Kinetic Friction Formula

Kinetic friction is the friction force that opposes sliding motion between two surfaces in contact.

The Formula

fk=μkNf_k = \mu_k N

When to use: Once something is moving, friction resists its motion — less than static friction, but still present.

Quick Example

A book sliding across a table slows down due to kinetic friction.

Notation

fkf_k is the kinetic friction force in newtons (N), μk\mu_k is the dimensionless coefficient of kinetic friction (typically 0.1–0.8), and NN is the normal force in newtons.

What This Formula Means

The friction force that opposes sliding motion between two surfaces in contact; in the simple dry-friction model its magnitude is fk=μkNf_k = \mu_k N, directed opposite to the motion.

Once something is moving, friction resists its motion — less than static friction, but still present.

Formal View

For a body sliding on a surface, kinetic friction is fk=μkNf_k = \mu_k N, directed opposite to the velocity of the sliding body relative to the surface. This force is approximately constant and independent of contact area and sliding speed.

Worked Examples

Example 1

medium
A 6 kg6\,\text{kg} block is pushed with 30 N30\,\text{N} horizontally on level ground with μk=0.2\mu_k = 0.2 and g=10 m/s2g = 10\,\text{m/s}^2. Find its acceleration.

Answer

a=3 m/s2a = 3\ \text{m/s}^2

First step

1
fk=μkmg=0.2⋅6⋅10=12 Nf_k = \mu_k m g = 0.2 \cdot 6 \cdot 10 = 12\,\text{N}.

See the full worked solution + why-it-works coaching

SetupKey insightWhy it worksCommon pitfallConnection

Unlock answer keys One Family plan — every worked solution, all subjects

Example 2

medium
A 4 kg4\,\text{kg} crate is pushed by a horizontal 30 N30\,\text{N} force and accelerates at 3 m/s23\,\text{m/s}^2 on level ground (g=10 m/s2g = 10\,\text{m/s}^2). Find μk\mu_k.

Example 3

hard
A 4 kg4\,\text{kg} block on level ground is pushed by a 30 N30\,\text{N} force directed 30∘30^\circ below horizontal. With μk=0.3\mu_k = 0.3 and g=10 m/s2g = 10\,\text{m/s}^2, find the acceleration.

Common Mistakes

  • Using the coefficient of static friction μs\mu_s instead of kinetic friction μk\mu_k once the object is already moving — μk\mu_k is typically smaller than μs\mu_s. - Fix this by naming the system, checking "Have I isolated one system and listed the external forces or torques acting on it before applying a law?", and attaching units or direction to the final statement.
  • Assuming kinetic friction depends on the speed of the object — for most surfaces at moderate speeds, fk=μkNf_k = \mu_k N is independent of velocity. - Fix this by naming the system, checking "Have I isolated one system and listed the external forces or torques acting on it before applying a law?", and attaching units or direction to the final statement.
  • Forgetting that kinetic friction converts mechanical energy to thermal energy — the work done by friction is W=fkdW = f_k d, and this energy appears as heat. - Fix this by naming the system, checking "Have I isolated one system and listed the external forces or torques acting on it before applying a law?", and attaching units or direction to the final statement.
  • Using kinetic friction from a keyword alone - Signal words like force, push, pull only point to a possible model; the system must match too.

Why This Formula Matters

Kinetic Friction is central because forces explain changes in motion and balance. Students who can isolate a system and draw the interactions can avoid treating every force word as the same kind of cause.

Frequently Asked Questions

What is the Kinetic Friction formula?

The friction force that opposes sliding motion between two surfaces in contact; in the simple dry-friction model its magnitude is fk=μkNf_k = \mu_k N, directed opposite to the motion.

How do you use the Kinetic Friction formula?

Once something is moving, friction resists its motion — less than static friction, but still present.

What do the symbols mean in the Kinetic Friction formula?

fkf_k is the kinetic friction force in newtons (N), μk\mu_k is the dimensionless coefficient of kinetic friction (typically 0.1–0.8), and NN is the normal force in newtons.

Why is the Kinetic Friction formula important in Physics?

Kinetic Friction is central because forces explain changes in motion and balance. Students who can isolate a system and draw the interactions can avoid treating every force word as the same kind of cause.

What do students get wrong about Kinetic Friction?

Students often know a formula related to kinetic friction but skip the recognition step: Have I isolated one system and listed the external forces or torques acting on it before applying a law? That leads to a correct-looking substitution attached to the wrong physical model.

What should I learn before the Kinetic Friction formula?

Before studying the Kinetic Friction formula, you should understand: friction, normal force.

← Back to Kinetic Friction See All Examples Practice Problems