Friction

There are two kinds of friction depending on whether or not the involved surfaces are actually moving against each other.

  • Static friction happens when one solid surface attempts to move (but does not actually move) against another.
  • Kinetic friction happens when two solid surfaces are actually moving against each other.

The force of friction \(F_f\) does not ‘automatically’ happen when two solid surfaces come in contact with one another. They must be pressed against each other to some extent, which means there must be a non-zero normal force \(F_N\) between the surfaces. The equation for calculating friction is the same for both kinds

\[F_f=\mu F_N\]

In this equation, \(\mu\) is called the coefficient of friction, and is the ratio between the force of friction and the normal force. Therefore, \(\mu\) has no units (it is a dimensionless quantity).

Coefficient of friction

  • It is determined empirically (through experimentation), not theoretically.
  • It depends on the exact nature and condition of the two surfaces involved. If we change the nature of one surface (e.g., from wood to glass) or the conditions of the surfaces (e.g., by wetting one of them), the coefficient changes.
  • It does not depend on the normal force. The force of friction \(F_f\) increases when \(F_N\) does, but the coefficient remains the same.
  • There are two different coefficients for each pair of surfaces: the coefficient \(\mu_s\) of static friction and coefficient \(\mu_k\) of kinetic friction.
  • The \(\mu_s\) is typically (almost always) larger than \(\mu_k\) for the same two surfaces under the same conditions.
  • In most everyday applications, \(0\lt \mu_k\lt \mu_s\lt 1\). There are uncommon situations, however, where \(\mu_s\ge 1\).

Interpretation of the force of friction

  • The force of static friction \(F_{max}\) calculated in the equation above is the maximum force of friction the surfaces can afford before beginning to slide against each other. The equation of static friction is written as \[F_{max}=\mu_s F_N\]
  • \(F_{max}\) is not the actual force of friction acting on a surface, but rather the ‘ceiling’ of the force of static friction that can possibly act on the surface. The actual force \(F_s\) of static friction is less than or equal to \(F_{max}\). \[F_s\le F_{max}\implies F_s\le \mu_s F_N\]
  • In physics problems, we typically realize \(F_{max}\) is involved when we have expression like ‘the maximum’ or ‘the minimum’. For instance, consider “the minimum applied force that is needed for the object to start moving” or “the maximum tension that will leave the system at rest”.
  • The force of kinetic friction \(F_k\) is the actual force of friction that acts on the surface while it is moving. The equation of kinetic friction is written as \[F_k=\mu_k F_N\]