Friction Formula
The friction formula calculates static and kinetic friction forces between surfaces.
Essential for mechanics and engineering problems.
The Formula
The friction force equals the coefficient of friction multiplied by the normal force. There are two types: static friction (object at rest) and kinetic friction (object in motion).
Variables
| Symbol | Meaning |
|---|---|
| f | Friction force (measured in Newtons, N) |
| μ | Coefficient of friction (dimensionless — μₛ for static, μₖ for kinetic) |
| N | Normal force perpendicular to the surface (measured in Newtons, N) |
Static vs. Kinetic Friction
Static friction keeps an object from starting to move. It can vary from zero up to a maximum value.
Kinetic friction acts on an object that is already sliding. It has a constant value.
Static friction is always greater than or equal to kinetic friction (μₛ ≥ μₖ). This is why it takes more force to start pushing a heavy box than to keep it moving.
Common Coefficients of Friction
| Surface Pair | μₛ (static) | μₖ (kinetic) |
|---|---|---|
| Rubber on dry concrete | 1.0 | 0.8 |
| Steel on steel | 0.74 | 0.57 |
| Wood on wood | 0.5 | 0.3 |
| Ice on ice | 0.1 | 0.03 |
| Teflon on teflon | 0.04 | 0.04 |
Example 1
A 50 kg wooden crate sits on a wooden floor (μₛ = 0.5). What force is needed to start it sliding?
Calculate the normal force: N = mg = 50 × 9.8 = 490 N
Apply the formula: fₛ = μₛN = 0.5 × 490
fₛ = 245 N
Example 2
Once the crate is sliding (μₖ = 0.3), how much force is needed to keep it moving at constant speed?
Normal force is still: N = 490 N
Apply kinetic friction: fₖ = μₖN = 0.3 × 490
fₖ = 147 N (less than the 245 N needed to start it moving)
When to Use It
Use the friction formula whenever objects are in contact with surfaces and forces are involved.
- Calculating the force needed to push or pull objects on surfaces
- Determining braking distances for vehicles on different road surfaces
- Analyzing inclined plane problems where objects may slide
- Engineering applications such as brake design, tire grip, and conveyor belts
- Determining if an object on a slope will remain stationary or begin to slide