Laws of Motion - Real-life applications
T HE F IRST L AW OF M OTION IN A C AR C RASH
It is now appropriate to return to the first law of motion, as formulated by Newton: an object at rest will remain at rest, and an object in motion will remain in motion, at a constant velocity unless or until outside forces act upon it. Examples of this first law in action are literally unlimited.
One of the best illustrations, in fact, involves something completely outside the experience of Newton himself: an automobile. As a car moves down the highway, it has a tendency to remain in motion unless some outside force changes its velocity. The latter term, though it is commonly understood to be the same as speed, is in fact more specific: velocity can be defined as the speed of an object in a particular direction.
In a car moving forward at a fixed rate of 60 MPH (96 km/h), everything in the car—driver, passengers, objects on the seats or in the trunk—is also moving forward at the same rate. If that car then runs into a brick wall, its motion will be stopped, and quite abruptly. But though its motion has stopped, in the split seconds after the crash it is still responding to inertia: rather than bouncing off the brick wall, it will continue plowing into it.
What, then, of the people and objects in the car? They too will continue to move forward in response to inertia. Though the car has been stopped by an outside force, those inside experience that force indirectly, and in the fragment of time after the car itself has stopped, they continue to move forward—unfortunately, straight into the dashboard or windshield.
It should also be clear from this example exactly why seatbelts, headrests, and airbags in automobiles are vitally important. Attorneys may file lawsuits regarding a client's injuries from airbags, and homespun opponents of the seatbelt may furnish a wealth of anecdotal evidence concerning people who allegedly died in an accident because they were wearing seatbelts; nonetheless, the first law of motion is on the side of these protective devices.
The admittedly gruesome illustration of a car hitting a brick wall assumes that the driver has not applied the brakes—an example of an outside force changing velocity—or has done so too late. In any case, the brakes themselves, if applied too abruptly, can present a hazard, and again, the significant factor here is inertia. Like the brick wall, brakes stop the car, but there is nothing to stop the driver and/or passengers. Nothing, that is, except protective devices: the seat belt to keep the person's body in place, the airbag to cushion its blow, and the headrest to prevent whiplash in rear-end collisions.
Inertia also explains what happens to a car when the driver makes a sharp, sudden turn. Suppose you are is riding in the passenger seat of a car moving straight ahead, when suddenly the driver makes a quick left turn. Though the car's tires turn instantly, everything in the vehicle—its frame, its tires, and its contents—is still responding
As the car turns, the tires may respond to this shift in direction by squealing: their rubber surfaces were moving forward, and with the sudden turn, the rubber skids across the pavement like a hard eraser on fine paper. The higher the original speed, of course, the greater the likelihood the tires will squeal. At very high speeds, it is possible the car may seem to make the turn "on two wheels"—that is, its two outer tires. It is even possible that the original speed was so high, and the turn so sharp, that the driver loses control of the car.
Here inertia is to blame: the car simply cannot make the change in velocity (which, again, refers both to speed and direction) in time. Even in less severe situations, you are likely to feel that you have been thrown outward against the rider's side door. But as in the car-and-brick-wall illustration used earlier, it is the car itself that first experiences the change in velocity, and thus it responds first. You, the passenger, then, are moving forward even as the car has turned; therefore, rather than being thrown outward, you are simply meeting the leftward-moving door even as you push forward.
F ROM P ARLOR T RICKS TO S PACE S HIPS
It would be wrong to conclude from the carrelated illustrations above that inertia is always harmful. In fact it can help every bit as much as it can potentially harm, a fact shown by two quite different scenarios.
The beneficial quality to the first scenario may be dubious: it is, after all, a mere parlor trick, albeit an entertaining one. In this famous stunt, with which most people are familiar even if they have never seen it, a full table setting is placed on a table with a tablecloth, and a skillful practitioner manages to whisk the cloth out from under the dishes without upsetting so much as a glass. To some this trick seems like true magic, or at least sleight of hand; but under the right conditions, it can be done. (This information, however, carries with it the warning, "Do not try this at home!")
