# Friction: static and kinetic

Canonical: https://duckyhelper.com/learn/physics/friction/
Updated: 2026-10-01

Friction is a force that resists sliding between two surfaces. Static friction holds an object still, and it can grow up to a maximum of \(\mu_s F_N\). Kinetic friction acts once the object slides, and it equals \(\mu_k F_N\). \(F_N\) is the normal force and \(\mu\) is the coefficient of friction for the two surfaces. \(\mu_k\) is usually smaller than \(\mu_s\), so starting a slide is harder than keeping it going.

## Key ideas

$$
f_s \le \mu_s F_N \qquad f_k = \mu_k F_N
$$

- \(f_s\) is static friction, in newtons (N). It matches whatever push it needs to, up to its maximum \(\mu_s F_N\).
- \(f_k\) is kinetic (sliding) friction, in newtons (N). It is constant while the object slides.
- \(\mu_s\) and \(\mu_k\) are the coefficients of static and kinetic friction. They have no units and depend on the two surfaces.
- \(F_N\) is the normal force, in newtons (N). On flat ground with no other vertical forces, \(F_N = mg\).

Friction always points along the surface, against the sliding or against the way the object would slide. In the simple model used in high school and AP Physics 1, friction does not depend on the contact area or on the speed.

**Some coefficients of friction (OpenStax College Physics 2e, Table 5.1)**

| Surfaces | Static \(\mu_s\) | Kinetic \(\mu_k\) |
| --- | --- | --- |
| Rubber on dry concrete | 1.0 | 0.7 |
| Rubber on wet concrete | 0.7 | 0.5 |
| Wood on wood | 0.5 | 0.3 |
| Steel on steel (dry) | 0.6 | 0.3 |
| Shoes on ice | 0.1 | 0.05 |
| Steel on ice | 0.04 | 0.02 |

## Worked examples

**Example 1: kinetic friction**

Problem: A 20.0 kg box slides across a floor where \(\mu_k = 0.30\). What is the friction force?

1. Flat floor, so the normal force equals the weight.

   $$
   F_N = mg = (20.0\ \text{kg})(9.8\ \text{m/s}^2) = 196\ \text{N}
   $$
2. Kinetic friction.

   $$
   f_k = \mu_k F_N = (0.30)(196\ \text{N}) = 58.8\ \text{N}
   $$
3. \(\mu_k\) has 2 significant figures, so round to 2.

Answer: 59 N, opposite the sliding

**Example 2: does it move?**

Problem: A 30.0 kg crate sits on a floor with \(\mu_s = 0.50\). You push it sideways with 120 N. Does it move? What is the friction force?

1. Find the most static friction can give.

   $$
   f_{s,\max} = \mu_s mg = (0.50)(30.0\ \text{kg})(9.8\ \text{m/s}^2) = 147\ \text{N}
   $$
2. Your 120 N push is less than 147 N, so static friction holds the crate still.
3. Static friction only matches the push. It does not use its full maximum.

   $$
   f_s = 120\ \text{N}
   $$

Answer: It does not move, and friction is 120 N

**Example 3: once it slides**

Problem: You push the same 30.0 kg crate with 200. N. The kinetic coefficient is \(\mu_k = 0.40\). What is its acceleration?

1. 200. N is more than the 147 N static maximum, so the crate starts to slide.
2. Kinetic friction.

   $$
   f_k = (0.40)(30.0)(9.8) = 117.6\ \text{N}
   $$
3. Net force and acceleration.

   $$
   a = \frac{200.\ \text{N} - 117.6\ \text{N}}{30.0\ \text{kg}} = 2.75\ \text{m/s}^2
   $$

Answer: 2.7 m/s²

**Example 4: measuring \(\mu_s\) with a ramp**

Problem: A block on a board starts to slide when the board is tilted to 31°. What is \(\mu_s\)?

