# FRICTION

## CONCEPT

Friction is the force that resists motion when the surface of one object comes into contact with the surface of another. In a machine, friction reduces the mechanical advantage, or the ratio of output to input: an automobile, for instance, uses one-quarter of its energy on reducing friction. Yet, it is also friction in the tires that allows the car to stay on the road, and friction in the clutch that makes it possible to drive at all. From matches to machines to molecular structures, friction is one of the most significant phenomena in the physical world.

## HOW IT WORKS

The definition of friction as "the force that resists motion when the surface of one object comes into contact with the surface of another" does not exactly identify what it is. Rather, the statement describes the manifestation of friction in terms of how other objects respond. A less sophisticated version of such a definition would explain electricity, for instance, as "the force that runs electrical appliances." The reason why friction cannot be more firmly identified is simple: physicists do not fully understand what it is.

Much the same could be said of force, defined by Sir Isaac Newton's (1642-1727) second law of motion as the product of mass multiplied acceleration. The fact is that force is so fundamental that it defies full explanation, except in terms of the elements that compose it, and compared to force, friction is relatively easy to identify. In fact, friction plays a part in the total force that must be opposed in order for movement to take place in many situations. So, too, does gravity—and gravity, unlike force itself, is much easier to explain. Since gravity plays a role in friction, it is worthwhile to review its essentials.

Newton's first law of motion identifies inertia, a tendency of objects in the physical universe that is sometimes mistaken for friction. When an object is in motion or at rest, the first law states, it will remain in that state at a constant velocity (which is zero for an object at rest) unless or until an outside force acts on it. This tendency to remain in a given state of motion is inertia.

Inertia is not a force: on the contrary, a very small quantity of force may accelerate an object, thus overcoming its inertia. Inertia is, however, a component of force, since mass is a measure of inertia. In the case of gravitational force, mass is multiplied by the acceleration due to gravity, which is equal to 32 ft (9.8 m)/sec2. People in everyday life are familiar with another term for gravitational force: weight.

Weight, in turn, is an all-important factor in friction, as revealed in the three laws governing the friction between an object at rest and the surface on which it sits. According to the first of these, friction is proportional to the weight of the object. The second law states that friction is not determined by the surface area of the object—that is, the area that touches the surface on which the object rests. In fact, the contact area between object and surface is a dependant variable, a function of weight.

The second law might seem obvious if one were thinking of a relatively elastic object—say, a garbage bag filled with newspapers sitting on the finished concrete floor of a garage. Clearly as more newspapers are added, thus increasing the weight, its surface area would increase as well. But what if one were to compare a large cardboard box (the kind, for instance, in which televisions or computers are shipped) with an ordinary concrete block of the type used in foundations for residential construction? Obviously, the block has more friction against the concrete floor; but at the same time, it is clear that despite its greater weight, the block has less surface area than the box. How can this be?

The answer is that "surface area" is quite literally more than meets the eye. Friction itself occurs at a level invisible to the naked eye, and involves the adhesive forces between molecules on surfaces pushed together by the force of weight. This is similar to the manner in which, when viewed through a high-powered lens, two complementary patches of Velcro™ are revealed as a forest of hooks on the one hand, and a sea of loops on the other.

On a much more intensified level, that of molecular structure, the surfaces of objects appear as mountains and valleys. Nothing, in fact, is smooth when viewed on this scale, and hence, from a molecular perspective, it becomes clear that two objects in contact actually touch one another only in places. An increase of weight, however, begins pushing objects together, causing an increase in the actual—that is, the molecular—area of contact. Hence area of contact is proportional to weight.

Just as the second law regarding friction states that surface area does not determine friction (but rather, weight determines surface area), the third law holds that friction is independent of the speed at which an object is moving along a surface—provided that speed is not zero. The reason for this provision is that an object with no speed (that is, one standing perfectly still) is subject to the most powerful form of friction, static friction.

The latter is the friction that an object at rest must overcome to be set in motion; however, this should not be confused with inertia, which is relatively easy to overcome through the use of force. Inertia, in fact, is far less complicated than static friction, involving only mass rather than weight. Nor is inertia affected by the composition of the materials touching one another.