To make the trick work, several things must align. Most importantly, the person doing it has to be skilled and practiced at performing the feat. On a physical level, it is best to minimize the friction between the cloth and settings on the one hand, and the cloth and table on the other. It is also important to maximize the mass (a property that will be discussed below) of the table settings, thus making them resistant to movement. Hence, inertia—which is measured by mass—plays a key role in making the tablecloth trick work.
You might question the value of the tablecloth stunt, but it is not hard to recognize the importance of the inertial navigation system (INS) that guides planes across the sky. Prior to the 1970s, when INS made its appearance, navigation techniques for boats and planes relied on reference to external points: the Sun, the stars, the magnetic North Pole, or even nearby areas of land. This created all sorts of possibilities for error: for instance, navigation by magnet (that is, a compass) became virtually useless in the polar regions of the Arctic and Antarctic.
By contrast, the INS uses no outside points of reference: it navigates purely by sensing the inertial force that results from changes in velocity. Not only does it function as well near the poles as it does at the equator, it is difficult to tamper with an INS, which uses accelerometers in a sealed, shielded container. By contrast, radio signals or radar can be "confused" by signals from the ground—as, for instance, from an enemy unit during wartime.
As the plane moves along, its INS measures movement along all three geometrical axes, and provides a continuous stream of data regarding acceleration, velocity, and displacement. Thanks to this system, it is possible for a pilot leaving California for Japan to enter the coordinates of a half-dozen points along the plane's flight path, and let the INS guide the autopilot the rest of the way.
Yet INS has its limitations, as illustrated by the tragedy that occurred aboard Korean Air Lines (KAL) Flight 007 on September 1, 1983. The plane, which contained 269 people and crew members, departed Anchorage, Alaska, on course for Seoul, South Korea. The route they would fly was an established one called "R-20," and it appears that all the information regarding their flight plan had been entered correctly in the plane's INS.
This information included coordinates for internationally recognized points of reference, actually just spots on the northern Pacific with names such as NABIE, NUKKS, NEEVA, and so on, to NOKKA, thirty minutes east of Japan. Yet, just after passing the fishing village of Bethel, Alaska, on the Bering Sea, the plane started to veer off course, and ultimately wandered into Soviet airspace over the Kamchatka Peninsula and later Sakhalin Island. There a Soviet Su-15 shot it down, killing all the plane's passengers.
In the aftermath of the Flight 007 shoot-down, the Soviets accused the United States and South Korea of sending a spy plane into their airspace. (Among the passengers was Larry McDonald, a staunchly anti-Communist Congressman from Georgia.) It is more likely, however, that the tragedy of 007 resulted from errors in navigation which probably had something to do with the INS. The fact is that the R-20 flight plan had been designed to keep aircraft well out of Soviet airspace, and at the time KAL 007 passed over Kamchatka, it should have been 200 mi (320 km) to the east—over the Sea of Japan.
Among the problems in navigating a transpacific flight is the curvature of the Earth, combined with the fact that the planet continues to rotate as the aircraft moves. On such long flights, it is impossible to "pretend," as on a short flight, that Earth is flat: coordinates have to be adjusted for the rounded surface of the planet. In addition, the flight plan must take into account that (in the case of a flight from California to Japan), Earth is moving eastward even as the plane moves westward. The INS aboard KAL 007 may simply have failed to correct for these factors, and thus the error compounded as the plane moved further. In any case, INS will eventually be rendered obsolete by another form of navigation technology: the global positioning satellite (GPS) system.
U NDERSTANDING I NERTIA
From examples used above, it should be clear that inertia is a more complex topic than you might immediately guess. In fact, inertia as a process is rather straightforward, but confusion regarding its meaning has turned it into a complicated subject.
In everyday terminology, people typically use the word inertia to describe the tendency of a stationary object to remain in place. This is particularly so when the word is used metaphorically: as suggested earlier, the concept of inertia, like numerous other aspects of the laws of motion, is often applied to personal or emotional processes as much as the physical. Hence, you could say, for instance, "He might have changed professions and made more money, but inertia kept him at his old job." Yet you could just as easily say, for example, "He might have taken a vacation, but inertia kept him busy." Because of the misguided way that most people use the term, it is easy to forget that "inertia" equally describes a tendency toward movement or nonmovement: in terms of Newtonian mechanics, it simply does not matter.
