Classical mechanics · Tribology
Friction Calculator
Drag the block to push or pull, watch static friction hold — then break free and slide. Normal load, friction, and acceleration update live on the free-body diagram.
Friction coefficients
Interactive free-body diagram
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Live state
Force balance
F = μ · N
Stays put
Static friction holds (67% of μs·N).
- Normal force
9.48 N
- Static friction
2.54 N
Max static μs·N: 3.79 N
- Driving along surface
2.54 N
- Margin before sliding
1.25 N
- Angle of repose: 21.80°
Static friction matches the driving force exactly while the box stays put.
Static and kinetic contact forces — what this sandbox solves.
Friction opposes relative motion (or the tendency to move) between surfaces in contact. Static friction holds objects at rest until the driving load exceeds μs·N; kinetic friction μk·N acts once sliding begins and is usually lower.
- Friction forceF = μ · N
- Normal (incline)N = mg · cos(θ)
- Down-slope componentW∥ = mg · sin(θ)
- Angle of reposeθmax = arctan(μs)
- Sliding accelerationa = (Fdrive − μk·N) / m
- Max static holdFstatic,max = μs · N
| Contact pair | μ (approx.) | Notes |
|---|---|---|
| Ice on ice | 0.03 | Among the slipperiest natural pairings |
| Steel on steel (dry) | 0.50–0.80 | Machinery, structural slip checks |
| Rubber on dry concrete | 0.90–1.00 | Tire grip design reference |
| Wood on wood | 0.25–0.50 | Furniture, timber structures |
| Teflon on Teflon | 0.04 | Low-friction bearings and coatings |
Amontons I
Friction is proportional to normal load: F ∝ N.
Amontons II
Friction does not depend on apparent contact area.
Coulomb
Kinetic friction is largely independent of sliding speed.
Automotive
Brakes, tire-road grip, clutch friction materials.
Civil
Slope stability, foundation slip, pavement skid resistance.
Manufacturing
Bearings, forming, conveyor belt traction.
Design
Fastener preload, slip fits, ergonomic grip surfaces.
- Leonardo da Vinci studied friction systematically — centuries before Amontons published the laws in 1699.
- Static friction is always ≥ kinetic friction for the same material pair.
- The coefficient μ is dimensionless — it is a ratio of forces, not a material property alone.
- Angle of repose on a ramp equals arctan(μs) when only gravity drives the block.
- True contact happens at microscopic asperities — tribology explains why μ is not simply “area divided.”
- Friction converts kinetic energy to heat — the reason brakes warm up after a stop.
Worked example: Will a 500 N block break free? (μs = 0.35, μk = 0.28, push = 200 N)
- Normal force N = 500 N (horizontal surface)
- Max static friction = μs × N = 0.35 × 500 = 175 N
- Push of 200 N > 175 N, so the block breaks free
- Kinetic friction = μk × N = 0.28 × 500 = 140 N
- Net force = 200 − 140 = 60 N
Block slides; net force ≈ 60 N (a = 60 N ÷ 51 kg ≈ 1.18 m/s²)
What is the coefficient of friction?
The coefficient of friction (μ) is the ratio of friction force to normal force. Static μ applies before motion; kinetic μ applies during sliding.
How do I choose static vs kinetic friction?
Use static friction when checking if an object will start to move. Use kinetic friction when the object is already sliding.
Why do friction values vary?
Surface finish, lubrication, temperature, and material pairing all affect μ. Use handbook values as a starting point and validate with testing for critical designs.