AP Physics 1  ·  Unit 2: Forces & Translational Dynamics  ·  Lesson 2.7

Deep Dive: Kinetic & Static Friction

🔬 Deep Dive
This is your textbook for this topic. Take your time. Read it more than once.
2.7.A.1Concept

What Friction Is

Friction is a contact force that resists the relative sliding of two surfaces. It acts parallel to the surfaceof contact and points opposite to the direction the object slides — or, if nothing is sliding yet, opposite to the direction it would slide. Microscopically it comes from the roughness and molecular bonding between two surfaces pressed together.

blockF_appfF_NF_gFriction acts along the surface,opposite to the sliding (or its tendency).

Two ingredients set the size of friction: how hard the surfaces are pressed together (the normal force F_N) and how rough they are (the coefficient of friction μ, a dimensionless number). More normal force or a rougher pairing means more friction.

2.7.A.2ConceptMath

Kinetic Friction

Kinetic friction acts whenever two surfaces are actually sliding against each other. It has a fixed magnitude given by:

f_k = μ_k · F_N

Here μ_k is the coefficient of kinetic friction and F_N is the normal force. Kinetic friction always opposes the direction of sliding, and — importantly — its size doesn't depend on how fast the object moves. Whether the block slides at 1 m/s or 10 m/s, f_k is the same as long as F_N doesn't change.

ExampleWorked Example — Sliding Crate

A 8 kg crate slides across a level floor with μ_k = 0.25. Find the kinetic friction force acting on it. Use g = 10 m/s².

2.7.A.2.iConceptMath

Friction on an Inclined Plane

When a surface is tilted, gravity still pulls straight down — but it now has to be split into two components relative to the incline. This is where the rotated coordinate system from Lesson 2.2 pays off.

Parallel to slope
F_∥ = mg sin θ
Pulls the block down the slope. This is what friction has to resist.
Perpendicular to slope
F_⊥ = mg cos θ = F_N
Pushes the block into the surface. Sets the normal force — and therefore friction.
🔑As the angle increases, sin θ grows (more force pulling down the slope) while cos θ shrinks (less normal force, less friction available to resist). The block slides when mg sin θ exceeds μₛ × mg cos θ — which simplifies to tan θ > μₛ. That's the critical angle condition.

Adjust the incline angle and surface properties. Watch how the parallel component of gravity and the friction force compete — and see exactly when the block breaks free.

Angle θ20°
Mass (kg)5 kg
μₛ0.50
μₖ0.30
20°F_Nmg sinθf_sCritical angle: 26.6°(where tan θ = μₛ)
F_parallel
17.1 N
mg sin θ — down the slope
F_N
47.0 N
mg cos θ — into surface
Max f_s
23.5 N
μₛ × F_N = 0.5 × 47
🔒 Block stays put — mg sinθ (17.1 N) ≤ μₛF_N (23.5 N)
f_s = 17.1N (matches parallel gravity)  |  a = 0

Critical angle is 26.6° for these surfaces. Below it the block holds; above it the block slides. Try setting θ exactly there — static friction is at its maximum and the block is right on the verge.

ExampleWorked Example — Block on a 30° Incline

A 6 kg block sits on a 30° incline with μₛ = 0.45 and μₖ = 0.28. Does it slide? If so find its acceleration. Use g = 10 m/s².

2.7.A.3Concept⚠ Watch Out

Static Friction

Static friction acts when the surfaces are not sliding. Its defining feature: it's a variable force. It automatically adjusts to exactly cancel whatever force is trying to start the motion — up to a maximum value. That's why the equation uses ≤:

f_s ≤ μ_s · F_N

If you push a heavy box gently, it doesn't move: static friction rises to match your push exactly, so the net force stays zero. Push harder and static friction grows with you. Only when your push exceeds the maximum, μ_s·F_N, does the box finally break loose.

⚠️Don't just plug into μ_s·F_N. That formula gives the maximum static friction, not its actual value. If a box isn't moving and you push with 8 N, static friction is 8 N — even if its maximum is 30 N. Only use the "=" form when you're finding the threshold to start sliding.
2.7.A.4ConceptMath

Breaking Free: Static → Kinetic

For most surface pairings, the maximum static friction is greaterthan the kinetic friction (μ_s > μ_k). That's why it takes a bigger shove to start a heavy object moving than to keep it moving. The moment it breaks free, friction drops and — if you keep pushing at the same force — the object suddenly accelerates.

A 5 kg block sits on a floor (μ_s = 0.5, μ_k = 0.3, F_N = 50 N). Push harder and harder. Static friction matches your push — until you exceed its maximum of 25 N, and the block breaks free into kinetic friction.

Your push15 N
🔒 STATIONARY — static friction
Static friction = 15 N (matches your push)
Max before sliding = μ_s·F_N = 25 N |  Net = 0, a = 0
Notice friction drops from 25 N (max static) to just 15 N (kinetic) the instant it breaks free.
ExampleGuided Example — Will It Move, and How Fast?

A 5 kg block sits on a floor with μ_s = 0.5 and μ_k = 0.3 (g = 10 m/s²). You push horizontally with 30 N. Does it move? If so, find its acceleration.

Step 1Find the normal force
Level floor, horizontal push: F_N = mg = (5)(10) = 50 N.
2.7.A.5Concept⚠ Watch Out

Why Contact Area Doesn't Matter

A frequent surprise: in the AP Physics 1 model, the friction force does not depend on the contact area. Look at the equations — f = μ·F_N contains only the coefficient and the normal force. Area appears nowhere. A brick sliding on its wide face and the same brick sliding on its narrow end experience the same friction (same weight, same μ).

💡The intuition: a larger contact area spreads the same weight over more surface, so the force per unit area drops. More area but less pressure — the two effects cancel, leaving the total friction unchanged.
Depends on

Normal force (F_N) and the coefficient of friction (μ) — the roughness of the two surfaces.

Does NOT depend on

Contact area, or the speed of sliding (for kinetic friction).

🔑Remember the friction toolkit: (1) find F_N from the vertical forces, (2) decide static or kinetic by comparing the push to μ_s·F_N, (3) use f_k = μ_k·F_N once sliding, and (4) feed friction into ΣF = ma. Friction almost never acts alone — it's one arrow on a bigger free-body diagram.
← Back to Lesson 2.7Next: Lesson 2.8 →Spring Forces — Hooke's Law and the restoring force.
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