There are primarily two ways in which atoms can be arranged to form a macroscopic object: (1) in a uniform, periodic, crystalline structure, or (2) in a random, amorphous agglomeration. Of course, most solids lie somewhere between these two extremes, and typically there will be regions of crystalline order randomly connected, sometimes separated by amorphous sections. The net result will be that even the smoothest macroscopic surface will not be truly flat when viewed on an atomic scale. In fact, one doesn’t have to go to such extremes: Even on length scales of a thousandth of a millimeter—much, much bigger than an individual atom—an object’s surface will more likely resemble a jagged mountain range than the stillness of a quiet lake. Consequently, when two objects are dragged past each other, regardless of the apparent smoothness of their finishes, on the atomic scale it is not unlike taking the Rocky Mountain range, turning it upside down, shoving it atop the Himalayas, and then dragging the upside-down Rockies at a steady speed across the Himalayan mountaintops. One would naturally expect enormous geological upheavals and large-scale distortions in this extreme form of plate tectonics, and the results are no less catastrophic at the atomic level. With every footstep, bonds between atoms are broken, new bonds are formed, and atom-size avalanches and atom-quakes are produced. All of this requires a great deal of force in order to keep these atomic-scale mountain ranges sliding past and through each other. The resistance to such atomic rearrangements is called “friction,” and without it, the Flash would only be running in place.
The amount of friction opposing the motion of an object along a horizontal surface is proportional to the weight of the object pressing down on the surface. The greater the weight of an object, the deeper the atomic “mountain ranges” interpenetrate, and the greater the frictional force that must be overcome to move the object. It is harder to get a big, heavy block to start moving than a smaller, lighter one. Engineering solutions for lifting heavy objects have been known since the time of the ancient Egyptians, who developed various ingenious schemes for moving giant limestone blocks during the pyramids’ construction.
One obvious trick is to use a ramp. On a horizontal flat surface, all of a block’s weight presses down perpendicular to the surface. On a sloped surface, on the other hand, the weight is still straight down, directed toward the center of the Earth (think of a plumb line held on the ramp). Only some of the weight is perpendicular to the surface of the tilted ramp, and the rest is directed down the ramp. The smaller the force pressing the atomic mountain ranges against each other, the less they will interpenetrate, and the easier it will be to move them past each other. So the frictional force, which is proportional only to the component of the weight perpendicular to the surface, is less for a block on a tilted surface compared with one on a horizontal surface. No matter how rough the surface, if the ramp is tilted at too steep an angle, the friction force holding the block in place will be insufficient to counteract the downward pull of the weight down the ramp, and the block will slide down the ramp. However, as the Flash runs up the vertical side of a building, there is no component of his weight perpendicular to the surface upon which he is running, that is, the building’s face. In principle, therefore, there should be no friction between his boots and the building’s wall, and without friction he cannot run at all.
So can he in fact run up the side of a building? Technically, no. At least, not “run” as we understand the term. He can, as he leaps up the side of the building, move his feet back and forth against the building’s side, which would make it appear as if he were running. In essence he is traveling a distance equivalent to the height of the building in the time between steps. Typically, as the Flash runs, his foot pushes down on the ground at an angle with the road’s surface so that the force the road exerts back on him (thanks to Newton’s third law) is also at an angle with the surface. The net effect is that he accelerates in both the vertical and horizontal direction. The vertical velocity gives him a bounce up off the ground, and the horizontal component propels him in the direction he is running. The greater the vertical velocity, the higher the bounce, while the larger the horizontal velocity, the farther he advances before gravity overcomes the small vertical velocity and brings his feet back to the ground, ready for another step. Very fast runners, which would certainly include the Flash, can have both feet up off the ground between steps. The faster they run, the longer their time “airborne” between steps. If the Flash bounces about 2 cm vertically with every step, then he is in the air for about one eighth of a second before gravity pulls him down for another step. But one eighth of a second is a long time for the Crimson Comet. If his horizontal velocity is 5,250 feet/sec or 3,600 mph, then the horizontal distance he travels between steps is more than 660 feet. This is approximately one eighth of a mile, which we used as the benchmark for the tall building that Superman leapt in Chapter 1. As long as the Flash maintains at least this minimum speed, he needn’t worry about losing his footing along the way, simply because he will scale the height of the building between steps.
