The Physics of Superheroes: Spectacular Second Edition (17 page)

There is considerable interest in commercial applications of webbing, which would require large quantities of spider silk. As it is not practical to harvest spiders for their silk (they are too territorial to farm in a conventional manner), genetic-engineering experiments have inserted spiders’ web-making genes into goats, so that the goats’ milk will contain webbing that can be more easily sieved and acquired. While the development of web-producing goats has hit some snags,
²⁴
other scientists have reported preliminary success with infecting spider cells in the laboratory with a genetically engineered virus that induces the cell to directly manufacture the proteins found in spiderwebs. The silk-producing gene from spiders has also been successfully introduced into E. coli and plant cells. Such research could have far-reaching practical applications. As Jim Robbins discussed in his article “Second Nature” in the July 2002 issue of
Smithsonian
: “In theory, a braided spider-silk rope the diameter of a pencil could stop a fighter jet landing on an aircraft carrier. The combination of strength and elasticity allows it to withstand an impact five times more powerful than Kevlar, the synthetic fiber used in bulletproof vests.”

The high tensile strength of real spider silk enables it to support a weight of more than ten tons per square centimeter. Even a webbing strand with a diameter of only a quarter inch could support more than six thousand pounds safely, well below the three hundred pounds of weight and centripetal force we estimated earlier. Unless Spider-Man is trying to carry both the Hulk and the Blob simultaneously, his webbing should be more than able to do the job.

Therefore, according to Newton’s laws of motion, it is entirely plausible that Spider-Man can swing from building to building, stop a runaway elevated train (as in the 2004 film
Spider-Man 2
), or weave a bulletproof shield out of very narrow lines of webbing. So, to answer the question posed in the title of this chapter: Simply take a look overhead!

8

CAN ANT MAN PUNCH HIS WAY OUT OF A PAPER BAG?—
TORQUE AND ROTATION

EVERY COMIC-BOOK HERO has some Achilles’ heel, and Ant-Man’s was only a millimeter big. There are certain obvious drawbacks to being the size of an ant. For example, just as Superman is susceptible to Kryptonite, Ant-Man must be ever vigilant against the more common hazard of being stepped on. In addition, his stride being only a few millimeters, he requires thousands of steps to cover the same distance he could walk in one step while normal height. The time required for him to walk a few feet would therefore increase correspondingly.
²⁵
No doubt this was his motivation for frequently hitching rides atop carpenter ants. The fact that he could ride on top of an ant without crushing it suggests that Ant Man’s mass decreased along with his size, implying that his density remained constant as he shrank. (Remember that density is the mass of an object divided by its volume; if the volume decreases by a factor of one thousand, and the mass is reduced by an identical factor, their ratio and, hence, the object’s density, is unchanged.) Pym made good use of his reduced mass and constructed a spring- loaded catapult that could shoot him across town. Of course, as we’ve discussed at length in Chapter 3, it’s not the journey but the stopping that is problematic. In order to avoid a messy finale to his trajectory, Pym called upon his special rapport with ants and used his cybernetic helmet to instruct hundreds of them to form a living air bag to cushion his landing. Ant Man’s kinetic energy would be distributed among the many, many ants so that no one insect would suffer too much for its participation in breaking his fall.

If Ant Man is such a lightweight that he could be propelled across several city blocks by a coiled spring and not harm the ants that stopped his motion, then how is he able to disable such foes as the Protector or the Hijacker, or meet “The Challenge of Comrade X”? In particular, how is Ant-Man able to punch his way out of a vacuum-cleaner bag (shown in fig. 15), as thrillingly rendered in
Tales to Astonish # 37
, or swing a crook overhead using a nylon lariat in the very next issue? As explained in
Tales to Astonish # 38,
Henry Pym retained “all the strength of a normal human,” even when ant-size. Not to nitpick, but the average normal-size human, not to mention the average biochemist, would be hard-pressed to swing a full-grown man overhead, even using a “practically unbreakable” nylon lasso. But leaving that issue aside, what does it mean to say that Ant-Man has the strength of a normal-size person, such that he can break a vacuum bag, but only the mass of an ant, whereby he is easily sucked up by the vacuum cleaner in the first place? Perhaps the more basic question is: Why do you have the strength that you do, in that you can easily lift a twenty-pound object, but struggle with one weighing two hundred pounds and cannot possibly lift two thousand pounds? Our strength comes from our muscles and skeletal structure that comprise a series of interconnected levers. It turns out that these levers are not that well suited to lifting things.

Let us stipulate that by “strength” (of its many definitions) we mean the ability to lift an object. Mankind’s ingenuity has led to the development of a wide range of machines to perform tasks such as heavy lifting. One of our earliest inventions employed to lift objects is the simple mechanical device of a lever. Many of us first encountered a lever as children in the form of a playground’s teeter-totter or seesaw, consisting of a horizontal board supported by a fulcrum point placed beneath the midpoint of the board. When seated at one end of the seesaw, you are able to lift a play-mate high in the air, through the mechanical advantage of the lever. With the fulcrum placed at the exact middle of the board, you can lift only a mass roughly equal to your own. If, however, the fulcrum point is placed much closer to one end, then a small child can lift a full-grown adult, provided the adult sits at the end of the seesaw nearer to the fulcrum point. This is because seesaws, and levers in general, do not balance forces but rather “torques.”

Fig. 15.
A scene from “Trapped by the Protector” from
Tales to Astonish # 37,
in which it is demonstrated that Ant-Man is both as light as an ant (and hence easily captured by a vacuum cleaner) and as strong as a normal-size human (and consequently able to punch his way out of the vacuum bag).

