Kinetic Friction

What kinetic friction is

Once a body begins to slide on a surface, the friction force changes character. It is no longer self-adjusting — it becomes a fixed value:

$f_k = \mu_k N$

This is kinetic friction (also called sliding friction or dynamic friction). It acts on a body that is already moving relative to the surface.

Key properties

It is constant — unlike static friction which adjusts, kinetic friction has a fixed value $\mu_k N$ regardless of the applied force. Whether you push harder or softer, $f_k$ stays the same (as long as the body keeps sliding).

It is less than limiting friction — always:

$\mu_k < \mu_s$

This means it takes more force to start sliding than to keep sliding. Once you overcome static friction and get the body moving, less force is needed to maintain motion.

It opposes relative motion — kinetic friction always acts opposite to the direction of sliding. It acts on each surface in the direction that opposes its motion relative to the other surface.

It is independent of speed — to a good approximation, $f_k$ does not depend on how fast the surfaces slide past each other. (At very high speeds this breaks down, but for typical problems it holds.)

It is independent of contact area — same as static friction.

Kinetic friction and deceleration

When kinetic friction is the only horizontal force acting on a sliding body:

$F_{net} = -f_k = -\mu_k N = -\mu_k mg$

$a = -\mu_k g$

The body decelerates at $\mu_k g$ until it stops (or until the applied force changes the situation).

Example: A block slides on a floor with $\mu_k = 0.4$. Deceleration:

$a = -\mu_k g = -0.4 \times 10 = -4 \text{ m/s}^2$

The friction vs applied force graph

A clear picture of how friction changes with applied force:

• From $F = 0$ to $F = \mu_s N$: friction $= F$ (static, self-adjusting, linear increase)
• At $F = \mu_s N$: friction $= \mu_s N$ (limiting — peak of graph)
• For $F > \mu_s N$: friction drops to $\mu_k N$ and stays constant (kinetic)

The drop from $\mu_s N$ to $\mu_k N$ at the onset of motion is a real, observable effect.

Heat generation

Kinetic friction converts kinetic energy into heat. The rate of heat generation:

$P = f_k \cdot v = \mu_k N v$

where $v$ is the sliding speed. This is why brakes get hot, why your hands warm up when rubbed together, and why meteors glow as they enter the atmosphere.