content_copy

Unit 2: Force and Translational Dynamics

2.7: Kinetic and Static Friction

Introduction

Friction is a force that opposes motion between two surfaces in contact. It arises due to microscopic interactions at the surface level. Friction is categorized into static friction, which prevents motion, and kinetic friction, which resists motion once an object is moving.

Key Concepts

  • Static Friction (\( f_s \)): The force that prevents an object from moving.
  • Kinetic Friction (\( f_k \)): The force that opposes motion once an object is sliding.
  • Coefficient of Friction (\( \mu \)): A dimensionless number that depends on the materials in contact.
  • Friction depends on the normal force but not on the contact area or speed.
Tip: The static friction force is variable up to a maximum limit, while kinetic friction remains constant for a given surface.

Equations of Friction

  • Maximum Static Friction: \( f_s \leq \mu_s N \)
  • Kinetic Friction: \( f_k = \mu_k N \)
  • Normal Force (Flat Surface): \( N = mg \)
  • Normal Force (Inclined Plane): \( N = mg \cos\theta \)
Important: Static friction adjusts to match the applied force until reaching \( f_s^{max} \), at which point the object starts moving.

Factors Affecting Friction

  • Material Properties: Different materials have different coefficients of friction.
  • Normal Force: The greater the normal force, the greater the frictional force.
  • Surface Roughness: Rougher surfaces tend to have higher friction.
  • Lubrication: Reduces friction by decreasing surface interactions.

Mathematical Routines

Frictional forces are often part of force balance problems. Steps to solving these problems:

  • Identify forces acting on the object, including normal force and friction.
  • Determine if the object is moving or at rest to decide whether to use static or kinetic friction.
  • Use Newton’s Second Law (\( F = ma \)) to analyze motion.
Exam Tip: On an incline, always resolve forces into parallel and perpendicular components before applying Newton’s laws.

Practice Activities

Activity 1: Finding Static Friction

A 10 kg box sits on a table. The coefficient of static friction is 0.5. What is the maximum force that can be applied before the box starts moving?

Activity 2: Kinetic Friction on an Inclined Plane

A 5 kg block slides down a 30° incline. The coefficient of kinetic friction is 0.2. Find the acceleration of the block.

Activity 3: Comparing Static and Kinetic Friction

A car tires grip the road due to friction. Which type of friction is responsible when the tires roll without slipping, and which applies when they skid?

Summary & Exam Preparation Tips

Understanding static and kinetic friction is essential for solving force-related problems. Key takeaways:

  • Static friction prevents motion; kinetic friction opposes motion.
  • Friction depends on the normal force but not on surface area.
  • Static friction can adjust up to a maximum limit before an object moves.
  • Kinetic friction is constant for a given surface.

Practice solving problems with both static and kinetic friction to strengthen problem-solving skills for AP Physics exams.