Friction (static and kinetic) Knowledge-Based Study

Study notes

1. What is Friction?

   Friction is a contact force that resists the relative sliding motion—or the tendency toward such motion—between two surfaces in contact. At the microscopic scale, even surfaces that appear smooth possess irregularities called asperities. When two surfaces are pressed together, these microscopic peaks interlock and form temporary intermolecular bonds (cold welds).

   Key characteristics of friction include:

   • Direction: Always parallel to the contact surface and directed opposite to the relative motion or impending motion.
   • Dependence on Normal Force: The frictional force depends directly on the magnitude of the normal force $N$, which represents how firmly the surfaces are pressed together.
   • Independence from Apparent Contact Area: To a good approximation, friction does not depend on the macroscopic surface area in contact.

   Static Friction ($f_s$)

   Static friction acts between surfaces that are not moving relative to each other. It is a self-adjusting force: it matches an applied tangential force up to a specific maximum threshold.

   The magnitude of static friction satisfies the inequality:

   $$f_s \le f_{s,\text{max}} = \mu_s N$$

   where:

   • $\mu_s$ is the coefficient of static friction (a dimensionless constant dependent on the two materials).
   • $N$ is the magnitude of the normal force.

   If an applied force is less than $\mu_s N$, the object remains at rest and $f_s$ exactly balances the applied force ($\Sigma F = 0$). If the applied force exceeds $\mu_s N$, static friction can no longer maintain equilibrium, and the surfaces begin to slide.

   Kinetic Friction ($f_k$)

   Once relative motion begins between two surfaces, static friction ceases, and kinetic friction takes over. Unlike static friction, kinetic friction is treated as constant in magnitude for typical speeds.

   Its magnitude is governed by:

   $$f_k = \mu_k N$$

   where $\mu_k$ is the coefficient of kinetic friction.

   Comparing Coefficients

   For nearly all material pairs:

   $$\mu_k < \mu_s$$

   Because the microscopic contact points have less time to interlock and bond while surfaces are in motion, it generally requires more force to start an object sliding than to keep it sliding at a constant speed.

   Systematic Problem-Solving Steps

   When solving dynamics problems involving friction, follow this systematic procedure:

   1. Draw a Free-Body Diagram (FBD): Identify all external forces acting on the body, resolving them into components perpendicular and parallel to the contact surface.
   2. Find the Normal Force ($N$): Apply equilibrium perpendicular to the surface ($\Sigma F_\perp = 0$) to calculate $N$. Note that $N$ is not always equal to $mg$ (e.g., on inclined planes or when angled external forces are present).
   3. Calculate $f_{s,\text{max}}$: Evaluate $f_{s,\text{max}} = \mu_s N$.
   4. Determine Motion State: Compare the net parallel applied force $F_{\text{net},\parallel}$ against $f_{s,\text{max}}$:
      • If $F_{\text{net},\parallel} \le f_{s,\text{max}}$, the object remains stationary, $f_s = F_{\text{net},\parallel}$, and $a = 0$.
      • If $F_{\text{net},\parallel} > f_{s,\text{max}}$, the object accelerates, friction switches to $f_k = \mu_k N$, and acceleration is found via $\Sigma F_\parallel = m a$.