As stated earlier, friction is proportional to weight, which suggests that another factor is involved. And indeed there is another factor, known as coefficient of friction. The latter, designated

THE RAISED TREAD ON AN AUTOMOBILE'S TIRES, COUPLED WITH THE ROUGHENED ROAD SURFACE, PROVIDES SUFFICIENT FRICTION FOR THE DRIVER TO BE ABLE TO TURN THE CAR AND TO STOP. (Photograph by
Martyn Goddard/Corbis
. Reproduced by permission.)
by the Greek letter mu (μ), is constant for any two types of surface in contact with one another, and provides a means of comparing the friction between them to that between other surfaces. For instance, the coefficient of static friction for wood on wood is 0.5; but for metal on metal with lubrication in between, it is only 0.03. A rubber tire on dry concrete yields the highest coefficient of static friction, 1.0, which is desirable in that particular situation.

Coefficients are much lower for the second type of friction, sliding friction, the frictional resistance experienced by a body in motion. Whereas the earlier figures measured the relative resistance to putting certain objects into motion, the sliding-friction coefficient indicates the relative resistance against those objects once they are moving. To use the same materials mentioned above, the coefficient of sliding friction for wood on wood is 0.3; for two lubricated metals 0.03 (no change); and for a rubber tire on dry concrete 0.7.

Finally, there is a third variety of friction, one in which coefficients are so low as to be negligible:

ACTOR JACK BUCHANAN LIT THIS MATCH USING A SIMPLE DISPLAY OF FRICTION: DRAGGING THE MATCH AGAINST THE BACK OF THE MATCHBOX. (Photograph by
Hulton-Deutsch Collection/Corbis
. Reproduced by permission.)
rolling friction, or the frictional resistance that a wheeled object experiences when it rolls over a relatively smooth, flat surface. In ideal circumstances, in fact, there would be absolutely no resistance between a wheel and a road. However, there exists no ideal—that is, perfectly rigid—wheel or road; both objects "give" in response to the other, the wheel by flattening somewhat and the road by experiencing indentation.

Up to this point, coefficients of friction have been discussed purely in comparative terms, but in fact, they serve a function in computing frictional force—that is, the force that must be overcome toset an object in motion, or to keep it in motion. Frictional force is equal to the coefficient of friction multiplied by normal force—that is, the perpendicular force that one object or surface exerts on another. On a horizontal plane, normal force is equal to gravity and hence weight. In this equation, the coefficient of friction establishes a limit tofrictional force: in order to move an object in a given situation, one must exert a force in excess of the frictional force that keeps it from moving.

## REAL-LIFE APPLICATIONS

### SELF-MOTIVATION THROUGH FRICTION

Friction, in fact, always opposes movement; why, then, is friction necessary—as indeed it is—for walking, and for keeping a car on the road? The answer relates to the differences between friction and inertia alluded to earlier. In situations of static friction, it is easy to see how a person might confuse friction with inertia, since both serve to keep an object from moving. In situations of sliding or rolling friction, however, it is easier to see the difference between friction and inertia.

Whereas friction is always opposed to movement, inertia is not. When an object is not moving, its inertia does oppose movement—but when the object is in motion, then inertia resists stopping. In the absence of friction or other forces, inertia allows an object to remain in motion forever. Imagine a hockey player hitting a puck across a very, very large rink. Because ice has a much smaller coefficient of friction with regard to the puck than does dirt or asphalt, the puck will travel much further. Still, however, the ice has some friction, and, therefore, the puck will come to a stop at some point.

Now suppose that instead of ice, the surface and objects in contact with it were friction-free, possessing a coefficient of zero. Then what would happen if the player hit the puck? Assuming for the purposes of this thought experiment, that the rink covered the entire surface of Earth, it would travel and travel and travel, ultimately going around the planet. It would never stop, because there would be no friction to stop it, and therefore inertia would have free rein.

The same would be true if one were to firmly push the hockey player with enough force (small in the absence of friction) to set him in motion: he would continue riding around the planet indefinitely, borne by his skates. But what if instead of being set in motion, the hockey player tried to set himself in motion by the action of his skates against the rink's surface?

He would be unable to move even a hair's breadth. The fact is that while static friction opposes the movement of an object from a position of rest to a state of motion, it may—assuming it can be overcome to begin motion at all—be indispensable to that movement. As with the skater in perpetual motion across the rink, the absence of friction means that inertia is "in control;" with friction, however, it is possible to overcome inertia.

### FRICTION IN DRIVING A CAR

The same principle applies to a car's tires: if they were perfectly smooth—and, to make matters worse, the road were perfectly smooth as well—the vehicle would keep moving forward when the driver attempted to stop. For this reason, tires are designed with raised tread to maintain a high degree of friction, gripping the road tightly and dispersing water when the roadway is wet.

