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Physics for Pilot Assessments

Friction

Mechanics · Lesson 6 of 13•10 min read

Friction is the force that shows up whenever two surfaces are pressed together and one tries to slide across the other, and it always acts to oppose that sliding. It is worth getting straight early, because it is the force most often left out of a diagram and most often misdescribed in an answer option — and because almost nothing you actually do, from braking to walking, works without it.

Which way it acts

Friction opposes relative motion between the surfaces, which is not always the same as opposing the motion of the object. Push a crate to the right and it slides right, so friction on the crate acts left — that much is intuitive. But the friction that accelerates you when you walk acts forwards: your foot pushes backwards against the ground, the ground's friction resists that backward slide, and the reaction drives you on. This is why the phrase to hold onto is opposes relative sliding, not opposes movement. An item that asks which way friction acts on a driven wheel is testing exactly this distinction, and the intuitive answer is the wrong one.

Sticking, then slipping

Friction is not a fixed amount. Lean gently against a heavy box and it does not move: the friction is exactly matching your push, whatever your push happens to be. Lean harder and it still does not move, and friction has grown to match again. This is static friction, and it adjusts itself to whatever it needs to be, up to a limit. Push past that limit and the box breaks away and begins to slide — and at that moment the friction drops, because kinetic friction, the friction of surfaces already sliding over one another, is smaller than the maximum static friction was. That drop is why a heavy object is hard to start and then noticeably easier to keep going, and why a skidding tyre grips less than a rolling one.

frictionapplied forcebreaks away herenot moving yetsliding
While the object is still, friction rises to match whatever you apply. Once it breaks away and slides, friction settles at a lower, roughly constant value.

Where friction actually comes from

No surface is as smooth as it looks. Magnified far enough, even polished metal is a landscape of ridges and hollows, and when two surfaces sit together they only genuinely touch at the high points — a tiny fraction of the area you can see. Sliding one across the other means those high points have to ride up over, deform around, or shear past each other, and at the points of real contact the two materials also tend to cling together slightly. Both effects resist the sliding, and both get stronger the harder the surfaces are pressed together, because pressing harder flattens more high points into contact. That is the mechanism behind everything in this lesson, and it is also why friction produces heat: the work you do deforming and shearing those contact points has to go somewhere, and it ends up as vibration of the atoms in both surfaces.

The normal force

Because friction depends on how hard the surfaces are pressed together, it needs a name for that pressing force: the normal force. Normal here is used in its geometric sense, meaning perpendicular — the normal force acts at right angles to the surface, pressing the two together. For a block sitting on level ground with nothing else pushing on it, the normal force is simply equal to the block's weight, because the ground has to push up exactly hard enough to stop the block sinking. Change the situation and the normal force changes with it: press down on the block and the normal force rises above its weight; tilt the surface and only part of the weight presses into it, so the normal force falls. It is worth separating the two ideas now, because items will vary the normal force without changing the mass and expect you to notice.

What it depends on

Two things, and one thing it conspicuously does not. Friction depends on the normal force, and on what the two surfaces are made of. That second factor is captured in a single number called the coefficient of friction, written with the Greek letter mu and pronounced "mew". It is just a ratio — friction force divided by normal force — so it has no units at all, and a bigger mu means a grippier pairing. Multiply mu by the normal force and you have the friction: rubber on dry tarmac has a mu of roughly 0.8, rubber on wet ice perhaps 0.1, so the same car with the same weight has around eight times the grip on one as the other.

Friction

Ffriction=μNF_\text{friction} = \mu N
FfrictionF_\text{friction}
the friction force, in newtons (N)
μ\mu
coefficient of friction — a bare ratio, no units
NN
the normal force pressing the surfaces together, in newtons (N)

Two quantities in, one out, and every friction question in the bank is some arrangement of those three. Note that mu carries no unit at all, because it is a force divided by a force — a fact worth remembering, since it is the quickest way to check you have not mixed up which quantity you were solving for.

