Newton's Laws of Motion

Overview

This chapter introduces the fundamental principles governing the motion of objects, as formulated by Isaac Newton. These laws form the foundation of classical mechanics and are essential for understanding how forces affect the motion of physical bodies.

• Force and Mass

• Newton’s First Law of Motion

• Newton’s Second Law of Motion

• Newton’s Third Law of Motion

• Vector Nature of Forces: Forces in Two Dimensions

• Weight

• Normal Forces

Force and Mass

Definition of Force

A force is a push or pull exerted on an object. Forces are vector quantities, meaning they have both magnitude and direction.

• Vector Nature: Forces can be represented by arrows indicating their direction and strength.

• Examples: Pulling a sled, pushing a box, gravitational attraction.

Definition of Mass

Mass is a measure of how difficult it is to change an object's velocity (i.e., its inertia). It also represents the quantity of matter in an object.

• SI Unit: Kilogram (kg)

• Typical Masses:

Newton’s First Law of Motion

Law of Inertia

Newton’s First Law states that an object will remain at rest or move at a constant velocity unless acted upon by a net external force.

• Inertia: The tendency of an object to resist changes in its state of motion.

• Application: A hockey puck slides on ice until friction (a force) slows it down.

Newton’s Second Law of Motion

Relationship Between Force, Mass, and Acceleration

Newton’s Second Law quantifies how forces affect motion. The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

• Equation:

• Net Force: The sum of all forces acting on an object.

• Units: Force is measured in newtons (N), where .

Free-Body Diagrams

A free-body diagram is a sketch showing all the forces acting on an object. It helps analyze the net force and predict the resulting acceleration.

• Isolate the object of interest.

• Sketch all forces (gravity, normal, applied, friction, etc.).

• Choose a coordinate system and resolve forces into components.

• Apply Newton’s Second Law to each direction.

Newton’s Third Law of Motion

Action-Reaction Principle

Newton’s Third Law states that for every action, there is an equal and opposite reaction. Forces always occur in pairs, acting on different objects.

• Equation:

If object 1 exerts a force on object 2, then object 2 exerts a force on object 1.

• Action-Reaction Pair: When you push on a wall, the wall pushes back on you with equal force.

• Contact Forces: Forces produced by two objects in physical contact.

Vector Nature of Forces: Forces in Two Dimensions

Analyzing Forces in Multiple Directions

Forces can act in more than one direction. The easiest way to analyze such situations is to treat each dimension separately, resolving forces into components.

• Use trigonometry to find force components along x and y axes.

• Apply Newton’s laws to each direction independently.

• Example: Two people pulling a sled at angles; resolve each force into horizontal and vertical components to find net force and acceleration.

Weight

Gravitational Force

The weight of an object is the gravitational force exerted on it by the Earth.

• Equation:

• Unit: Newton (N)

• Apparent Weight: The contact force felt from a scale or floor, which may differ from actual weight if the surroundings are accelerating (e.g., in an elevator).

• Example: A 5.2-kg salmon in an elevator: apparent weight changes if the elevator accelerates up or down.

Normal Forces

Contact Force Perpendicular to Surface

The normal force is the force exerted by a surface perpendicular to an object resting on it.

• May be equal to, greater than, or less than the object's weight, depending on the situation.

• Equation (flat surface):

• Equation (inclined plane):

• Example: A child on a toboggan sliding down an icy hill; normal force is less than the weight due to the incline.

Summary of Key Concepts

• Force: A push or pull; vector quantity.

• Mass: Measures resistance to acceleration.

• Newton's First Law: Objects maintain constant velocity if net force is zero.

• Newton's Second Law:

• Newton's Third Law: Forces come in equal and opposite pairs.

• Free-Body Diagram: Tool for analyzing forces.

• Weight: Gravitational force,

• Apparent Weight: Contact force felt from a scale or floor.

• Normal Force: Perpendicular contact force from a surface.

Additional info: Inertial frames of reference are those in which Newton's first law holds true. Forces can be analyzed component-wise in two or three dimensions for complex problems.