The force of friction, in fact, pervades the entire operation of a car, and makes it possible for the tires themselves to turn. The turning force, or torque, that the driver exerts on the steering wheel is converted into forces that drive the tires, and these in turn use friction to provide traction. Between steering wheel and tires, of course, are a number of steps, with the engine rotating the crankshaft and transmitting power to the clutch, which applies friction to translate the motion of the crankshaft to the gearbox.

When the driver of a car with a manual transmission presses down on the clutch pedal, this disengages the clutch itself. A clutch is a circular mechanism containing (among other things) a pressure plate, which lifts off the clutch plate. As a result, the flywheel—the instrument that actually transmits force from the crankshaft—is disengaged from the transmission shaft. With the clutch thus disengaged, the driver changes gears, and after the driver releases the clutch pedal, springs return the pressure plate and the clutch plate to their place against the fly-wheel. The flywheel then turns the transmission shaft.

Controlled friction in the clutch makes this operation possible; likewise the synchromesh within the gearbox uses friction to bring the gearwheels into alignment. This is a complicated process, but at the heart of it is an engagement of gear teeth in which friction forces them to come to the same speed.

Friction is also essential to stopping a car—not just with regard to the tires, but also with respect to the brakes. Whether they are disk brakes or drum brakes, two elements must come together with a force more powerful than the engine's, and friction provides that needed force. In disk brakes, brake pads apply friction to both sides of the spinning disks, and in drum brakes, brake shoes transmit friction to the inside of a spinning drum. This braking force is then transmitted to the tires, which apply friction to the road and thus stop the car.

### EFFICIENCY AND FRICTION

The automobile is just one among many examples of a machine that could not operate without friction. The same is true of simple machines such as screws, as well as nails, pliers, bolts, and forceps. At the heart of this relationship is a paradox, however, because friction inevitably reduces the efficiency of machines: a car, as noted earlier, exerts fully one-quarter of its power simply on overcoming the force of friction both within its engine and from air resistance as it travels down the road.

In scientific terms, efficiency or mechanical advantage is measured by the ratio of force output to force input. Clearly, in most situations it is ideal to maximize output and minimize input, and over the years inventors have dreamed of creating a mechanism—a perpetual motion machine—to do just that. In this idealized machine, one would apply a certain amount of energy to set it into operation, and then it would never stop; hence the ratio of output to input would be nearly infinite.

Unfortunately, the perpetual motion machine is a dream every bit as elusive as the mythical Fountain of Youth. At least this is true on Earth, where friction will always cause a system to lose kinetic energy, or the energy of movement. No matter what the design, the machine will eventually lose energy and stop; however, this is not true in outer space, where friction is very small—though it still exists. In space it might truly be possible to set a machine in motion and let inertia do the rest; thus perhaps perpetual motion actually is more than a dream.

It should also be noted that mechanical advantage is not always desirable. A screw is a highly inefficient machine: one puts much more force into screwing it in than the screw will exert once it is in place. Yet this is exactly the purpose of a screw: an "efficient" one, or one that worked its way back out of the place into which it had been screwed, would in fact be of little use.

Once again, it is friction that provides a screw with its strangely efficient form of inefficiency. Nonetheless, friction, in spite of the advantages discussed above, is as undesirable as it is desirable. With friction, there is always something lost; however, there is a physical law that energy does not simply disappear; it just changes form. In the case of friction, the energy that could go to moving the machine is instead translated into sound—or even worse, heat.

### WHEN SPARKS FLY

In movement involving friction, molecules vibrate, bringing about a rise in temperature. This can be easily demonstrated by simply rubbing one's hands together quickly, as a person is apt to do when cold: heat increases. For a machine composed of metal parts, this increase in temperature can be disastrous, leading to serious wear and damage. This is why various forms of lubricant are applied to systems subject to friction.

An automobile uses grease and oil, as well as ball bearings, which are tiny uniform balls of metal that imitate the behavior of oil-based substances on a large scale. In a molecule of oil—whether it is a petroleum-related oil or the type of oil that comes from living things—positive and negative electrical charges are distributed throughout the molecule. By contrast, in water the positive charges are at one end of the molecule and the negative at the other. This creates a tight bond as the positive end of one water molecule adheres to the negative end of another. With oil, the relative absence of attraction between molecules means that each is in effect a tiny ball separate from the others. The ball-like molecules "roll" between metal elements, providing the buffer necessary to reduce friction.

