistance depends not only on the surface area, but also on the speed of an object (it takes more effort to push the fluid out of the way of a rapidly moving object than one progressing slowly). As the bubble rises and moves faster and faster, the drag force increases and eventually balances out the upward lift, and once there is no net force, the bubble continues to move at a steady uniform speed (Newton’s first law) known as the terminal (or final) velocity.
Now that this tour of the world of physics, through the agency of superheroes and their villainous foes, is completed, perhaps you should pause for some hands-on experimentation with a bubbly drink of your choice, in order to verify some of what we’ve have learned—but purely in the interest of science, of course!
SECTION 4
WHAT HAVE WE LEARNED?
26
ME AM BIZARRO!—SUPERHERO BLOOPERS
WE STARTED THIS BOOK with a discussion of how Superman, applying Newton’s laws of motion, can leap a tall building in a single bound, and ended with Iron Man’s transistorized armor and the materials science of superhero costumes. Along the way we have addressed many of the major subjects that would be covered in a basic undergraduate physics curriculum, from the first topics addressed in introductory physics (such as Newton’s laws of motion and the Principle of Conservation of Energy) to upper-level material (quantum mechanics and solid-state physics). However, I would be remiss if I left you, Fearless Reader, with the impression that absolutely everything in superhero comic books is 100-percent consistent with the laws of physics. I therefore would like to conclude by discussing some of those very few, rare examples where comic books actually get their physics wrong, no matter how many miracle exceptions one is willing to grant.
CYCLOPS OF THE X MEN’S SECOND MUTANT POWER
The first young mutant that Prof. Charles Xavier recruited to join his nascent superteam the X-Men was Scott Summers, code named Cyclops. Scott’s mutant gift, and also his curse, was that beams of “pure force” were emitted from his eyes. These force beams could punch a hole through a concrete wall and deflect a falling two-ton boulder. Only two materials were immune to Scott’s optic beams: his own skin (which was a good thing, or else his eye blasts would blow his eyelids off his face) and “ruby quartz.” Scott was forced to either constantly wear sunglasses made of this exotic material—or a wraparound visor when he was on superhero duty. He could raise this ruby-quartz shield using buttons either on the side of the visor or in the palms of his gloves. When he wore the visor, his eye blasts were projected as a single, broad, red beam of force, from which his nom de superhero was derived. When the ruby-quartz shield was lowered, Scott could see the (red-tinged) world clearly, with the visor or sunglasses safely absorbing the destructive brunt of his optic-force beams.
Quartz is the name that geologists have ascribed to the crystalline form of silicon dioxide. If the silicon dioxide molecules are arranged in a disordered fashion, as in a large number of marbles randomly poured into a container, then the resulting material is called “glass,” but if the molecular units are carefully stacked in an ordered array, the mineral is called “quartz.” Just as there are different ways that a collection of marbles can be stacked in a regular pattern, there are different crystalline configurations of quartz. If the mineral contains a very small amount of iron and titanium, the resulting crystal will have a slight pinkish hue (as in our discussion of stained glass in Chapter 24), in which case it is called “rose quartz.” A suspension of ruby dots in the quartz will result in cloudy brown and beige veins, and this dark, smoky, nearly opaque mineral is termed “ruby quartz.”
As strange and inconvenient as it would be to have force beams projecting from your eyes, such that you would always have to look at the world through ruby-quartz glasses, we cannot really protest, for no matter how physically implausible this may be, it is covered by our miracle-exception policy. However, regardless of the mechanism by which Cyclops’s optic blasts work, there is a key scene that is always missing in the X-Men comics and motion pictures whenever Scott lets loose with his mutant power. What we never see, yet know must occur by the laws of physics described earlier, is Scott’s head snapping backward due to the recoil of his force beams.
Newton’s third law informs us that forces always come in pairs—that is, every action is accompanied by an equal and opposite reaction. You cannot push against something if there is nothing to push against. Rockets depend on this principle when they expel hot gases at high velocities, so through Newton’s third law, the recoil propels the ship in the opposite direction of the exhaust. Similarly, a large beam of force, sufficient to keep a two-ton boulder suspended in midair (from which we conclude that the force of the optic blasts must be at least 4,000 pounds), should push back on Cyclops’s head with an equivalent recoil force of 4,000 pounds. From Newton’s second law of motion—that is, Force equals mass times acceleration—his body (assuming a mass of 80 kilograms) would rapidly acquire an acceleration of more than twenty times that of gravity. From an initial stationary position, his head should be moving backward at several hundred miles per hour whenever he makes use of his special gift. Therefore, we must conclude that Cyclops possesses two mutant powers: force beams from his eyes, and exceptionally strong neck muscles.
PUT THAT BUILDING DOWN!
