Why Kinetic Friction is Less than Limiting Friction
In classical mechanics, we distinguish between different types of friction. When an object is at rest on a surface, the force required to initiate motion is governed by limiting friction (or maximum static friction). Once the object is in motion, the force required to maintain that motion is kinetic friction.
The Microscopic Perspective
To understand why kinetic friction ($f_k$) is usually less than limiting friction ($f_{s,max}$), we must look at the surfaces at a microscopic level. No surface is perfectly smooth; they all have microscopic peaks and valleys called asperities.
The Static State (Limiting Friction): When an object is at rest, these asperities from the two surfaces interlock deeply. Think of it like two pieces of velcro or puzzle pieces settling into one another. Because they are stationary for some time, they form "cold welds" or strong molecular bonds at the points of contact. To move the object, you must apply enough force to break these bonds and "lift" the top asperities out of the depressions of the bottom surface.
The Kinetic State (Kinetic Friction): Once the object is moving, it is essentially "skimming" over the peaks of the surface. Because the object is moving rapidly, the surfaces do not have enough time to settle into each other, and new, strong bonds cannot form as effectively as they do when the object is at rest. Consequently, the resistance to motion is reduced.
Summary of Intuition
- Limiting Friction: Overcoming the maximum interlocking of asperities and established chemical/molecular bonds.
- Kinetic Friction: Sliding over surface irregularities with insufficient time for significant bonds to re-establish.
This behavior is captured by the relationship: $f_k < f_{s,max}$ or $\mu_k < \mu_s$, where $\mu_k$ and $\mu_s$ are the coefficients of kinetic and static friction, respectively.