Friction

Three types of friction

Type	When it acts	Magnitude	Direction
Static (μ_s)	Surfaces at rest relative to each other	0 ≤ f_s ≤ μ_s·N (adjusts to balance applied force, up to max)	Opposes impending motion
Kinetic (μ_k)	Surfaces sliding against each other	f_k = μ_k·N (constant)	Opposes relative velocity
Rolling (μ_r)	Rolling without slipping (wheels, balls)	f_r = μ_r·N (much smaller than kinetic)	Opposes rolling direction
Fluid (drag)	Object moving through liquid/gas	F ∝ v (low speed), F ∝ v² (high speed)	Opposes velocity

Note — μ_s ≥ μ_k always (you need more force to start motion than to maintain it). Typical ratio: μ_s/μ_k ≈ 1.2-1.5.

Common coefficients of friction

Surfaces	μ_s	μ_k
Rubber on dry asphalt	~0.9	~0.7
Rubber on wet asphalt	~0.6	~0.4
Rubber on ice	~0.15	~0.10
Steel on steel (dry)	~0.6	~0.4
Steel on steel (lubricated)	~0.1	~0.05
Wood on wood	~0.4	~0.3
Glass on glass	~0.9	~0.4
Teflon on Teflon	~0.04	~0.04
Cartilage (joint)	~0.003	~0.003

Mechanics of friction

Microscopically, surfaces are rough. Even polished metal has bumps (asperities) ~10-100 nm tall. When pressed together, the real contact area is the sum of asperity tips — much smaller than the apparent area. Pressure at contact points can reach the yield strength of the material, causing plastic deformation, cold welding, or material transfer.

The macroscopic friction force comes from:

1. Adhesion — molecular bonds at contact points; takes force to break.
2. Plowing — harder asperities scratching grooves into softer material.
3. Hysteresis — energy lost as material deforms and rebounds (especially for rubber).

Why μ_s > μ_k

When surfaces sit at rest, asperities settle into local minima — micro-bonds form. To start sliding, these bonds must break, requiring extra force. Once sliding, the asperities don't have time to re-bond, so less force is needed to maintain motion.

This is why pushing a stalled car is hardest at first — once it starts rolling (or sliding), pushing becomes easier.

Rolling friction — why wheels work

A perfectly rigid wheel on rigid ground would have zero rolling friction — no sliding, no energy loss. In reality, both deform slightly under load.

The wheel flattens at the bottom (forming a contact patch). The ground depresses slightly. As the wheel rolls forward, the leading edge encounters new ground (compressing it), and the trailing edge releases (decompressing). Some energy is lost in each deformation cycle (hysteresis).

For typical car tires, μ_r ≈ 0.005-0.015. So rolling resistance on a 1500 kg car is only 75-225 N — vs sliding friction of 7,500-15,000 N. Wheels reduce friction by 100-1000×.

JavaScript — friction simulation

// Simulate a block on a surface with kinetic friction
function blockWithFriction(mass, v0, mu_k, g = 9.81, dt = 0.01) {
  let v = v0;
  let x = 0;
  let t = 0;
  const trajectory = [];
  while (Math.abs(v) > 0.01) {
    const N = mass * g; // normal force on flat surface
    const friction = mu_k * N;
    // Friction opposes velocity
    const F = -Math.sign(v) * friction;
    const a = F / mass;
    v += a * dt;
    x += v * dt;
    t += dt;
    trajectory.push({ t, x, v });
    if (t > 100) break; // safety
  }
  return { stoppingDistance: x, stoppingTime: t, trajectory };
}

// 1500 kg car at 30 m/s with rubber-on-wet asphalt
const result = blockWithFriction(1500, 30, 0.4);
console.log(`Stops in ${result.stoppingTime.toFixed(1)} s, distance ${result.stoppingDistance.toFixed(0)} m`);

// Static friction problem: push a block. Will it slide?
function staticFrictionTest(mass, appliedForce, mu_s, g = 9.81) {
  const N = mass * g;
  const maxStatic = mu_s * N;
  if (appliedForce <= maxStatic) {
    return { sliding: false, friction: appliedForce };
  } else {
    return { sliding: true, friction: maxStatic };
  }
}

console.log(staticFrictionTest(50, 100, 0.5));   // 50 kg, 100 N push, μ=0.5: sliding=true
console.log(staticFrictionTest(50, 200, 0.5));   // 200 N push: friction matches at 245 N until exceeded
// Actual max = 50 * 9.81 * 0.5 = 245 N

// ABS vs locked-wheel braking
function abs_vs_locked(mass, v0, mu_s, mu_k, g = 9.81) {
  const N = mass * g;
  // Locked wheels: kinetic friction
  const decel_locked = mu_k * g;
  const dist_locked = v0 * v0 / (2 * decel_locked);
  // ABS keeps rolling = static friction
  const decel_abs = mu_s * g;
  const dist_abs = v0 * v0 / (2 * decel_abs);
  return {
    locked: { decel: decel_locked, distance: dist_locked },
    abs: { decel: decel_abs, distance: dist_abs },
    improvement: ((dist_locked - dist_abs) / dist_locked * 100).toFixed(1) + '%'
  };
}

console.log(abs_vs_locked(1500, 30, 0.9, 0.7));
// ABS reduces stopping distance by ~22% on dry asphalt

Where friction shows up

• Locomotion. Walking, running, vehicles — all rely on friction between feet/tires and ground. Without it, no traction.
• Braking. Car brakes, bicycle brakes, train brakes — convert kinetic energy to heat via friction.
• Engineering. Bearings, clutches, belts, brake pads — friction is designed in or out depending on use.
• Climbing and grip. Rock climbing relies on shoe-rock friction. Tires on track need careful balance — too much sticky rubber means more friction (heat) but also more wear.
• Sports. Skiing/snowboarding/skating use very low friction (ice melt). Curling uses sweepers to fine-tune friction in real time.
• Manufacturing. Drilling, polishing, sanding — controlled friction. Lubricants reduce friction in machine parts.
• Geology. Earthquake faults — static friction holds plates locked; sudden release (sliding) is the earthquake; energy = heat + seismic waves.

Common mistakes

• Using friction = μN when surfaces aren't sliding. Static friction is variable up to μ_s·N. If you push with 50 N on a block needing 100 N to start moving, static friction adjusts to 50 N — not the maximum.
• Forgetting that f opposes RELATIVE motion. Friction direction depends on which way one surface is sliding relative to the other. For a car driving forward, the tire pushes the road backward; the road pushes the tire forward (static friction).
• Assuming friction depends on contact area. Coulomb's law says no — only μ and N matter. Tire width affects grip via softness, heat, and pressure distribution, not contact-area-driven friction.
• Confusing kinetic with rolling friction. Sliding tires (skid) have μ_k ≈ 0.5-0.9; rolling tires have μ_r ≈ 0.005-0.015. ABS exploits this — keep rolling for better stopping.
• Treating fluid drag as Coulomb friction. Drag through air or water is velocity-dependent (F ∝ v² at high speed), not constant. Different physics, different formulas.
• Forgetting that friction generates heat. All friction work goes into heat. Brake pads can glow red. Earthquakes melt rock at fault lines. Friction "lost" energy isn't gone — it's thermalized.