As mentioned in the beginning of this book, in the early days of the Golden Age of comics, Superman’s powers were attributed to the fact that his home planet, Krypton, had a much stronger gravitational pull than Earth’s. By using the benchmark that he is able to leap a tall building in a single bound on Earth, we calculated in Chapter 1 that the acceleration due to gravity on Krypton had to have been at least fifteen times greater than our own. The Man of Steel was therefore not really made of metal, but had muscles and a skeletal structure adapted to a much larger gravity. Imagine lifting a full gallon container of milk, which weighs nearly nine pounds. If you want to experience what life would be like on a planet with a gravity fifteen times weaker than Earth’s, you should empty the gallon container and refill it with just a little more than a half pint of milk. Compared with hefting the full gallon, you would find the same container with only eight ounces of milk to be much easier to pick up. Similarly, in Action Comics # 1, Superman is able to raise an automobile weighing roughly 3,000 pounds over his head. A 3,000-pound weight to Superman (adapted to Krypton’s heavier gravity) is similar to us lifting a 200-pound weight overhead. Difficult, but not impossible.
We noted earlier that with his rising popularity, Superman morphed from being the champion of the little
guy into the star of a multimillion-dollar marketing empire. The threats that Superman faced became more extreme and his foes became more superpowered. Big Blue’s strength level correspondingly increased to fantastic levels. Before long, he was lifting tanks, trucks, locomotives, ocean liners, jumbo jets, and high rise office buildings. Similarly, Marvel Comics’ hero the Incredible Hulk possessed a strength that also strained credulity. The Hulk’s strength is usually, though not always, ascribed to his bloodstream’s adrenaline levels, which is why emotional stress triggers his transformation from puny Bruce Banner into eight feet of thickly muscled green rage. The correlation with adrenaline also accounts for the fact that the madder the Hulk gets, the stronger he becomes. When suitably aggravated, he has been known to pick up and throw a castle; the side of a cliff; and even hold up a mountain threatening to crush him and a collection of other Marvel superheroes in the Secret Wars miniseries. While Reed Richards races to modify Iron Man’s armor to channel both the Human Torch’s nova-flame and Captain Marvel’s electromagnetic energy in order to blast an escape tunnel out of the mountain, Reed deliberately insults and taunts the Hulk, knowing that their survival depends on a suitably steamed Jade Giant.
Eventually, Superman would become so strong that, as shown in fig. 42 from World’s Finest # 86, he could carry two high-rise office buildings—one in each hand—as if he were carrying two pizza pies, while flying at the same time! An examination of this figure reveals one reason he is able to cart off these buildings from Gotham City to an open-air exhibit in Metropolis: They were not connected to any city water or electrical utilities. As astounding as this display of strength is, that’s not even the strangest aspect of this scene, compared with Superman’s comment: “I got permission to borrow the two Gotham City buildings you asked for.” Who would you ask for “permission” to carry off two high-rise buildings? I doubt that either of those buildings’ superintendents has the authority to allow Superman to borrow their building, especially if he informed them that he would carry them using only one hand each! When Superman first appeared in Action # 1 in 1938, people fled in terror when he hefted a car over his head. But by the late 1950s, crowds would cheer as Superman flew overhead, carrying office buildings to a charity event, risking killing all!
Even if you accept that any person, whether a strange visitor from another planet or a nuclear scientist accidentally bombarded with gamma radiation, could indeed be strong enough to pick up a building, there is a separate violation of physics principles associated with these scenes: Simply put, buildings, ocean liners, and jumbo jets are not designed to be picked up. They are either intended to remain stationary, such as an office building, or to be supported at several points, such as the three wheels under an airplane on the runway, or, in the case of a battleship, uniformly buoyed by water. The problem with lifting an office tower, for example, is that any slight deviation from the vertical will result in gravity creating an unbalanced torque, trying to twist the building even further toward the horizontal.
Buildings such as high rise towers or castles are large, so the distance from the edge of the building to its center of mass is very long (termed the “moment arm” in Chapter 8). These structures are quite heavy, so there is significant weight trying to rotate the building. The bigger the object, the larger the distance from its edge to the point where Superman or the Hulk is holding it, and the larger the moment arm of the torque trying to twist it. The torque for the buildings carried by Superman in fig. 42 is many times greater than reinforced concrete (concrete with steel rods threaded through it to increase its rigidity) can withstand before fracturing. Realistically, if you picked up a building and flew it somewhere, there would be a continuous stream of construction debris left behind you. Superman should arrive at the Gotham City charity event holding a few cinder blocks in each hand, and not two office towers with their structural integrity intact. Rather than asking for permission to borrow the buildings, Superman should practice asking for forgiveness for destroying these towers by picking them up in the first place.
