Friction is the force that either holds an object in place or slows it down when sliding on a surface. Opposes motion (or the tendency to move). Two kinds:
Static friction
Before motion. Object on a surface, you push but it doesn't move — static friction resists.
\[ f_s \leq \mu_s N \]
where:
\mu_s= coefficient of static friction (dimensionless,0.05-2)N= normal force
Note: f_s takes whatever value up to \mu_s N. Push lightly, f_s small. Push harder, f_s grows — until it hits its ceiling, then the object moves.
Kinetic friction
During motion. Object slides, kinetic friction opposes the motion.
\[ f_k = \mu_k N \]
Nearly constant (independent of speed, at least at moderate speeds). Typically \mu_k < \mu_s.
Why \mu_s > \mu_k?
Before motion, microscopic bumps on both surfaces interlock — very firm grip. Once moving, bumps have no time to lock — a weaker bond.
Everyday example: to start pushing a heavy fridge takes a lot of force. Once it's moving, keeping it going is easier.
Typical coefficients
| Surfaces | \mu_s |
\mu_k |
|---|---|---|
| Steel on steel | 0.6 |
0.5 |
| Steel on ice | 0.03 |
0.02 |
| Rubber on dry asphalt | 1.0 |
0.7 |
| Rubber on wet asphalt | 0.7 |
0.5 |
| Wood on wood | 0.5 |
0.3 |
| Shoe on grass | 0.9 |
0.7 |
"Frictionless": very smooth ice, Teflon — but nothing is truly frictionless.
Independence from contact area
Counterintuitive: \mu does not depend on contact area — only on the two materials.
Why? Increasing area lowers pressure at each point — total force stays the same.
Example — box on a horizontal surface
Box of 20 kg on horizontal (\mu_s = 0.4, \mu_k = 0.3). How much force to get it moving? If you apply 90 N, what acceleration?
Normal force: N = mg = 196\ N
Maximum static friction: \mu_s N = 78.4\ N
So any push below 78.4 N leaves the box at rest.
With 90 N:
- Box starts moving
- Kinetic friction:
f_k = 58.8\ N - Net force:
90 - 58.8 = 31.2\ N - Acceleration:
a = 1.56\ m/s^2
Example — inclined plane with friction
Box on a slope at angle \theta. When does it start to slide?
- Normal:
N = mg\cos\theta - Weight along slope:
mg\sin\theta - Maximum static:
\mu_s N = \mu_s mg\cos\theta
Slip condition: mg\sin\theta > \mu_s mg\cos\theta \Rightarrow \tan\theta > \mu_s
\[ \theta_\text{slip} = \arctan\mu_s \]
Beautiful: by tilting a surface up to the slip angle, you can measure \mu_s — a simple high-school lab experiment.
Air drag
A form of friction with air:
- Low speed:
F_\text{drag} \propto v(linear) - High speed:
F_\text{drag} \propto v^2(skydiving, projectiles)
Terminal velocity when drag = weight. For a skydiver, ~55 m/s.
A few notes and common mistakes
1. Static friction can be zero.
No applied force → f_s = 0. \mu_s N is a ceiling, not the actual value.
2. Kinetic friction is nearly independent of speed. Up to moderate speeds. Very high speeds show some increase.
3. Smoother surfaces don't always mean less \mu.
Two very smooth surfaces can adhere (molecular bonding). Polished wood can have higher friction than rough wood.
What you should be able to do
- Distinguish static vs kinetic friction
- Compute maximum static:
\mu_s N - Compute kinetic:
f_k = \mu_k N - Apply on inclined plane — slip angle
- Recognize independence from contact area
Preview of §5.7
Applications of Newton's laws in real systems: pulleys, inclined planes with friction, elevators, coupled objects. §5.7.
📚 See also: Halliday Vol 1, Ch 5, §5.6.
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