Friction

• The three types of friction and when each occurs
• What factors determine how strong friction is
• How to calculate friction force using the formula f = μN
• Why friction is both useful and sometimes a nuisance

What is friction? Friction is a contact force that opposes the relative motion (or tendency of motion) between two surfaces in contact. It acts along the surface, in the direction opposite to motion or intended motion. Friction arises because no surface is perfectly smooth — at a microscopic level, surfaces have tiny peaks and valleys (called asperities) that interlock.

Three types of friction

Static friction acts when an object is at rest but a force is trying to move it. It adjusts itself to match the applied force, up to a maximum value. Only when the applied force exceeds this maximum does the object begin to move. Static friction is always greater than or equal to kinetic friction for the same surfaces.

Kinetic friction (also called sliding friction) acts when two surfaces are sliding past each other. It has a roughly constant value regardless of speed or the area of contact — only the normal force and the type of surfaces matter.

Rolling friction occurs when a round object (wheel, ball) rolls over a surface. It is significantly smaller than both static and kinetic friction, which is why wheels were one of humanity's most important inventions. Rolling friction arises mainly from deformation at the contact patch.

Order of magnitude: f_static >= f_kinetic > f_rolling

The friction formula The magnitude of friction force is given by:

f = μN

where:

• f = friction force (in Newtons)
• μ = coefficient of friction (dimensionless, depends on the two surfaces in contact)
• N = normal force (in Newtons) — the perpendicular contact force the surface exerts on the object

The coefficient μ_s applies to static friction and μ_k applies to kinetic friction; μ_s > μ_k for the same pair of surfaces.

Factors affecting friction

1. Nature of the surfaces — rougher surfaces (sandpaper on wood) give higher μ; smoother surfaces (ice on steel) give lower μ.
2. Normal force — pressing harder increases friction proportionally.
3. What does NOT affect friction: speed of motion, area of contact (for rigid bodies under Amontons' laws).

Real-world examples

• Car brakes: brake pads press against the disc, static/kinetic friction slows the wheel.
• Tyres: the rubber-road interface needs high μ for grip; wet roads reduce μ causing skidding.
• Shoes: soles are designed for high friction with the ground. Smooth-soled shoes on a polished floor are dangerous.
• Lubricants (oil, grease) reduce μ between machine parts to cut energy loss and wear.

Problem: A 10 kg wooden box rests on a concrete floor. The coefficient of static friction μ_s = 0.5 and coefficient of kinetic friction μ_k = 0.4. Find: (a) The maximum static friction force before the box moves. (b) The kinetic friction force once it is sliding.

Solution:

Step 1 — Find the normal force. On a flat horizontal surface, the normal force equals the weight: N = mg = 10 kg × 10 m/s² = 100 N

Step 2 — Maximum static friction: f_s(max) = μ_s × N = 0.5 × 100 = 50 N

This means you need to push with more than 50 N to start moving the box.

Step 3 — Kinetic friction (once sliding): f_k = μ_k × N = 0.4 × 100 = 40 N

So once the box is moving, the friction force drops to 40 N — less than when it was stationary. This is why it takes more force to get something moving than to keep it moving.

• Confusing normal force with weight on inclines. On a slope, the normal force N = mg cos θ, not mg. If you use mg instead of mg cos θ, your friction calculation will be too high.
• Assuming friction always equals μN. Static friction is at most μ_s N — it can be less if the applied force is less. Only at the point of slipping does it equal μ_s N.
• Thinking larger contact area increases friction. For rigid bodies, friction force is independent of the area of contact; only the normal force and surface types matter.
• Forgetting direction. Friction always opposes relative motion or tendency of motion, so always draw it pointing opposite to the direction the object moves or would move.

1. A 5 kg block is on a surface with μ_k = 0.3. What is the kinetic friction force? (Use g = 10 m/s²)
2. Why is rolling friction less than sliding friction for the same object and surface?
3. A car is parked on a slope. Which type of friction prevents it from sliding down?