Before he can scale a skyscraper, the Flash has to radically alter his direction from the horizontal to the vertical. As will be discussed in a later chapter, any change in the direction of motion, whether it is Spider-Man swinging on his webbing or the Flash changing his path at the side of a building, is characterized by an acceleration that requires a corresponding force. Rotating his trajectory by ninety degrees up the building’s face entails a large force, provided by the friction between the Sultan of Speed’s boots and the ground. In addition to superspeed, the Flash’s “miracle exception” must therefore also extend to his being able to generate and tolerate accelerations that few superheroes not born on Krypton could withstand.
Newton’s laws of motion can also explain how the Flash is able to run along the surface of the ocean, or any body of water, for that matter. Just as Gwen Stacy had to be concerned as she was about to strike the water while moving at her large, final velocity, the great speed of the Flash’s strides enables him to run across its surface. As one moves through any fluid, be it air, water, or motor oil, the fluid has to move out of your way. The denser the medium, the harder this is to accomplish. It requires more effort to walk through a swimming pool, pushing the water out of your way, than to walk through an empty pool (that is, one filled only with air), and it is harder still if the swimming pool is filled with molasses. The resistance of a fluid to flow is termed “viscosity,” which typically increases the denser the medium and the faster one tries to move through the fluid.
The density of water is much greater than that of air—water molecules are in contact with one another, while there are large, open spaces between air molecules. It is even more difficult to move through water when traveling at high speeds. But for the Flash, when running on top of the water’s surface, this is a good thing. Just as someone is able to water-ski if he or she is towed at a large velocity, the Flash is able to run faster than the response time of the water molecules. As his foot strikes the water’s surface at speeds greater than 100 mph, the water acts more like a solid than a liquid beneath the Flash’s fleet feet (to test this, try rapidly slapping a pool of water), and therefore his oft-shown ability to run across bodies of water is indeed consistent with the laws of physics. In fact, at the speeds at which he typically runs, it is practically impossible for him to not run across the water’s surface. However, in order to acquire forward momentum, the Flash must push back against the water. That is, even if the water does behave like a solid under the rapid compression under his feet, would the Flash be able to obtain traction in order to run? One way he could accomplish this is by generating backward propagating vortices under his feet, thereby gaining a forward thrust under Newton’s third law. This mechanism was proposed as the means by which water-strider insects propel themselves along the water’s surface. Here again comics were ahead of the curve. The Flash’s ability to run across a body of water was likened to a rapidly skipping shell skimming over the water in Flash # 117, m
ore than thirty years before scientists understood the water strider’s method of locomotion.19
When it comes to air, there is a lot of space between neighbor ing molecules. At room temperature and pressure, for example, the distance between adjacent air molecules is about ten times larger than the diameter of an oxygen or nitrogen molecule. Moreover, each air molecule at room temperature is zipping around with an average speed of approximately 1,100 feet/sec or 750 mph (which is the speed of sound in air). When we run through air, we don’t build up a high-density region in front of us, because our speed is much less than the average air molecule’s velocity. Think about herding cattle: If the cows are running when you try to push one into the herd, the others will just run away. If they are walking very slowly, and you push at the same rate, the others don’t have time to get out of the way, and they pile up into a herd. One can, of course, move faster than the speed of sound (a feat first performed by Col. Chuck Yeager in 1947), but the expended effort is large. When trying to displace a volume of air faster than the air molecules are moving, a high-density region (that is, a shock front) would pile up in front of you.
