Friction
The Force Hiding in Every Contact
Two Surfaces Touch at Almost Nothing
Push a book across a table and let go, and it slows and stops. Friction did that, at the one surface nobody looks at. Look at that surface closely, and the first surprise is how little of it is really there.
The oldest rule about friction sounds wrong. Friction grows in step with the weight pressing two surfaces together, and does not depend on the size of the face that rests on the other. A brick takes as hard a push to slide on its narrow side as on its broad face. Twice the surface does not mean twice the rubbing.
The reason has been measured. Physicists passed an electric current from one metal block into another, knowing it could flow only where metal truly met metal. The joint resisted the current far more than two whole faces in touch would have: the current was squeezing through a scatter of tiny spots. Surfaces that look flat, even ones polished to a mirror, are hills and valleys at a small enough scale, and two of them meet only at the tips of their highest summits. For a steel block resting on a steel plate, the summits that touch add up to well under a ten-thousandth of its face.
That one fact is the whole rule. Whether the summits give way like putty, as in metals, or flatten and spring back, as in glass, the count works out the same: more weight brings more summits into touch. The true contact grows in step with the weight. Stand the brick on end and the same weight bears down on a smaller face. Each part of that face is pressed harder, more of its summits touch, and the true contact comes out the same. Friction lives in the true contact, so it follows the weight and ignores the face.
The true contact can even be watched. Rest a block of clear glass on a roughened plate and light the two from beneath: the roughened face scatters the light everywhere except where the two touch, so through the block the true contact shows as points of light.
What happens there is mostly not bumps catching on bumps, which is how friction is usually pictured. Where two summits touch, their atoms come close enough to bond, and to slide is to tear those bonds. That is why polishing makes two surfaces more slippery only up to a point: very smooth, clean surfaces meet over more of their area and can grip harder. Two clean pieces of metal in a vacuum, with no skin of oxide or water between them, bond so well that they weld. Then why does a book lift off a table without sticking? As the weight comes off, the squeezed summits spring back, and their bonds break one by one before they can hold.
The rule comes with a number, the coefficient of friction: the push it takes to slide, divided by the weight. For most dry pairs it falls between a fifth and one. Rubber on a dry road comes near one, dry steel on steel is about six tenths, and a speed skate on good ice is about a two-hundredth. Why that band, and not a hundred? In the picture of bonded summits, the number compares two strengths of the same solid: the push that shears a bonded summit sideways, and the pressure that crushes one. For a metal the ratio comes to about a sixth, and the summits grow as they are sheared, which raises it.
Why Starting Is Harder Than Keeping Going
Push a heavy box and nothing happens. Push harder, still nothing, and then it lurches, and once it moves it takes less to keep it going than it took to start. The gap can be large. In careful tests, oak that had rested on oak for a few minutes took more than four times as much push to start as to keep it sliding. Wood resting on metal went on getting harder to start for four or five days.
The holding kind is called static friction and the sliding kind kinetic, and why the first grows with time can be seen directly. Through clear blocks of acrylic and glass, the true contact shows as points of light. Held still, the points slowly grow as the summits creep into each other, by the same amount for every tenfold stretch of time. Sliding keeps tearing the contact and replacing it with young ones, which never get the chance.
Holding is not only a hindrance. Every step you take is static friction at work: your foot pushes back on the floor without slipping, and the floor’s grip pushes you forward. A car is driven the same way, by the road’s grip on its tires. Friction always works against one surface slipping over another, and that is not the same as working against motion.
Even the letting go takes time. Filmed through its lit contact, a clear block does not break free all at once. A front of breaking contacts runs across the face from the edge being pushed, sometimes nearly as fast as sound travels in the material and sometimes more than ten times slower. The block moves only when a front has crossed the whole of it.
Pull a block with a spring and the two kinds of friction set up a rhythm. The spring stretches while the contacts hold and grow. When its pull reaches their strength they tear, and the block jumps forward against the weaker friction of sliding. Its momentum carries it past the point where the pull and that friction balance, and it stops on fresh contacts. Then the spring stretches again. This is stick and slip.
Stick and Slip, From Violins to Faults
Stick and slip is the squeak of a door hinge, of chalk on a blackboard and of sneakers on a gym floor. It is also the note of a violin. The bow’s hair, rubbed with rosin, grips the string and carries it sideways. A kink runs along the string to the far end and back, and as it passes under the bow it knocks the string loose. The string flies back across the hair, and the hair catches it again.
This happens hundreds of times a second, and it is the string, not the friction, that keeps time: one slip each time the kink comes round, at the string’s own note. The rosin helps in its own way. It grips hard while it is cool, and each slip warms it enough to soften it for an instant.
Scaled up to a continent, stick and slip is an earthquake. Blocks of granite, squeezed and slid past each other in the laboratory, stick and slip in sudden jumps, and faults do the same. On either side of a fault the ground is carried along by the slow drift of the plates, a few centimeters a year, but the fault itself is held by friction. The rock beside it bends instead, for decades or centuries, until the fault lets go in a front that runs along it at kilometers a second.
After the great San Francisco earthquake, fences and roads that crossed the San Andreas fault were found cut through, their two halves shifted apart by up to six meters. Surveys made before it showed the ground on either side had been bending, by about three meters over the half century before. Nearly every rock has much the same friction, between 0.6 and 0.85. The same rule that holds a book still on a tilted table holds a fault locked for a century.
