Chapter 4: Newton's Laws of Motion

Introduction to Newton's Laws

Newton's laws of motion form the foundation of classical mechanics, describing the relationship between forces and the motion they produce. These laws were formulated by Sir Isaac Newton in the late 1600s and are based on extensive experimental evidence.

• Newton's laws explain how and why objects move.

• They are simple to state but can be intricate in their application.

Goals for Chapter 4

• Understand the meaning of force in physics.

• View force as a vector and learn how to combine forces.

• Understand the behavior of a body when forces balance (Newton's First Law).

• Learn the relationship between mass, acceleration, and force (Newton's Second Law).

• Relate mass and weight.

• See the effect of action-reaction pairs (Newton's Third Law).

• Learn to make free-body diagrams.

Forces in Physics

Definition and Types of Forces

A force is a push or pull resulting from the interaction between a body and its environment. In physics, force is described quantitatively and is a vector quantity, having both magnitude and direction.

• Contact forces: Require direct contact between objects (e.g., normal force, friction, tension).

• Field forces: Act over a distance without direct contact (e.g., gravity, electromagnetic forces).

Common Types of Forces

• Normal force: Perpendicular contact force exerted by a surface.

• Friction force: Parallel contact force resisting motion between surfaces.

• Tension force: Pulling force transmitted through a rope, string, or cable.

• Weight: Gravitational force acting on an object.

Examples of Forces

• Gravity: near Earth's surface.

• Electric and magnetic forces: Fundamental interactions studied in electromagnetism.

• Subatomic forces: Weak and strong nuclear forces.

Magnitudes of Common Forces

Forces in nature vary widely in magnitude. The following table summarizes typical values:

Forces as Vectors

Vector Representation and Addition

Forces are vectors and can be expressed in terms of their components:

• Units:

Vector Addition and Superposition Principle

The net force acting on an object is the vector sum of all individual forces:

• Superposition principle: Forces add linearly and independently.

• For forces:

Notation for Vector Sum

The resultant force is:

Newton's Laws of Motion

Newton's First Law (Law of Inertia)

Statement: An object at rest remains at rest, and an object in motion continues in motion with constant velocity unless acted upon by a net external force.

• Inertia: The tendency of an object to resist changes in its velocity. The measure of inertia is mass.

• Valid only in inertial frames of reference (non-accelerating frames).

• Uniform motion: Constant speed in an unchanging direction.

Examples

• Car on a freeway, puck on ice, spaceship in deep space.

Newton's Second Law

Statement: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The direction of acceleration is the direction of the net force.

• Formula:

• Component form: , ,

• Defines mass as a measure of inertia.

Units of Force, Mass, and Acceleration

• 1 N = 1 kg·m/s2

• 1 lb = 4.448 N

Examples

• Calculating acceleration: If a 40 kg box is pulled with a 20 N force, m/s2.

• Friction: A 0.20 kg ketchup bottle slides to rest due to a friction force; can be used to find the force.

Newton's Third Law

Statement: If object 1 exerts a force on object 2, then object 2 exerts a force on object 1. Forces always occur in pairs, equal in magnitude and opposite in direction.

• Action-reaction pairs act on different objects.

• Examples: Pushing a wall, firing a rifle, pulling a rope.

Mass and Weight

Definitions and Differences

• Mass: Scalar quantity measuring inertia (kg).

• Weight: Vector quantity, gravitational force exerted by Earth: .

• Value of (acceleration due to gravity) depends on location (Earth, Moon, etc.).

• Do not confuse mass (kg) and weight (N).

Inertial vs. Gravitational Mass

• Inertial mass: Appears in Newton's Second Law, measures resistance to acceleration.

• Gravitational mass: Source of gravitational attraction.

• Experimentally, inertial and gravitational mass are equal.

Normal Forces and Tension

Normal Force

• Contact force perpendicular to the surface between two objects.

• Reaction pair: Table pushes up on box, box pushes down on table.

Tension in Strings and Ropes

• Assume massless ropes and ideal pulleys.

• Tension is the same throughout a massless string.

• Pulleys change direction of tension, not magnitude.

Free-Body Diagrams

Purpose and Construction

• Visual representation of all forces acting on a single object.

• Used to apply Newton's Second Law:

• Do not include reaction forces acting on other objects.

Problem Solving Strategies

• Consider all external forces and calculate their vector sum.

• Draw diagrams and choose coordinate axes.

• Apply Newton's laws only in inertial frames.

• Distinguish between mass and weight.

• Use action-reaction pairs and tension relationships for connected objects.

Summary Table: Key Equations

Additional info:

• Inertial frames are required for Newton's laws to be valid.

• Free-body diagrams are essential for analyzing forces and solving problems.