In fact, in “The Challenge of the Weather Wizard,” the Flash uses just such a shock front to knock out the Weather Wizard. Mark Mardon, a small-time crook, stole his deceased scientist brother’s “weather stick,” a device that enabled him to control the weather. Much like any other self respecting comic-book villain, once in possession of a weapon giving him mastery over the fundamental forces of nature, he immediately adopts a colorful costume, calls himself the “Weather Wizard,” and sets upon robbing banks and vandalizing police stations. The finale of the story, as shown in fig. 9, comes when, “with a tremendous surge of speed, the Flash slams toward his foe so fast that the air in front of him piles up into a wave-front and a split instant later strikes Mardon like a solid sheet of glass.” This is indeed a physically accurate consequence of the Flash’s supersonic velocity, and the variation in the compressibility of air at high velocities bedeviled fighter pilots in the 1940s attempting to break the “sound barrier.” Whenever the Flash runs at or faster than the speed of sound, the pressure waves he generates create a “sonic boom.” Just such a loud crash heralded the first appearance of the Flash in Showcase # 4.
Fig. 9. Panels from “The Challenge of the Weather Wizard” (Flash # 110) demonstrating that the faster one moves, the harder it is to get the air out of the way.
Once the Flash has moved the air before him out of his path, he leaves a region of lower-density air in his wake. Compared with the surrounding air at normal density, this lower-density trail behind the Flash can be considered a partial vacuum. Air rushes in to fill any vacuum, and anything standing in the way of this rushing air behind the Flash will be pushed into the wake region. The faster he runs, the greater the pressure difference between the air behind him and the surrounding air, and the larger the force as this pressure imbalance is corrected. This effect is noticeable even for slower-moving objects, such as when a subway train enters a tunnel. The enclosed geometry of the tunnel accentuates the updraft behind the departing train, pulling loose newspapers and litter in its wake. Lacking a confined space, the Flash can generate a low-pressure region that can slow the descent of falling people, cars, or giant bombs, or as shown in fig. 10, or help detain and levitate a crook by using a vortex created by running in a circle.
Returning to the topic of the speed of sound in air, whenever the Flash runs faster than a velocity of 1,100 feet/sec (or 750 mph), his communication with others must become visual only. The Flash would not be able to hear anyone standing behind him or even at his sides, as he would outrace the sound waves trying to reach him. Of course, for anyone standing in front of him, the Flash outracing the sound waves would not be a problem, but there would still be a barrier to communication. Even when he can hear someone talking to him, the speech will have a high and tinny quality as heard by the Flash.
Fig. 10. When the Flash runs at high velocity in a circle, he leaves a low-pressure region in his wake, which makes it easy to bring Toughy Boraz (yes, that’s actually his name) and his stolen loot to police headquarters. From Flash # 117.
What we term “sound waves” are variations in density consisting of alternating regions of expansion and compression. The “wavelength” of a sound wave is the distance between adjacent compressed (or expanded) regions in the medium (whether it be air, water, or a solid), which is related to the pitch that we hear. The pitch, or frequency, measures the number of complete wave cycles that pass a given point per second. Long wavelengths have low pitches (think of the deep tones from a bass violin, where the length of the strings is related to the wavelength of the sounds they can produce) while shorter wavelengths are heard as higher pitches. As the Flash runs, even if he does not outrace the sound wave, his high-speed motion affects the pitch that he hears. Let’s say he runs toward someone who is yelling a warning to him. The sound waves have some wavelength, which marks the average distance between adjacent compressed or expanded regions. If the Flash were standing still when these alternating density regions reach him, the tone he would hear would be determined by the wavelength originating from the speaker. But as the Flash runs, one region of compressed air reaches him, and as he is running toward the speaker, the next region of compressed air reaches his eardrum sooner than it would if he were standing still. The Flash thus hears a smaller wavelength and hence a higher frequency due to the fact that he is running toward the source of the sound. The faster he runs, the greater this shift in the wavelength and frequency of the detected sound.
This phenomenon is known as the Doppler effect, and if one knows the wavelength of a stationary source of waves, and measures the wavelength of the detected waves with a moving detector, one can determine the speed of the detector. Alternatively, if one sends out a wave of a known wavelength and it bounces off a stationary target, it should return with the exact same wavelength. If the target is moving toward the source, the reflected wave will have a shorter wavelength, while if the target is moving away from the source, the detected wavelength will be longer. Doppler radar, as often used in predicting weather, involves detection of this wavelength shift, which enables meteorologists to calculate the wind velocity in an approaching storm front.