Where the Energy Goes
Nearly all that friction takes from the sliding ends up as warmth, the jiggle of atoms, and it is made at the true contact and just beneath it. Since the true contact is so small, the energy is poured into specks perhaps a hundredth of a millimeter across. Those flash to hundreds of degrees Celsius for an instant, sometimes past a thousand, while the surfaces around them stay cool. The flashes can be measured by using the two sliding metals themselves as a thermometer. That is how a match lights, and why sparks fly from a grinding wheel.
The flashes can change the friction itself. Rock that grips at about six tenths when it slides slowly lets go at the speed of an earthquake, about a meter a second: the flashes at its summits weaken them, and in the laboratory its friction falls to a fraction of the slow value. A fault lubricates itself as it slips.
Friction was also the instrument that pinned down the exchange rate between motion and warmth. Falling weights drove paddles through water and through mercury, or turned a cast-iron wheel against another, and the warming of each was measured. Whatever was rubbing, the same fall gave the same warming, to within half a percent. It came to about 4.15 joules for each calorie, within one percent of today’s 4.18.
How, exactly, does sliding become warmth? Look closely enough and friction is stick and slip again, atom by atom. Drag a tungsten tip, sharpened almost to a point, across graphite, and the friction rises and falls with the spacing of the carbon atoms. The tip catches in each hollow between atoms, the pull builds up, and it snaps to the next.
Each snap sets the atoms near it shaking. The shaking runs off through the crystal as waves and settles into the even jiggle we feel as warmth. It never gathers again to push the tip on, for the same reason the warmth of a collision never turns back into motion: there are vastly more ways for the atoms to shake than to move in step. Bigger contacts tear and shove their atoms in messier ways, but the energy ends up the same way, as shaking.
How to Slide for Almost Nothing
If friction is the snapping, a contact that never snaps should slide almost for free. That happens when two perfectly flat crystals are turned out of step with each other. The bumps of one can then never all fall into the hollows of the other at once: wherever some atoms are being pushed back, as many elsewhere are pushed forward, and the pushes cancel. This is called superlubricity.
Drag a flake of graphite, stuck to a tungsten tip, across graphite. Its friction all but vanishes, except when the flake is turned back into step, once every sixth of a turn. For years the trick worked only on specks a few hundredths of a millimeter across at most, because ordinary graphite is a patchwork of small crystals turned every which way. Recently it was made to work across a single contact a fraction of a millimeter wide, cut from nearly flawless crystal. Pressing it five hundred times harder barely changed its friction, which under the heaviest load was about a hundred-thousandth of that load.
The older tricks work on the same account. Oil keeps the summits apart. When railway axle bearings were tested, a hole drilled to feed one with oil had oil welling out of it instead, and a wooden plug driven into the hole was slowly pushed back out. The turning axle was dragging oil into the narrowing gap between itself and the bearing, and the pressure built there held the two apart. What resists is then the oil being sheared, far gentler than summits being torn.
The wheel avoids sliding almost entirely. Each patch of its rim is set down on the road and lifted off again rather than dragged. What it pays for instead is the flexing at the contact, so a car tire rolls against about a hundredth of its weight, and a steel railway wheel against about a thousandth.
Ice is the trick most people think they understand. The usual story is that a skate’s pressure melts the ice under it, and it is wrong: the pressure lowers the melting point by a few degrees at most, and people skate at thirty degrees Celsius below freezing. What is widely agreed is that a skate rides on a watery film far thinner than a hair, up to a hundred times more sluggish than ordinary water. What makes the film is still argued. One long-standing idea is that ice is wet on its surface even below freezing; another is that friction melts it. Recent computer simulations found the sliding itself scrambling the top layers of ice into a liquid-like film, even far below freezing. A study posted since argued instead that at skating speeds the warming by friction does most of the work. What would settle it is a measurement under a real blade at skating speed. The small probes used so far disagree a hundredfold on how thick the film is.
What Cannot Yet Be Calculated
The oldest rule of friction is not a law of nature. It is a summary of what hard, rough, dry surfaces do, and it bends wherever one of those words fails. Much of a tire’s grip comes from its rubber being flexed by the bumps of the road as it slips over them, and that grip changes with speed and warmth, which the rule says it should not. Clean metals in a vacuum weld, and rock lets go at the speed of an earthquake. A single summit a few millionths of a millimeter wide has a smooth contact whose size does not grow in step with the load. Its friction follows the number of atoms that actually touch, though, and that number does: the old rule, found again one level down.
And the coefficient of friction for two named materials cannot yet be worked out from first principles. It has to be measured, and measured again when the air is damper. The mechanism is known in outline: summits, bonds, snaps, warmth. For two perfect, clean crystals, computers can now follow the friction atom by atom. For a real pair of surfaces the answer runs through roughness at every scale from millimeters to atoms at once, through films of oxide and water, and through the dust the sliding grinds off. What would settle it is a way to carry the answer for single contacts, which can now be both measured and computed, up through every scale of roughness to a whole face. No method yet does. Friction is one of the most common forces in daily life and one of the least finished pieces of physics: a thing you can feel with your hand, and cannot yet calculate.