What friction does not depend on, to a good approximation, is the area of contact. This is genuinely counter-intuitive and it is examined for precisely that reason. A wide tyre and a narrow tyre carrying the same load have much the same friction, and the reason follows from the mechanism above: spreading the same force over a larger area reduces the pressure at every point in exact proportion to the extra area gained, so the total number of high points actually flattened into contact barely changes. You gain area and lose pressure, and the two cancel.

Putting it to work

Notice what did not enter that calculation: the size of the crate's base, and how fast you intended to move it. Neither is relevant, and both will be offered to you as if they were.

Real tyres are chosen wide for reasons this simple model does not cover — heat, wear, and rubber that deforms rather than sliding cleanly — and it is worth knowing that the model is an approximation rather than the last word. But for the purposes of these items, the rule holds: change the normal force or change the materials, and the friction changes; change the area alone, and it does not.

Rolling is not sliding

A wheel that rolls without slipping is not sliding across the ground at all: the point in contact is momentarily stationary relative to the surface, and it is replaced by the next point as the wheel turns. That is why rolling something is so much easier than dragging it, and the resistance that remains — rolling resistance, caused mainly by the tyre and surface deforming and springing back imperfectly — is far smaller than sliding friction would be. It also explains why a locked, skidding wheel stops a vehicle less effectively than one still rotating: the moment it locks, the contact patch starts genuinely sliding, and you drop from static friction's higher limit to kinetic friction's lower value at exactly the point you most need grip.

Friction is not simply waste

It is easy to file friction under losses, and in a bearing or a pipe that is fair — the work done against it ends up as heat, which is why brakes get hot and why a rubbed surface warms. But grip is friction, and every time you accelerate, corner or stop, friction is the force doing it. Reduce it to zero and a wheel would spin without moving you, a screw would not hold, and a knot would not stay tied. When an item frames friction as purely a nuisance, that framing is usually the thing being tested.

Why it matters in aviation

The friction described here is what stops an aircraft, and its behaviour is the reason landing performance is calculated rather than judged. Braking depends on the coefficient of friction between tyre and runway surface, and that coefficient belongs to the pairing rather than to the aircraft. Dry asphalt or concrete gives good grip; water, slush, snow and ice give far less, and above a certain speed a film of water can lift the tyre clear of the surface altogether, at which point very little friction is available at any brake pressure. This is why reported braking action matters to a crew, why the landing distance required on a contaminated runway is factored upwards from the dry figure, and why the static-to-kinetic drop is designed around: a locked, skidding wheel grips less than a rolling one, so anti-skid systems release brake pressure before the wheel stops turning.

It is also why deceleration is not left to the wheels alone. Spoilers raised on touchdown add drag and press the wheels more firmly onto the runway, and reverse thrust turns engine thrust rearwards. Both are most effective at high speed, which is exactly where wheel braking is least dependable.

What the test asks

Three traps recur. The first is contact area: an option will offer a larger surface as having more friction, and it does not. The second is direction: friction will be described as acting along the direction of travel, which is only ever true when the surfaces are sliding the other way. The third is the static-to-kinetic drop — expect to be asked why a load is harder to start moving than to keep moving, with an answer option blaming the object's weight changing, which it does not.

Check you understood

Three questions from this lesson — one straightforward, one that applies it, one that pushes a little further. Nothing is recorded, and you can draw a new set as often as you like.

  1. 1. Warm-up

    The coefficient of friction between two surfaces is measured in:

  2. 2. Applying it

    A 20 kg crate stands on level ground, and someone stands on top of it pressing down with an extra 300 N. Taking g = 10 m/s², what is the normal force from the ground on the crate?

  3. 3. Pushing it

    A 40 kg crate on level ground begins to slide when the horizontal pull reaches 100 N. Taking g = 10 m/s², what is the coefficient of static friction?

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