Some later comic-book writers have realized that it’s impossible, regardless of your level of superstrength, to pick up a building and not have it crumble under its own weight in your hands. In Marvel’s Fantastic Four # 249, a Superman stand-i n, code-named Gladiator, picks up the edge of the Baxter Building (the FF’s headquarters) at its base and rocks it back and forth, but without physically harming the tower. Reed Richards, the smartest man in the Marvel universe, instantly recognizes that what Gladiator is doing is impossible. He theorizes that Gladiator must actually possess a previously unnamed superpower of tactile kinesis, defined in comic books as the ability to levitate an object that one is in physical contact with. Of course, there is no such thing as tactile kinesis, but it does reduce down to a manageable number the quantity of miracle exceptions that are needed for the story to progress.
Fig. 42. Panel from World’s Finest # 86, where the Man of Steel demonstrates a much-improved strength level compared with his first appearance in Action # 1, where he lifted an automobile over his head, provoking the startled onlookers to flee in panic. In contrast, no one in the amphitheater is overly perturbed that a flying man is carrying two high-rise office buildings over their heads.
If we compare Giant-Man to a redwood tree (and not just because his personality was sometimes a little stiff), we note that the taller the tree, the wider the trunk. In order to provide support for the large mass above it, a tree needs a very broad base. Around the time of the signing of the American Declaration of Independence, two mathematicians, Euler and LaGrange, proved that a column shorter than a certain height is stable, and will be compressed by the weight of material pressing down on its base, but above a certain height (whose value depends on the strength of the material comprising the column), the tower becomes unstable against bending. The slightest perturbation away from a perfectly vertical orientation leads to a large twisting force, that is, a “torque,” as in the case of the seesaw in Chapter 8, that will cause the column to bend under its own weight. Giant-Man could, in principle, grow as tall as a redwood tree, but he would have to be just as mobile (assuming he stayed below the height limit set by the cube-square law—see Chapter 25). Any attempt to run after or fight a supervillain would inevitably lead to the upper portion of his body leaning forward over his legs. The weight of his upper trunk would then cause his body to rotate, and before you could say “Stan Lee,” old High-pockets would be flat on the ground.
Just such a fate inevitably befell Stilt Man, an early foe of Daredevil’s. Stilt Man possessed a mechanized suit that contained two hydraulic legs that, when fully extended, enabled him to stand several stories tall. As sure as summer follows spring, Daredevil would use the cable in his billy club to tangle up Stilt Man’s legs, and the resulting loss of stability would bring the issue’s adventure to a rapid close.
Another mystery related to the center of mass is how Spider-Man’s foe, Doctor Octopus, is able to walk. Research scientist Otto Octavius employed four robotic arms that were attached to a harness around his waist, with which he manipulated radioactive isotopes. The inevitable explosive radioactive accident caused this harness and the arms to be fused to Octavius, and Doctor Octopus was born. But these arms are very heavy, and we frequently see him standing on his two legs while all four arms move behind him! They should therefore create a large torque that would put Doc Ock flat on his back, or on his face if they’re in front of him. Spidey should be able to disable (if not disarm) Doctor Octopus by simply tossing an apple at him whenever he spots the arms not anchoring him to the ground. The quick and unsatisfying resolution of these stories when the physics is taken too seriously should make abundantly clear why there is not a great demand for physics professors to write superhero comic books. Careful viewers will note that in the film Spider-Man 2, the filmmakers took care to ensure that Doc Ock always had his heavy robotic arms balanced around his body, or some of them tethered to the ground, in order to give Octavius
at least some stability. After all, they couldn’t feature it in a film if it wasn’t true!
THE JUSTICE LEAGUE HAS THE MOON ON A STRING
Another unrealistic feat of strength occurs in the conclusion of a 2001 adventure of the Justice League (by this time they had dropped the “of America” part of their team name, though the comic featuring their adventures still went by the acronym JLA). In JLA # 58, Superman, Wonder Woman, and Green Lantern are shown pulling the moon into Earth’s atmosphere in order to defeat a group of renegade Martians. Perhaps I had better back up and explain why they considered this a good idea.
Martians were introduced into the DC universe in 1955’s Detective Comics # 225, when a physics professor trying to develop an interstellar communication device accidentally created a transporter beam instead. He thereby forcefully brought J’onn J’onzz (the Martian Manhunter) to Earth. J’onn eventually adopted a costumed identity as a superhero crime-fighter, and was a founding member of the Justice League of America back in 1960. J’onn J’onzz possessed a dazzling array of superpowers that matched Superman’s—including flight, superstrength, invulnerability, Martian-breath (equivalent to Superman’s super-breath), super-hearing, Martian vision, and several that Superman could only dream of, such as mental telepathy, invisibility, and shape-shifting. Just as Superman needed Kryptonite to keep him from always solving every problem in a nanosecond, the Martian Manhunter, being more powerful, required an even more common Achilles’ heel in order to justify why he would ever bother teaming up and forming a league with other superheroes. It was therefore revealed that J’onn suffered, as did all Martians, from a vulnerability to fire. Consequently, rather than having to search for an exotic meteorite from the doomed planet Krypton, all you would need is a penny book of matches to incapacitate the Martian Manhunter.
The Physics of Superheroes: Spectacular Second Edition Page 37