1. Right at the slipping point, the pull down the slope equals the maximum static friction.

   $$
   mg\sin\theta = \mu_s\, mg\cos\theta
   $$
2. Mass and g cancel.

   $$
   \mu_s = \tan\theta = \tan 31^\circ = 0.601
   $$

Answer: \(\mu_s = 0.60\)

## Common mistakes and how to fix them

- **Always using \(\mu_s F_N\) for static friction.** That is only the maximum. Fix: if the object stays still, static friction equals the force trying to move it.
- **Using \(F_N = mg\) on a ramp or with an angled pull.** Fix: find \(F_N\) from the forces perpendicular to the surface first.
- **Pointing friction the wrong way.** Fix: friction opposes the sliding, or the sliding that would happen without it.
- **Giving \(\mu\) units.** \(\mu\) is a ratio of two forces, so it has no units.

**Practice problems**

1. A 10. kg sled slides on snow with \(\mu_k = 0.10\). What is the kinetic friction force?
   A. 0.98 N
   B. 9.8 N
   C. 98 N
   D. 1.0 N

   Answer: 9.8 N. \(f_k = \mu_k mg = 0.10 \times 10. \times 9.8 = 9.8\) N.

2. A 50.0 kg box just starts to move when you push it with 196 N. What is \(\mu_s\)?

   Answer: 0.400. At the start of sliding, the push equals the maximum static friction: \(\mu_s = 196 \div (50.0 \times 9.8) = 196 \div 490 = 0.400\).

3. In the simple friction model, what happens to the friction on a brick if you turn it from its wide face onto its narrow side?
   A. It increases
   B. It decreases
   C. It stays the same

   Answer: It stays the same. Friction depends on the normal force and the surfaces, not on the contact area. The brick's weight, and so the normal force, has not changed.

4. Using the table on this page, which pair of surfaces has the higher static coefficient: rubber on dry concrete or shoes on ice?
   A. Rubber on dry concrete
   B. Shoes on ice

   Answer: Rubber on dry concrete. 1.0 for rubber on dry concrete vs 0.1 for shoes on ice. That is why tires grip roads and people slip on ice.

5. A 15 kg box slides at constant velocity when pushed with 45 N. What is \(\mu_k\)?

   Answer: 0.31. Constant velocity means net force zero, so friction equals the push: \(\mu_k = 45 \div (15 \times 9.8) = 45 \div 147 = 0.306\), which is 0.31.

## Frequently asked questions

### Why is static friction bigger than kinetic friction?

When surfaces sit still, their tiny bumps settle into each other and form small bonds. Breaking those takes more force than keeping the surfaces sliding, when the bumps have less time to lock together. That is why a heavy couch gets easier to push once it starts moving.

### Can the coefficient of friction be more than 1?

Yes. \(\mu\) greater than 1 just means friction can be larger than the normal force. Racing tires on dry pavement and some rubber on rough surfaces go above 1. Most everyday pairs are between 0.05 and 1.

### Is friction always bad?

No. Friction lets you walk, lets cars brake and turn, and keeps a nail in wood. Without static friction between tires and road, a car could not round a curve, see [circular motion](https://duckyhelper.com/learn/physics/circular-motion/). Friction also wastes energy as heat in engines, which is why oil is used.

## Sources

- [OpenStax College Physics 2e, 5.1 Friction](https://openstax.org/books/college-physics-2e/pages/5-1-friction), accessed 2026-10-01

## Related

- [How to draw free body diagrams](https://duckyhelper.com/learn/physics/free-body-diagrams/)
- [Newton's laws of motion](https://duckyhelper.com/learn/physics/newtons-laws-of-motion/)
- [Work and energy](https://duckyhelper.com/learn/physics/work-and-energy/)
- [Physics study guides](https://duckyhelper.com/learn/physics/)

## Try asking Ducky

- "Did the crate move in problem 2? Check whether I compared the push to the right friction value."
- "Check my free body diagram for a box on a ramp with friction. Did I miss a force?"
- "Why did my answer come out with units on mu? Show me where the units cancel."

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