Applications of Newton's Laws of Motion: Frictional and Normal Forces

Chapter 5 – Applications of Newton’s Laws of Motion

Introduction

This chapter explores the practical applications of Newton's Laws of Motion, focusing on frictional and normal forces. These concepts are fundamental in understanding how objects interact with surfaces and how forces affect motion in real-world scenarios.

Frictional Forces

Definition and Microscopic Origin

• Frictional force is the force that resists the relative motion or tendency of such motion of two surfaces in contact.

• On a microscopic scale, surfaces are jagged, leading to friction when they interact.

Types of Friction

• Static friction (f_s): The force that must be overcome to start moving an object at rest. It acts up to a maximum value before motion begins.

• Kinetic friction (f_k): The force that opposes the motion of two surfaces sliding past each other. It acts once the object is already in motion and is generally less than the maximum static friction.

Normal Forces

• When an object is supported by a surface, the surface exerts a force perpendicular (normal) to the surface, called the normal force (N).

• The normal force balances the weight of the object when on a horizontal surface: $N = W = mg$

• In equilibrium, the sum of forces in the vertical direction is zero: $F = W + N = 0$

Static Friction

• The force of static friction depends on the applied force and increases to match it, up to a maximum value.

• Once the applied force exceeds this maximum, the object begins to move.

• The maximum static frictional force is given by: $f_{s,\text{max}} = \mu_s N$

• Where $\mu_s$ is the coefficient of static friction and $N$ is the normal force.

• The static friction force satisfies: $0 \leq f_s \leq \mu_s N$

Kinetic (Dynamic) Friction

• Once motion begins, kinetic friction acts, which is generally less than the maximum static friction.

• Kinetic friction is nearly constant and is given by: $f_k = \mu_k N$

• Where $\mu_k$ is the coefficient of kinetic friction.

• Kinetic friction always acts in the direction opposite to the velocity of the moving object.

• Kinetic friction is largely independent of the contact area and the relative speed of the surfaces (within typical ranges).

Comparison: Static vs. Kinetic Friction

• Static friction prevents motion up to a maximum value; kinetic friction acts during motion and is usually less than the maximum static friction.

• Typically, $\mu_k < \mu_s$ for a given pair of materials.

Example: In-Class Experiment

• If you pull gently on a stationary object resting on a surface, the object does not move until the applied force exceeds the maximum static friction.

• Once the object moves, kinetic friction takes over, and the force required to keep it moving at constant speed is less than the force needed to start the motion.

Key Formulas

• Maximum static friction: $f_{s,\text{max}} = \mu_s N$

• Kinetic friction: $f_k = \mu_k N$

• Normal force on a horizontal surface: $N = mg$

Applications

• Understanding friction is essential in sports (e.g., skiing), engineering (e.g., brake systems), and everyday activities (e.g., walking, driving).

• Design of materials and surfaces often aims to optimize frictional properties for safety and efficiency.

Additional info: The provided slides are part of a larger lecture on Newton's Laws, focusing here on frictional and normal forces. The notes above expand on the brief points and diagrams shown in the images, providing definitions, formulas, and context for college-level physics students.