Friction: Static & Kinetic

Friction is the force that resists the relative motion — or tendency of motion — between two surfaces in contact. Without friction, you could not walk, cars could not brake, and a book placed on a tilted desk would slide straight off. Friction arises from microscopic interactions between surface irregularities: even surfaces that look smooth are covered in tiny bumps and hollows that interlock and resist sliding. It acts parallel to the surfaces in contact and always opposes the direction of motion or attempted motion, making it a reactive force rather than an applied one. Physicists distinguish two main types of friction: static friction and kinetic (sliding) friction. Static friction acts when two surfaces are stationary relative to each other, preventing motion from starting. Kinetic friction acts once surfaces are already sliding. A key experimental finding is that kinetic friction is typically smaller than the maximum static friction — this explains why it is harder to get a heavy box moving than to keep it moving once it has started. Both types depend on the normal force pressing the surfaces together and the nature of the materials involved. Friction is not always a nuisance. Engineers deliberately increase friction in brake pads, tyres, and shoe soles. Understanding and controlling friction is central to mechanical engineering, sports science, and even surgery. The study of friction falls within a broader field called tribology, and its principles are captured elegantly by two simple proportionality laws that are accurate enough for the vast majority of everyday situations.

Key takeaways
  • The Normal Force
  • Static Friction and Its Limit
  • Kinetic Friction
  • The Coefficient of Friction
  • Direction of Friction

The Normal Force

Friction depends on how hard two surfaces are pushed together, quantified by the normal force N — the contact force perpendicular to the surfaces. If you stack books on a box, N increases, and so does the maximum friction available. Think of N as controlling how tightly the microscopic bumps of the two surfaces are pressed into each other.

Static Friction and Its Limit

Static friction fs adjusts itself to exactly cancel any applied force — up to a maximum value fs,max = μs N, where μs is the coefficient of static friction. Below this limit, the surfaces stay stationary. Push harder than fs,max and the object begins to move. This is why gradually increasing the force on a heavy crate eventually causes it to suddenly lurch into motion.

Kinetic Friction

Once sliding begins, kinetic friction fk takes over. It has a fixed magnitude fk = μk N, regardless of speed (for everyday speeds). Because μk < μs for the same pair of surfaces, kinetic friction is smaller than the static maximum. This is why ABS (anti-lock braking systems) in cars prevent wheels from skidding: rolling contact (static friction) gives more braking force than sliding contact (kinetic friction).

The Coefficient of Friction

The coefficients μs and μk are dimensionless numbers that characterise a pair of surfaces — not a single material alone. Rubber on dry concrete: μs ≈ 0.8. Steel on ice: μs ≈ 0.03. Crucially, for simple models, friction does not depend on the area of contact or the speed of sliding — only on N and the material pair. This is Amontons' law, verified experimentally and sufficient for most A-level problems.

Direction of Friction

Friction always acts along the surface and opposes relative motion or the tendency of motion. If a box is being pushed to the right, static or kinetic friction points to the left. On a slope, if a block tends to slide down, static friction points up the slope. Identifying this direction correctly before drawing a free-body diagram is essential for solving problems accurately.

The Key Equation

fk=μkNandfs≤μsNf_k = \mu_k N \quad \text{and} \quad f_s \leq \mu_s N
  • f_k — Kinetic friction force (Newton (N)): The friction force acting between two surfaces that are sliding relative to each other; constant for a given N.
  • f_s — Static friction force (Newton (N)): The friction force preventing two stationary surfaces from sliding; can range from zero up to its maximum value.
  • \mu_k — Coefficient of kinetic friction (Dimensionless): A material-pair constant (typically 0.01–0.8) characterising resistance to sliding; always less than μs for the same surfaces.
  • \mu_s — Coefficient of static friction (Dimensionless): A material-pair constant characterising resistance to the onset of motion; always greater than or equal to μk.
  • N — Normal force (Newton (N)): The contact force perpendicular to the surfaces; equals mg cos θ on a slope of angle θ, and mg on a horizontal surface.

Worked Example

Problem. A 12 kg wooden crate rests on a horizontal concrete floor. The coefficient of static friction is μs = 0.50 and the coefficient of kinetic friction is μk = 0.35. (a) What is the minimum horizontal force needed to start the crate moving? (b) Once moving, what force is needed to keep it sliding at constant velocity? (Take g = 9.8 m s⁻².)

fs,max⁡=58.8 N;fk=41.2 Nf_{s,\max} = 58.8\text{ N};\quad f_k = 41.2\text{ N}

Answer. Minimum force to start motion: 58.8 N; force to maintain constant sliding: 41.2 N.

Figure
Diagram
12 kg BoxN = 117.6 NW = mgF appliedf (friction)Static: f ≤ μsN = 58.8 NKinetic: f = μkN = 41.2 NSurface (concrete)
Origins · 1 minGuillaume Amontons and how this was discovered
GA
Guillaume Amontons
1663–1705 · French

Amontons rediscovered and systematically established the two fundamental laws of friction in 1699: that friction force is proportional to the normal load, and that it is independent of the apparent area of contact. These are the same laws encoded in the equations f = μN used today, later extended by Charles-Augustin de Coulomb who added the distinction between static and kinetic friction and confirmed independence from sliding speed. Amontons became almost completely deaf as a teenager but went on to make major contributions to thermometry and pneumatics as well as friction — his barometric work even led him close to the concept of absolute zero temperature, over a century before Kelvin.

  • Newton's First Law & Inertia — Static friction is what keeps objects at rest when forces are applied; understanding the first law clarifies why friction must be overcome before motion can begin.
  • Newton's Second Law — Once friction is included as a force in F_net = ma, it directly affects acceleration; solving friction problems always requires applying the second law.
  • Normal Force & Contact Forces — Friction is directly proportional to the normal force; understanding what determines N is essential for calculating friction on slopes and in more complex setups.
  • Forces on Inclined Planes — Inclined plane problems combine friction with resolved components of gravity, providing the most common application of friction equations at this level.