The Physics of Superheroes: Spectacular Second Edition (6 page)

By the late 1940s, Superman would gain the power of true flight, able to choose and alter his trajectory after leaving the ground.
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At this point, Superman can be considered to have gained free will over the laws of physics. Over time, he acquired a host of other abilities that could not be reasonably accounted for by the stronger gravity of his home planet. These powers included various visions (heat, X-ray, and others), super-hearing, super-breath, and even super-hypnotism.
⁸

The origin of Superman’s powers was subsequently revised, beginning in the March 1960 issue of
Action Comics # 262,
to claim that Superman’s fantastic abilities derived from the fact that the Earth orbited a yellow sun, as opposed to the red sun of Krypton. The color of a sun is a function of both its surface temperature and the atmosphere through which it is viewed. The blue portion of the solar spectrum is strongly scattered by the atmosphere, which is why the sky looks blue. Viewed straight on, our sun appears yellow because the atmosphere is also more absorptive toward the blue end of the spectrum, except at dawn or sunset when the position of the sun is low on the horizon and sunlight must travel a greater distance through the atmosphere. Nearly all wavelengths are then absorbed, except for lower-energy red light, which gives sunsets their characteristic hues (the greater number of particulates in the air at the end of the day compared with the beginning also contributes to the difference in shading between sunset and dawn). These spectral features are for the most part independent of the chemical composition of the gases making up the Earth’s atmosphere. There is no physical mechanism by which a shift in the primary wavelength of sunlight from yellow (a wavelength of 570 nanometers, or 570 billionths of a meter) to red light (650 nanometers) would endow someone with the ability to bend steel in his bare hands. Consequently, at this stage in his history,
Superman
ceased being a science-fiction strip and became a comic book about a fantasy hero. Changing a superhero’s origin in order to accommodate new powers or circumstances occurs so frequently in comic books that comic-book fans have coined a term, “retconning,” to describe this retroactive continuity repair.

Interestingly, Superman’s foes went through a similar evolution around this same time. In the early years of Action and Superman comics, Siegel and Shuster gave voice to the revenge fantasies of their young and economically disadvantaged Depression-era readers. Superman first used his powers to fight corrupt slum-lords, coal-mine owners, munitions manufacturers, and Washington lobbyists. In his very first story, he psychologically tormented a lobbyist by holding him as they both fell from a tall building. At this early stage of his career, the story lines indicated that only a few people knew of Superman’s existence, and the lobbyist believed that the fall would be fatal. He willingly divulged the information Superman was after rather than risk another such fall. In the 1940s and 1950s, in addition to selling millions of comics per month, Superman had become a star of radio serials, movie shorts (both animated and live action), and a popular television program. His adversaries subsequently morphed into criminal masterminds with colorful personas and costumes, such as the Toyman, the Prankster, and Lex Luthor, whose schemes for grand larceny or world domination Superman would foil while keeping the corporate power structure safely undisturbed. As befits the escalating capabilities of the villains he faced, Superman entered a superpower arms race, eventually growing so powerful that it became difficult for writers to concoct credible threats to challenge his godlike abilities. Radioactive fragments of his home planet, known as Kryptonite, became a frequent device to extend any given story beyond the first page of the comic.
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It is the simpler, original Superman of the Golden Age, the last son of Krypton, that I wish to consider here.

In the first years of his comic-book history, Superman was unable to fly but could simply “leap tall buildings in a single bound,” thanks to Earth’s weaker gravity.

Well, how high could he leap? According to his origin story in
Superman # 1
, Superman’s range was given as one-eighth of a mile, or 660 feet. Assuming he could jump this high straight up, this is approximately equivalent to the height of a thirty- to forty-story building, which in 1938 would have been considered quite tall. So our question can be rephrased as: What initial velocity would Superman need, lifting off from the sidewalk, to vertically rise 660 feet?

Whether we wish to describe the trajectory of a leaping Man of Steel or of the tossed ball from our earlier example in the Introduction, we employ the three laws of motion as first elucidated by Isaac Newton in the mid 1600s. These laws are frequently expressed as: (1) an object at rest remains at rest or, if moving, keeps moving in a straight line if no external forces act upon it; (2) if an external force is applied, the object’s motion will change in either magnitude or direction, and the rate of change of the motion (its acceleration) when multiplied by the object’s mass is equal to the applied force; and (3) for every force applied to an object, there is an equal and opposite force exerted back by the object. The first two laws can be expressed succinctly through one simple mathematical equation:

That is, the force F applied to an object is equal to the resulting rate of change in the object’s velocity (its acceleration a) when multiplied by the object’s mass m, or
F
=
ma
.

Acceleration is a measure of the rate of change of the velocity of an object. A car starting from rest (velocity = 0) and accelerating to 60 mph would have a change in velocity of 60 mph - 0 mph = 60 mph. The acceleration is found by dividing this change in velocity by the time needed to make the change. The longer the time, the lower the acceleration needed for a given change in speed. An automobile speeding up from 0 to 60 mph in six seconds will have a much larger acceleration than if it does so in six hours or six days.
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The final speed will be the same for all three cases, namely, 60 mph, but the accelerations will be radically different owing to the different times needed to affect this change in velocity. From Newton’s
F
=
ma
, the force needed to create the former, faster acceleration is obviously much larger than for the latter, slower case.

When the acceleration is zero, there is no change in the motion. In that case, a moving object keeps moving in a straight line, or if sitting still, remains so. From the expression
F
=
ma
, when a = 0, then the force F = 0, which is the whole point of Newton’s first law of motion.

