The friction formula
Friction force equals the coefficient of friction times the normal force: f = μN. The normal force is the push of the surface on the object, perpendicular to the surface.
On level ground with no other vertical forces, N = mg. On an incline at angle θ, only part of the weight presses into the surface, so N = mg cos θ. The calculator uses standard gravity g = 9.80665 m/s².
| Situation | Normal force N |
|---|---|
| Horizontal surface | m × g |
| Incline at angle θ | m × g × cos θ |
| Known force | enter N directly |
Static versus kinetic friction
Kinetic friction μkN acts while surfaces slide over each other. Static friction can take any value up to μsN; that maximum is what you must overcome to start motion. μs is usually larger than μk for the same surfaces.
On a slope, an object at rest starts to slide when the gravity component along the slope, mg sin θ, exceeds μsN, which happens when tan θ > μs.
Worked example
A 10 kg crate on level ground with μk = 0.3: N = 10 × 9.80665 = 98.07 N and f = 0.3 × 98.07 = 29.42 N.
On a 30° slope, N = 98.07 × cos 30° = 84.93 N and kinetic friction is 25.48 N. Gravity along the slope is 49.03 N, so the sliding crate accelerates at (49.03 − 25.48) ÷ 10 = 2.36 m/s².