# Coefficient of friction varies with sliding distance

## Statement

As two surfaces slide against each other, the coefficients of friction (i.e., the coefficient of kinetic friction as well as the limiting coefficient of static friction) change. This change is due to microscopic alterations in the contact surfaces. can be quantitatively captured by a graph whose horizontal axis is the sliding distance and the vertical axis is the coefficient of friction (typically, the coefficient of kinetic friction (?)).

Two phenomena are at work, one of which is responsible for a decrease in the coefficient of friction and the other is responsible for an increase in the coefficient of friction. The actual effect is thus ambiguous and depends on the relative magnitude of the two phenomena. The following overall kinds of patterns have been observed:

- For some pairs of surfaces, the coefficient of friction increases steadily from its initial value, toward an asymptotic stable value.
- For some pairs of surfaces, the coefficient of friction increases steadily with sliding distance up to a point, after which it decreases to an asymptotic value. The new asymptotic value may be smaller or larger than the initial value of friction coefficient.
- For some pairs of surfaces, the graph is jagged, with alternating increases and decreases.

The graph obtained for a given pair of surfaces is empirical and dependent on the specific surfaces. It cannot be described by a theoretical formula, but its overall qualitative properties can be predicted based on the nature of surfaces.

## References

### Lecture notes

- MIT OpenCourseWare Tribology course lecture notes, see Page 14 for graphs