Notes on Friction Forces in Physics 225

Chapter 6: Force and Motion II

Learning Objectives

  • Understand the concepts of friction force, drag force, and forces in uniform circular motion.

Friction Forces

  • Two Types of Friction:

    • Static Friction ($oldsymbol{f_s}$): Prevents sliding when an external force is applied but does not exceed the maximum limit.

    • Kinetic Friction ($oldsymbol{f_k}$): Opposes the motion when sliding occurs.

Definition of Friction

  • Friction ($F_{friction}$): A resistance force that prevents or opposes sliding motion.

    • Acts parallel to the surface.

    • Opposes relative sliding motion along the surface.

    • Originates from molecular roughness of surfaces.

Real-life examples of friction:

  • Wanted Friction:

    • E.g. Walking - friction gives traction and aids motion of foot.

  • Unwanted Friction:

    • E.g. Friction can cause overheating in machines, making them inefficient.

Static vs. Kinetic Friction

  • Static Friction: No sliding occurs.

    • Magnitude satisfies:
      |fs| ext{ }(applied) ext{ } ≤ ext{ } oldsymbol{ ext{μ}s} |N|

    • For maximum value:
      f{s,max} = oldsymbol{ ext{μ}s} |N|

  • Kinetic Friction: Sliding occurs.

    • Magnitude is constant and given by:
      |fk| = oldsymbol{ ext{μ}k} |N|

    • Here $ ext{μ}s$ and $ ext{μ}k$ are static and kinetic friction coefficients respectively.

Force and Motion Examples

  • When a box of weight 100 N is at rest on a horizontal surface with a static friction coefficient $ ext{μ}s = 0.4$, the maximum static friction force can be calculated using: f{s,max} = oldsymbol{0.4} imes 100 ext{ N} = 40 ext{ N}

  • Determining Motion:

    • If an applied force $oldsymbol{T} = 30 ext{ N}$ is exerted, static friction counters it until the maximum is reached.

    • Box will not move until the applied force exceeds the maximum static friction.

Inclined Plane Example

  • A box with mass $oldsymbol{m = 1 ext{ kg}}$ on an incline with angle $ heta = 15^{ ext{o}}$ has:

    • Static friction coefficient, oldsymbol{ ext{μ}_s = 0.3}

    • Kinetic friction coefficient, oldsymbol{ ext{μ}_k = 0.2}

    • To determine if it starts sliding or the friction force, the component forces along the incline must be analyzed using frictional force equations.

Summary of Key Concepts

  • Static Friction: Prevents motion until the applied force exceeds its maximum value.

    • Ensures no sliding occurs with steady applied forces.

  • Kinetic Friction: Occurs during sliding motion against surfaces.

    • A consistent force opposing the direction of motion.

Remember to analyze forces carefully in the context of the problem, considering both the gravitational and frictional forces.

Important Equations

  1. Maximum Static Friction: f{s,max} = oldsymbol{ ext{μ}s} |N|

    • Where ( |N| ) is the normal force, and ( ext{μ}_s ) is the static friction coefficient.

  2. Kinetic Friction: |fk| = oldsymbol{ ext{μ}k} |N|

    • Where ( ext{μ}_k ) is the kinetic friction coefficient.

Key Concepts

  • Static Friction (fs): Prevents sliding; active until applied force exceeds ( f_{s,max} ).

  • Kinetic Friction (fk): Opposes motion when sliding occurs; remains constant during sliding.

  • Frictional Forces: Resists relative motion, acting parallel to surfaces due to molecular roughness.

  • Applications:

    • Wanted Friction: Enhances movement (e.g., walking).

    • Unwanted Friction: Causes wear and overheating in machines.

  • Inclined Plane: Understand component forces acting down the incline including friction when analyzing motion.