Friction

Friction is a force that opposes relative motion between surfaces in contact. Learn about static and kinetic friction.

Types of Friction

Static friction ( $f_s$ ): prevents motion from starting; can range from 0 up to its maximum value.
Kinetic friction ( $f_k$ ): opposes motion when surfaces slide against each other.

Friction Force

f = \mu N

μ is the coefficient of friction (dimensionless), N is the normal force.

Type	Coefficient	Typical Range
Static $\mu_s$	Higher	0.3 – 0.8
Kinetic $\mu_k$	Lower	0.2 – 0.6

A 10 kg block on a surface with μk = 0.4. Find kinetic friction force.

$N = mg = 10 \times 9.8 = 98 \text{ N}$

$f_k = \mu_k N = 0.4 \times 98 = 39.2 \text{ N}$

Real world: car braking

When a driver presses the brake pedal, brake pads press against the wheel disc. On a dry road ( $\mu_k \approx 0.7$ ), a 1 200 kg car has a normal force of about 11 760 N per axle, producing a braking friction force of roughly 8 230 N per axle — enough to stop from 60 km/h in about 20 m. Wet roads reduce $\mu_k$ significantly, which is why braking distances increase in rain.

Real world: walking and slipping on ice

Walking relies on static friction between your shoe sole and the ground pushing you forward. On dry concrete $\mu_s \approx 0.8$ ; on wet ice $\mu_s \approx 0.05$ . The maximum static friction force drops to almost nothing on ice, so even a small forward push causes your foot to slip — that is why walking on ice is so dangerous.

Real world: rock-climbing chalk

Rock climbers coat their hands with magnesium carbonate chalk to raise $\mu$ between skin and rock from about 0.5 (moist) to over 1.0 (dry). A higher $\mu$ means a larger maximum static friction force for the same grip strength (normal force), reducing the chance of a hand slipping off a hold.

Tip

Where do you see friction? Car brakes and tyres, shoe soles, bicycle brake pads, sandpaper, conveyor belts, and the writing of a pencil all rely on friction. Engineers try to increase friction (grippy tyres, rubber soles) or decrease it (lubricating oil in engines, PTFE coating in non-stick pans).

Practice Problems

A 5 kg box on a floor (μk = 0.3). Find the friction force (g = 10 m/s²).

Show answer

N = 50 N. f = 0.3 × 50 = 15 N