Friction
The idea
Surfaces grip each other, and friction is the force that expresses that grip along the surface. It comes in two varieties: static friction holds objects still and adjusts itself up to a maximum of μₛN, while kinetic friction acts on sliding objects with the nearly constant value μₖN. Here N is the normal force and μ is the coefficient of friction — a unitless number that captures how grippy the pair of surfaces is. You already know friction as the force that opposes sliding; now you can compute it.
The mental model is that friction opposes RELATIVE sliding between surfaces, not motion itself. Static friction is what pushes a car forward: the tire pushes backward on the road, and friction from the road pushes the tire forward. Because static friction adjusts to whatever is needed (up to its limit), you cannot compute it from a formula unless the object is right at the verge of slipping.
The big misconception is writing friction = μN in every situation. That product is the maximum available static friction or the actual kinetic friction — but the actual static friction on a non-slipping object is only as large as it needs to be. A book resting on a level table has zero friction on it, no matter how large μ is, because nothing is trying to slide it.
Worked example
A 2.0 kg book is shoved across a level floor and released sliding at 6.0 m/s. The coefficient of kinetic friction between book and floor is 0.30. How far does the book slide before stopping?
- Find the normal force first: the floor is level and there is no vertical acceleration, so N = mg = 2.0 × 9.8 = 19.6 N.
- Compute the kinetic friction force: f = μₖN = 0.30 × 19.6 = 5.88 N, pointing opposite the slide since friction opposes relative motion.
- Get the deceleration from the second law: a = f/m = 5.88/2.0 = 2.94 m/s², directed against the velocity.
- Use the kinematic relation v² = v₀² − 2ad with final velocity zero: 0 = 6.0² − 2 × 2.94 × d, so d = 36/5.88 ≈ 6.1 m.
- Notice the mass canceled along the way: d = v₀²/(2μₖg) = 36/(2 × 0.30 × 9.8), so a heavier book sliding at the same speed stops in the same distance — more friction force, but also more inertia.
Answer. The book slides about 6.1 m before friction brings it to rest.
Check your understanding
- Why is the static coefficient usually larger than the kinetic one, and what does that mean for a box you are trying to push from rest?
- How would you explain to a friend that friction is what accelerates a car forward, even though friction supposedly opposes motion?
- What happens to the stopping distance if the book is shoved twice as fast, and why is the answer not simply twice as far?
- When is it wrong to compute friction as μ times the normal force, and what should you do instead in those cases?
Build the foundations first
Friction builds on these concepts. If any feel shaky, start there.