Friction

A skidding tyre on dry concrete has a friction coefficient of about 0.7; on wet concrete it drops to about 0.5.

The force that opposes sliding

Friction is the force between two surfaces in contact that opposes their sliding past each other. It is why a sliding book stops, why brakes work, and also why you can walk at all: try walking on smooth ice and you find out how much you depend on it. Friction always acts along the surface and against the motion, or against the motion that would happen if friction were absent. OpenStax notes that, common as it is, friction behaves in a very complicated way and is still not completely understood, so we rely heavily on simple rules measured in experiments.

Look at two surfaces under a microscope and even polished ones are rough, touching only at the tips of tiny bumps. Some friction comes from these bumps catching on each other, and much of it from the molecules of the two surfaces sticking together where they touch.

Static and kinetic friction

Push gently on a heavy crate and nothing happens. Static friction is matching your push exactly, so the net force is zero. Push harder and static friction grows to match, up to a limit. Once you exceed that limit, the crate breaks free and slides, and now kinetic friction acts. Kinetic friction is usually smaller, which is why a crate that is already moving is easier to keep going. The rules are f_s ≤ μ_s N for static friction and f_k = μ_k N for kinetic friction, where N is the normal force and μ (the Greek letter mu) is the coefficient of friction for that pair of surfaces.

OpenStax gives these values to one or two digits on purpose: friction varies with how clean, rough or damp the surfaces are, so the coefficients are approximate. Take a 100 kg crate on a level floor with μ_s = 0.45 and μ_k = 0.30. Its weight, and so the normal force, is 100 × 9.81 = 981 N. To start it moving you must push with more than 0.45 × 981 ≈ 441 N. To keep it sliding at steady speed you need only 0.30 × 981 ≈ 294 N.

What friction does not depend on

Surprisingly, friction hardly depends on the area of contact. A brick slides with about the same friction whether it lies flat or stands on its narrow end. The real contact happens only at the bumps, and pressing harder increases that true contact area; spreading the weight over a bigger face does not. Friction depends on the normal force and the materials. At ordinary speeds kinetic friction also changes little with speed, unlike air resistance.

Measure μ with a book and a coin

Put a coin on a hardcover book and slowly tilt the book. At some angle the coin starts to slide; tap the book and find the angle at which it slides down at steady speed. At that angle the pull of gravity down the slope, m g sin θ, equals kinetic friction, μ_k m g cos θ, so μ_k = tan θ. If the coin slides steadily at 17°, μ_k ≈ tan 17° ≈ 0.31.

Friction also sets how quickly a car can stop. If the wheels lock and the tyres skid, kinetic friction is the only horizontal force, so the deceleration is μ_k g and the skid distance is v² ÷ (2 μ_k g). At 25 m/s (90 km/h) with μ_k = 0.7 on dry concrete the car skids about 45.5 m; on wet concrete with μ_k = 0.5 it skids about 63.7 m. This is a simplified model: it leaves out the driver’s reaction time and the anti-lock brakes of modern cars, which keep the tyres gripping with static friction instead.