While this may be straightforward from a mathematical point of view, from a common-sense perspective it is nothing short of revolutionary. Newton is saying (correctly) that if an object is moving, and there is no net outside force acting on it, then the object will simply continue moving in a straight line. However, you and I, and Isaac Newton for that matter, have never seen this occur! Our everyday experiences tell us that to keep something moving, we must always keep pulling it or pushing it with an external force. A car in motion does not remain in motion unless we keep pressing the accelerator pedal, which ultimately provides a force. Of course, the reason that moving objects slow down and come to rest when we stop pushing or pulling them is that there are forces of friction and air resistance that oppose the object’s motion. Just because we stop pulling or pushing does not mean, in the real world, that there are no forces acting on the object. There’s nothing wrong with Newton’s laws—we just have to make sure we account for friction and air resistance when applying them. It is these unseen “drag forces” that we must overcome in order to maintain uniform motion. Once our pulling or pushing exactly balances the friction or air drag, then the net force on the object is zero, and the object will then continue in straight-line motion. Increasing the push or pull further will yield a net nonzero force in the direction of our push or pull. In this case, there will be an acceleration proportional to the net force. The constant of proportionality connecting the force to the acceleration is the mass,
m
, reflecting how much the object resists changing its motion.

It is worth pointing out here that mass is not the same as weight. “Weight” is another term for “force on an object due to gravity.” Mass, on the other hand, is a measure of how much stuff (“atoms” for you specialists) an object contains. The mass of the atoms in an object is what gives it its “inertia,” a fancy term to describe its resistance to change when a force is applied. In outer space, an object’s mass is the same as it is on the Earth’s surface, because the number and type of atoms it contains does not change. An object in outer space may be “weightless,” in that it is subject to a negligible attractive force from nearby planets, but it still resists changes in motion, due to its mass. A space-walking astronaut in deep space cannot just pick up and toss a space station around (assuming she had a platform on which to stand), even though the station and everyone on it is “weightless.” The mass of the space station is so large that the force the astronaut’s muscles can apply produces only a negligible acceleration.

For objects on the Earth’s surface (or that of any other planet, for that matter), the acceleration due to gravity is represented by the letter g (we’ll discuss this more in a moment). The force that gravity exerts on the object of mass, m, is then referred to as its Weight. That is,
Weight
=
(mass)
×
(acceleration due to gravity)
or
W
=
mg
, which is just a restatement of
F
=
ma
when
a
=
g
. Mass is an intrinsic property of any object, and is measured in kilograms in the metric system, while Weight represents the force exerted on the object due to gravity, and is measured in pounds in the United States. In Europe, Weight is commonly expressed in units of kilograms, which is not strictly correct, but easier to say than “kilo gram-meter/sec
²
,” the unit of force in the metric system (also known as a “Newton”). When a weight in the metric system is compared to one in the United States, the conversion ratio is 1 kilogram is equivalent to 2.2 pounds. I say “equivalent” and not “equal” because a pound is a unit of force, while kilograms measure mass. An object will weigh less than 2.2 pounds on the moon and more than 2.2 pounds on Jupiter, but its mass will always be 1 kilogram. When calculating forces in the metric system, we’ll stick with kg-meter/sec
²
rather than “Newtons,” in order to remind ourselves that any force can always be described by
F
=
ma
.

To recap, Superman’s mass at any given moment is a constant, because it reflects how many atoms are in his body. His weight, however, is a function of the gravitational attraction between him and whatever large mass he is standing on. Superman has a larger weight on the surface of Jupiter, or a lesser weight on the moon, compared with his weight on Earth, but his mass remains unchanged. The gravitational attraction of a planet or moon decreases the farther away one moves from the planet, though technically it is never exactly zero unless one were infinitely far from the planet. It is tempting to equate mass with weight, and easy to do so when dealing only with objects on Earth for which the acceleration due to gravity is always the same. As we will soon be comparing Superman’s weight on Krypton to that on Earth, we will resist this temptation.

Finally, the third law of motion simply makes explicit the commonsense notion that when you press on something, that thing presses back on you. This is sometimes expressed as “For every action, there is an equal and opposite reaction.” 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 through the wall. When the astronaut mentioned above pushes on the space station, the force her muscles exert provides a very small acceleration to the station, but the station pushes back on her, and her acceleration is much larger (since her mass is much smaller).

Imagine Superman and the Hulk holding bathroom scales against each other (which are simply devices to measure a force, namely, your weight due to gravity). When they press against each other’s scale, no matter how hard Superman pushes on the left, if they remain stationary, then the Hulk’s scale on the right will read exactly the same force. Moreover, no matter how hard Superman is pushing, his scale will read zero pounds of force if the Hulk offers no resistance and just moves his scale out of the way and steps aside.
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Forces always come in pairs, and you cannot push or pull on something unless it pushes or pulls back. When you stand on the sidewalk, your feet exert a force on the ground due to gravity pulling you toward the center of the Earth. People on the opposite side of the planet do not fall off because gravity pulls everyone in toward the center of the planet, regardless of where they are located. You do not accelerate while standing; the ground provides an equal and opposite force exactly equal to your weight. During the brief moment when Superman jumps, his legs exert a force greater than just his normal standing weight. Because forces come in pairs, his pushing down on the pavement causes the pavement to push back on him. Thus, he experiences an upward force lifting him up and away.

And that’s it—all of Newton’s laws of motion can be summarized in two simple ideas: that any change in motion can only result from an external force (
F
=
ma
), and that forces always come in pairs. This will be all we need to describe all motions, from the simple to the complex, from a tossed ball to the orbits of the planets. In fact, we already have enough physics in hand to figure out the initial velocity Superman needs to leap a tall building.