The significance of the clause "unless or until outside forces act upon it" in the first law indicates that the object itself must be in equilibrium—that is, the forces acting upon it must be balanced. In order for an object to be in equilibrium, its rate of movement in a given direction must be constant. Since a rate of movement equal to 0 is certainly constant, an object at rest is in equilibrium, and therefore qualifies; but also, any object moving in a constant direction at a constant speed is also in equilibrium.
T HE S ECOND L AW : F ORCE , M ASS , A CCELERATION
As noted earlier, the first law of motion deserves special attention because it is the key to unlocking the other two. Having established in the first law the conditions under which an object in motion will change velocity, the second law provides a measure of the force necessary to cause that change.
Understanding the second law requires defining terms that, on the surface at least, seem like a matter of mere common sense. Even inertia requires additional explanation in light of terms related to the second law, because it would be easy to confuse it with momentum.
The measure of inertia is mass, which reflects the resistance of an object to a change in its motion. Weight, on the other hand, measures the gravitational force on an object. (The concept of force itself will require further definition shortly.) Hence a person's mass is the same everywhere in the universe, but their weight would differ from planet to planet.
This can get somewhat confusing when you attempt to convert between English and metric units, because the pound is a unit of weight or force, whereas the kilogram is a unit of mass. In fact it would be more appropriate to set up kilograms against the English unit called the slug (equal to 14.59 kg), or to compare pounds to the metric unit of force, the newton (N), which is equal to the acceleration of one meter per second per second on an object of 1 kg in mass.
Hence, though many tables of weights and measures show that 1 kg is equal to 2.21 lb, this is only true at sea level on Earth. A person with a mass of 100 kg on Earth would have the same mass on the Moon; but whereas he might weigh 221 lb on Earth, he would be considerably lighter on the Moon. In other words, it would be much easier to lift a 221-lb man on the Moon than on Earth, but it would be no easier to push him aside.
To return to the subject of momentum, whereas inertia is measured by mass, momentum is equal to mass multiplied by velocity. Hence momentum, which Newton called "quantity of motion," is in effect inertia multiplied by velocity. Momentum is a subject unto itself; what matters here is the role that mass (and thus inertia) plays in the second law of motion.
According to the second law, the net force acting upon an object is a product of its mass multiplied by its acceleration. The latter is defined as a change in velocity over a given time interval: hence acceleration is usually presented in terms of "feet (or meters) per second per second"—that is, feet or meters per second squared. The acceleration due to gravity is 32 ft (9.8 m) per second per second, meaning that as every second passes, the speed of a falling object is increasing by 32 ft (9.8 m) per second.
The second law, as stated earlier, serves to develop the first law by defining the force necessary to change the velocity of an object. The law was integral to the confirming of the Copernican model, in which planets revolve around the Sun. Because velocity indicates movement in a single (straight) direction, when an object moves in a curve—as the planets do around the Sun—it is by definition changing velocity, or accelerating. The fact that the planets, which clearly possessed mass, underwent acceleration meant that some force must be acting on them: a gravitational pull exerted by the Sun, most massive object in the solar system.
Gravity is in fact one of four types of force at work in the universe. The others are electromagnetic interactions, and "strong" and "weak" nuclear interactions. The other three were unknown to Newton—yet his definition of force is still applicable. Newton's calculation of gravitational force (which, like momentum, is a subject unto itself) made it possible for Halley to determine that the comet he had observed in 1682—the comet that today bears his name—would reappear in 1758, as indeed it has for every 75-76 years since then. Today scientists use the understanding of gravitational force imparted by Newton to determine the exact altitude necessary for a satellite to remain stationary above the same point on Earth's surface.
