Laws of Friction & Its Origin
Four compact rules, a table of numbers, and a look at surfaces up close.
Lesson at a glanceShow the key points
- Sliding: fₖ = μₖN, opposite to the velocity relative to the other surface.
- Not sliding: fₛ ≤ μₛN, with direction and size set by the no-slip condition.
- For a given normal force, friction does not depend on the apparent area of contact.
- Real contact happens at a few microscopic high points; bonds form and break there, deforming material and producing heat.
- Clean, oxide-free metal surfaces in vacuum can stick (cold welding) with μ far above 1.
Everything we know about dry friction fits on an index card. The reasons behind it take us down to the atoms.
The laws of friction
- If the surfaces slip, friction has magnitude , where is the normal force and the coefficient of kinetic friction.
- Kinetic friction on a body is opposite to its velocity relative to the body applying the friction.
- If the surfaces do not slip, friction satisfies ; its direction and size are whatever is needed to prevent slipping.
- For a given normal force, neither nor the limiting depends on the area of contact.
Typical values
Friction coefficients depend on smoothness, cleanliness, moisture and even the surrounding air, so tables give only rough guides. Approximate coefficients of static friction:
| Surfaces | μₛ | Surfaces | μₛ |
|---|---|---|---|
| Steel on steel | 0.58 | Copper on copper | 1.6 |
| Steel on brass | 0.35 | Teflon on Teflon | 0.04 |
| Glass on glass | 1.0 | Rubber tyre on dry concrete | 1.0 |
| Wood on wood | 0.35 | Rubber tyre on wet concrete | 0.7 |
| Wood on metal | 0.40 | Ice on ice | 0.10 |
Why friction exists
A polished steel plate looks flat to the eye, but at atomic scale its surface is a landscape of hills and valleys. Put two such surfaces together and they touch only at the tips of the highest bumps. The real area of contact is a tiny fraction of the apparent area.
At those contact points atoms come so close that molecular bonds form. To slide one surface over the other, these bonds must be broken; the material around them is deformed, and new bonds form further along. The deformation sends vibrations into both bodies, which die away as random thermal motion: the surfaces get warm. That is why a force is needed both to start sliding and to keep it going, and why rubbing your hands heats them.
This picture also explains the laws. Press the surfaces harder and more bumps touch, so the real contact area, and with it the friction, grows in proportion to the normal force. Spread the same load over a bigger apparent area and each bump is pressed less hard; the real contact area, and so the friction, stays about the same.
A 12 kg crate rests on a floor with μₛ = 0.50 and μₖ = 0.40. Find the friction and acceleration when it is pushed horizontally with (a) 50 N and (b) 70 N. (g = 9.8 m/s²)
- 1Sliding: fₖ = μₖN, opposite to the relative velocity.
- 2Not sliding: fₛ ≤ μₛN, set by the no-slip condition.
- 3Friction is independent of apparent contact area for a given N.
- 4Real contact happens at microscopic bumps; breaking and re-forming bonds there costs force and makes heat.
Check yourself
Keep exploring
Hand-picked videos, simulations and readings that explain this idea from a different angle.