Yet for every statement one can make concerning friction, there is always another statement with which to counter it. Earlier it was noted that the wheel, because it reduced friction greatly, provided an enormous technological boost to societies. Yet long before the wheel—hundreds of thousands of years ago—an even more important technological breakthrough occurred when humans made a discovery that depended on maximizing friction: fire, or rather the means of making fire. Unlike the wheel, fire occurs in nature, and can spring from a number of causes, but when human beings harnessed the means of making fire on their own, they had to rely on the heat that comes from friction.

By the early nineteenth century, inventors had developed an easy method of creating fire by using a little stick with a phosphorus tip. This stick, of course, is known as a match. In a strike-anywhere match, the head contains all the chemicals needed to create a spark. To ignite this type of match, one need only create frictional heat by rubbing it against a surface, such as sandpaper, with a high coefficient of friction.

The chemicals necessary for ignition in safety matches, on the other hand, are dispersed between the match head and a treated strip, usually found on the side of the matchbox or match-book. The chemicals on the tip and those on the striking surface must come into contact for ignition to occur, but once again, there must be friction between the match head and the striking pad. Water reduces friction with its heavy bond, as it does with a car's tires on a rainy day, which explains why matches are useless when wet.

### THE OUTER LIMITS OF FRICTION

Clearly friction is a complex subject, and the discoveries of modern physics only promise to add to that complexity. In a February 1999 online article for Physical Review Focus, Dana Mackenzie reported that "Engineers hope to make microscopic engines and gears as ordinary in our lives as microscopic circuits are today. But before this dream becomes a reality, they will have to deal with laws of friction that are very different from those that apply to ordinary-sized machines."

The earlier statement that friction is proportional to weight, in fact, applies only in the realm of classical physics. The latter term refers to the studies of physicists up to the end of the nineteenth century, when the concerns were chiefly the workings of large objects whose operations could be discerned by the senses. Modern physics, on the other hand, focuses on atomic and molecular structures, and addresses physical behaviors that could not have been imagined prior to the twentieth century.

According to studies conducted by Alan Burns and others at Sandia National Laboratories in Albuquerque, New Mexico, molecular interactions between objects in very close proximity create a type of friction involving repulsion rather than attraction. This completely upsets the model of friction understood for more than a century, and indicates new frontiers of discovery concerning the workings of friction at a molecular level.

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## KEY TERMS

### ACCELERATION:

A change in velocity.

### COEFFICIENT OF FRICTION:

A figure, constant for a particular pair of surfaces in contact, that can be multiplied by the normal force between them to calculate the frictional force they experience.

### FORCE:

The product of mass multiplied by acceleration.

### FRICTION:

The force that resists motion when the surface of one object comes into contact with the surface of another. Varieties including sliding friction, static friction, and rolling friction. The degree of friction between two specific surfaces is proportional to coefficient of friction.

### FRICTIONAL FORCE:

The force necessary to set an object in motion, or to keep it in motion; equal to normal force multiplied by coefficient of friction.

### INERTIA:

The tendency of an object in motion to remain in motion, and of an object at rest to remain at rest.

### MASS:

A measure of inertia, indicating the resistance of an object to a change in its motion—including a change in velocity.

The ratio of force output to force input in amachine.

### NORMAL FORCE:

The perpendicular force with which two objects press against one another. On a plane without any incline (which would add acceleration in addition to that of gravity) normal force is the same as weight.

### ROLLING FRICTION:

The frictional resistance that a circular object experiences when it rolls over a relatively smooth, flatsurface. With a coefficient of friction much smaller than that of sliding friction, rolling friction involves by far the least amount of resistance among the three varieties of friction.

### SLIDING FRICTION:

The frictional resistance experienced by a body in motion. Here the coefficient of friction is greater than that for rolling friction, but less than for static friction.

### SPEED:

The rate at which the position of an object changes over a given period of time.

### STATIC FRICTION:

The frictional resistance that a stationary object must overcome before it can go into motion. Its coefficient of friction is greater than that of sliding friction, and thus largest among the three varieties of friction.

### VELOCITY:

The speed of an object in a particular direction.

### WEIGHT:

A measure of the gravitational force on an object; the product of mass multiplied by the acceleration due to gravity.