The second law is so fundamental to the operation of the universe that you seldom notice its application, and it is easiest to illustrate by examples such as those above—of astronomers and physicists applying it to matters far beyond the scope of daily life. Yet the second law also makes it possible, for instance, to calculate the amount of force needed to move an object, and thus people put it into use every day without knowing that they are doing so.
T HE T HIRD L AW : A CTION AND R EACTION
As with the second law, the third law of motion builds on the first two. Having defined the force necessary to overcome inertia, the third law predicts what will happen when one force comes into contact with another force. As the third law states, when one object exerts a force on another, the second object exerts on the first a force equal in magnitude but opposite in direction.
Unlike the second law, this one is much easier to illustrate in daily life. If a book is sitting on a table, that means that the book is exerting a force on the table equal to its mass multiplied by its rate of acceleration. Though it is not moving, the book is subject to the rate of gravitational acceleration, and in fact force and weight (which is defined as mass multiplied by the rate of acceleration due to gravity) are the same. At the same time, the table pushes up on the book with an exactly equal amount of force—just enough to keep it stationary. If the table exerted more force that the book—in other words, if instead of being an ordinary table it were some sort of pneumatic press pushing upward—then the book would fly off the table.
There is no such thing as an unpaired force in the universe. The table rests on the floor just as the book rests on it, and the floor pushes up on the table with a force equal in magnitude to that with which the table presses down on the floor. The same is true for the floor and the supporting beams that hold it up, and for the supporting beams and the foundation of the building, and the building and the ground, and so on.
These pairs of forces exist everywhere. When you walk, you move forward by pushing backward on the ground with a force equal to your mass multiplied by your rate of downward gravitational acceleration. (This force, in other words, is the same as weight.) At the same time, the ground actually pushes back with an equal force. You do not perceive the fact that Earth is pushing you upward, simply because its enormous mass makes this motion negligible—but it does push.
If you were stepping off of a small unmoored boat and onto a dock, however, something quite different would happen. The force of your leap to the dock would exert an equal force against the boat, pushing it further out into the water, and as a result, you would likely end up in the water as well. Again, the reaction is equal and opposite; the problem is that the boat in this illustration is not fixed in place like the ground beneath your feet.
Differences in mass can result in apparently different reactions, though in fact the force is the same. This can be illustrated by imagining a mother and her six-year-old daughter skating on ice, a relatively frictionless surface. Facing one another, they push against each other, and as a result each moves backward. The child, of course, will move backward faster because her mass is less than that of her mother. Because the force they exerted is equal, the daughter's acceleration is greater, and she moves farther.
Ice is not a perfectly frictionless surface, of course: otherwise, skating would be impossible. Likewise friction is absolutely necessary for walking, as you can illustrate by trying to walk on a perfectly slick surface—for instance, a skating rink covered with oil. In this situation, there is still an equally paired set of forces—your body presses down on the surface of the ice with as much force as the ice presses upward—but the lack of friction impedes the physical process of pushing off against the floor.
It will only be possible to overcome inertia by recourse to outside intervention, as for instance if someone who is not on the ice tossed out a rope attached to a pole in the ground. Alternatively, if the person on the ice were carrying a heavy load of rocks, it would be possible to move by throwing the rocks backward. In this situation, you are exerting force on the rock, and this backward force results in a force propelling the thrower forward.
This final point about friction and movement is an appropriate place to close the discussion on the laws of motion. Where walking or skating are concerned—and in the absence of a bag of rocks or some other outside force—friction is necessary to the action of creating a backward force and therefore moving forward. On the other hand, the absence of friction would make it possible for an object in movement to continue moving indefinitely, in line with the first law of motion. In either case, friction opposes inertia.
The fact is that friction itself is a force. Thus, if you try to slide a block of wood across a floor, friction will stop it. It is important to remember this, lest you fall into the fallacy that bedeviled Aristotle's thinking and thus confused the world for many centuries. The block did not stop moving because the force that pushed it was no longer being applied; it stopped because an opposing force, friction, was greater than the force that was pushing it.
WHERE TO LEARN MORE
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Suplee, Curt. Everyday Science Explained. Washington, D.C.: National Geographic Society, 1996.