Friction

You’ll be able to

Distinguish static friction from kinetic friction
Compute the friction force from f = μN
Decide whether an applied force is enough to start an object sliding

Two kinds of friction

Friction is a force that resists sliding between two surfaces in contact, always directed opposite to the motion (or the tendency to move). Static friction acts when the surfaces are not yet sliding; it adjusts itself, from zero up to a maximum, to prevent motion. Kinetic friction acts once the surfaces are sliding and has a fixed value. Static friction’s maximum is usually a bit larger than kinetic friction, which is why an object is hardest to get moving in the very first instant.

Friction depends on the normal force

The strength of friction is set by two things: how hard the surfaces are pressed together (the normal force N) and how rough they are (the coefficient of friction μ). Notably, friction does not depend on the contact area or on how fast the object slides. The kinetic friction force is f_k = μ_k N, and static friction can be anything from 0 up to its maximum f_s,max = μ_s N.

Friction force

f_k = μ_k N · f_s ≤ μ_s N

On flat ground with no vertical push, N = mg. Static friction is an inequality: it only reaches its maximum right at the verge of slipping.

Worked example

A 10 kg box is pushed horizontally with 50 N across a floor where μ_k = 0.3 (g = 10 m/s²). Find the friction force and the box’s acceleration.

1.On flat ground the normal force balances weight: N = mg = 10 × 10 = 100 N.
2.Kinetic friction opposes the push: f_k = μ_k N = 0.3 × 100 = 30 N.
3.Net horizontal force: ΣF = 50 − 30 = 20 N in the push direction.
4.Acceleration: a = ΣF ÷ m = 20 ÷ 10 = 2 m/s².

Answer: f_k = 30 N and a = 2 m/s²

Tip

Find the normal force first — friction depends on it. On a flat surface N = mg, but if something presses down on (or lifts) the object, N changes, and the friction changes right along with it.

Checkpoint

A 5 kg box slides across level ground where the coefficient of kinetic friction is 0.4 (g = 10 m/s²). What is the kinetic friction force?

Checkpoint

A 10 kg crate rests on level ground with a coefficient of static friction of 0.5 (g = 10 m/s²). What minimum horizontal force is needed to just start it sliding?

On the exam

Watch the difference between "is it moving yet?" and "how fast does it slow down?" Use static friction (an inequality, up to μ_s N) to test whether motion starts; use kinetic friction (a fixed μ_k N) once it is already sliding.

Answer the 2 checkpoints as you read.