If a force is defined as the ability to push or pull an object in a straight line, then a torque is a measure of the ability to rotate an object. A torque is mathematically defined as the product of the applied force and the distance between the force and the point where the object is to be rotated. While both “torque” and “work” are defined mathematically as the product of force and distance, in the case of work, the distance is the displacement of the object—that is, the distance over which the force pushes or pulls the object (more on work, in Chapter 12). The force must be acting in the same direction as this distance in order to change the object’s energy. In contrast, for a torque that causes a twist, the force should be at a right angle to the separation between the applied force and the point about which the object is to be rotated. This distance is referred to as the “moment arm” of the torque. For a given applied force, the larger the force’s distance from the point where the object is to be rotated, the greater the torque.

This is why doorknobs are placed at the end of the door as far away from the hinges as possible. Try closing a door by pushing it at the end that’s immediately adjacent to the hinges, and then apply the same force to the other end, where the doorknob is located. The same force is used, but increasing the moment arm by increasing the distance between the push and the hinges magnifies the torque, and makes closing the door much easier. A wrench is another simple machine that amplifies a force applied at one end to produce a rotation at the other. When trying to loosen a particularly stubborn nut, one sometimes makes use of a “cheater,” basically an extension arm for the wrench by which the moment arm, and hence the applied torque, can be increased when the available force that can be applied is already at a maximum. Returning to the example of the seesaw, a small child is able to lift a full-grown adult only when the fulcrum of the seesaw is placed near the adult’s end (in a playground seesaw, the adult usually sits closer to the fixed fulcrum in the center). In this case, the moment arm for the child is increased, and the torque she applies is large enough to lift the adult up into the air, which the child could not accomplish without the mechanical advantage provided by the lever.

Levers also play a role in determining the strength of Ant-Man’s tiny punch. Our arms are able to lift and throw by making use of the principle of levers. An object, let’s say a rock, is placed on one end of the lever, which we’ll call a “hand.” A force is exerted by the compression of the bicep muscle, causing the other end of the lever (the forearm) to move down, which in turn raises the far end of the lever—that is, the hand holding the rock. The biceps pulls the hand upward—when we need to lower the rock, the triceps contracts and in so doing pushes the hand back downward. Muscles can only contract and pull; they cannot push. Consequently, an ingenious series of levers, consisting of muscles attached to various points of our skeletal structure, have evolved in order to enable a wide range of movement. The fulcrum of the lever that is your forearm is located at the elbow. It may seem odd to have both forces applied on the same side of the fulcrum, but this type of lever is essentially the same as a fishing rod, where the force applied to one end—very near the fulcrum located near the reel—causes a rotation and consequent lifting of a fish at the other end of the rod. Your bicep applies a pulling force approximately two inches in front of your elbow, and most people’s forearms are fourteen inches long. The ratio of moment arms is thus 1:7, which means that the force applied by your biceps is reduced by a factor of seven at the location of your hand. That’s right, reduced—in order to lift a rock weighing 20 pounds, your biceps has to provide a lifting force of 140 pounds.

A reasonable response to this news would be: What’s the point in that? Why have a lever built into your arm that increases the force needed to lift an object? There wouldn’t seem to be any point at all if the primary function of our arms were to lift rocks. Because the bicep is attached much closer to the fulcrum point (the elbow) than your hand, the biceps contracts two inches and the hand rises fourteen inches, due to the same ratio of 1:7 in moment arms. This ratio also holds when we want to get rid of this rock we are holding. In this case a muscle contraction of less than two inches produces a displacement of the hand of roughly twelve inches. This requires only 0.1 seconds to occur, and the hand holding the rock can get rid of it with a velocity of 12 inches in 0.1 second, or 10 feet per second (that is, 7 mph). This is a low estimate, and the average person can provide a much larger release velocity using other levers connecting her upper arm to her shoulder. A very, very small subset of the general population can throw baseball-size objects at speeds of up to 100 mph. And that’s the point of the inverse lever in our arms—it’s not intended to lift up large rocks; it’s there to enable us to throw smaller rocks at high velocities. Those of our ancestors who were better rock- or spear-throwers were, on average, better hunters. Being a better hunter increased one’s chance of securing dinner, and that in turn increased the odds of getting a date. In this way, certain hunters were able to pass these “good throwing-arm” genes down to their progeny.

Meanwhile ... I haven’t forgotten about Ant-Man trapped in a vacuum-cleaner bag. For the tiny crime-fighter, all length scales are obviously reduced, but the ratio of moment arms of 1:7 in his arms still holds for Henry Pym, regardless of whether he is ant-size or normal height. Punching involves the same muscles and similar motions as throwing, only instead of a rock, one is throwing a fist. The force provided by your muscles does not depend on their length, but on their cross-sectional area (that is, the area one would measure in a magnetic resonance imaging slice though the thickness of the bicep, not the surface area around the outside of the arm). If Ant-Man is 0.01 times his normal height, then the force his muscles can provide is reduced by a factor of (0.0 1)
²
= 0.0001. If Pym can punch with a force of two hundred pounds when full size, his scaled-down punch delivers a wallop of two hundredths of a pound. At his miniature size, his fist is much smaller and has a cross-sectional area of 0.0005 square inches (assuming his hand is just a millimeter wide). The pressure that his punch provides is defined as the “force per unit area,” which is 0.02 pounds divided by 0.0005 square inches—or 40 pounds per square inch.
²⁶
This is to be compared with his normal- height punching force of 200 pounds divided by his normal-size fist’s cross-sectional area of 5 square inches, for a pressure of 40 pounds per square inch. That is, Henry Pym’s punches exert the same pressure when he is ant-size as they do when he’s at his normal height. If he can punch through the vacuum bag while normal sized, then he can do so at his reduced height. It appears that Ant Man can indeed punch his way out of paper bag. In this way, he serves as a role model and inspiration to all comic-book fans.