This is also the basic premise underlying radar guns, which use radio waves of a known wavelength. From the shift in wavelength of the reflected wave to the incident wave, they can determine the velocity of the object (such as a thrown baseball or a speeding automobile) that reflected the waves. The faster the target is moving, the greater the wavelength shift, and the higher the pitch of the detected wave. If the Flash were to run at 500 mph toward someone who was using a normal speaking voice with a pitch of about 100 cycles per second, the sound waves reaching the Viceroy of Velocity’s ears would be shifted to 166 cycles per second. It would sound strange, but the Flash could hear the person. Could he run so fast that the frequency shift would make the sound undetectable? In order for the pitch of the sound waves reaching the Flash to be greater than 20,000 cycles/sec, the upper range of human hearing, the Flash would have to run toward the speaker with a speed greater than 150,000 mph (that is, 0.02 percent of the speed of light). There would be other problems, aside from Doppler shifts, were the Flash to run toward someone at that speed.
The Flash’s preferred technique for stopping bullets is also consistent with Newton’s laws of motion. You don’t need to be bulletproof when you can outrun a bullet. But what about the innocent bystanders caught in the line of fire? Fig. 11 shows a physically accurate use of superspeed in this situation. As narrated by one such potential victim in Flash # 124, “the amazing speedster merely made his hand travel at the same speed as the bullets whizzing at him, and with a sweeping motion plucked them right out of the air before they could harm him.” That is, the Flash would first match his velocity to the bullets so that the relative speed between him and the bullet is zero. Just as one can easily pick up a book or a cup on an
airplane in flight if it is not moving relative to you, the Flash is then able to pluck the bullet out of the air, since he is also moving at approximately 1,500 feet/sec or more than 1,000 mph in the same direction as the bullet. An “editor’s note” in Flash # 124 correctly points out that “Flash’s action in stopping the bullets is similar to that of a baseball fielder who stops a hot grounder by letting his glove travel momentarily in the same direction as the ball.”
As discussed Chapter 3, the problem with high velocities is not the speed but the deceleration. For Gwen Stacy, the braking time was very short, so the stopping force was large. The boxer rolling with a punch, as noted earlier, deliberately increases the contact time in order to minimize the stopping force. The Flash, as the editor’s note correctly points out, is applying the same principle in this situation. In addition to being able to run at amazing speeds, Barry Allen also apparently gained the ability to withstand crushing accelerations every time he sped up or slowed down. Thus, when the Flash stops running, the bullet he is holding stops as well, and he can then drop the slug at the gunman’s feet for dramatic effect.
Fig. 11. The Flash demonstrates that Impulse and Momentum principles are still important, even when you can run as fast as a speeding bullet. From Flash # 124.
5
IF THIS BE MY DENSITY—PROPERTIES OF MATTER
BEFORE DR. HENRY PYM began moonlighting, fighting crooks and capturing Communist spies as Ant Man, he was a fairly typical biochemist. In his first appearance in “The Man in the Ant Hill,” Pym was shown struggling with the bane of a modern scientist’s life: funding! As difficult as it is nowadays to secure funding for scientific research, Pym’s travails as relayed in Tales to Astonish # 27 indicate that we have it pretty good compared with the early 1960s. As we learn in a flashback, at a recent scientific convention, a panel of scientists went beyond merely rejecting Pym’s request for financial support of his search for a shrinking potion and took the additionally cruel step of personally taunting him. “Bah! You’re wasting your time with your ridiculous theories,” jeers one professor, “but they never work!” Another counsels: “You should stick to practical projects!” To which Pym replies, “No! I’ll work only on things that appeal to my imagination . . . like my latest invention!” I should point out that two aspects of this exchange ring particularly true: namely (1) there continues to this day a tension at universities and research laboratories between research that is motivated by the search for practical applications and those investigations that are “curiosity-driven,” and (2) unlike the public at large, scientists routinely use the expression “Bah!” in everyday conversation.
The Physics of Superheroes: Spectacular Second Edition Page 8