Newton's third law

Newton’s Third Law of Motion — Notes

Basic Idea

• Newton’s Third Law states:

  For every action, there is an equal and opposite reaction.

• This means that forces always come in pairs.

• The two forces:

  • Are equal in magnitude

  • Are opposite in direction

  • Act on different objects

Horse and Wagon Example

• The horse pulls the wagon forward.

• The wagon pulls back on the horse with an equal force.

• These two forces form an action–reaction pair.

Common Misconception

• It may seem that because the forces are equal and opposite, the net force should be zero, so nothing should move.

• This confusion happens because:

  • The forces act on different objects, not the same one.

Net Force vs. Action–Reaction Forces

• Net force refers to the sum of forces acting on a single object.

• Action–reaction forces:

  • Do not cancel out because they act on different objects.

Example:

• Force on the wagon ≠ force on the horse (when calculating net force).

• Each object has its own net force.

Equilibrium

• An object is in equilibrium when:

  • The net force on it is zero

  • It is either:

    • At rest, or

    • Moving at constant velocity

• To change motion, an external unbalanced force is required.

Key Question Raised

• If the horse and wagon exert equal and opposite forces on each other:

  • Why does the system move from rest?

• The answer lies in:

  • Identifying which forces act on which object

  • Understanding how external forces (like friction with the ground) affect motion

Big Takeaway

• Newton’s Third Law does not prevent motion.

• Motion occurs because:

  • Action–reaction forces act on different objects

  • The net force on each object can still be nonzero

Newton’s Third Law of Motion — Notes

Scientist Background

• Sir Isaac Newton (1642–1727) was the first scientist to accurately describe the forces between interacting objects.

• He showed that forces in interactions always involve two objects, not just one.

Core Principle

• In any interaction:

  • Both objects are acted on equally

  • Forces come in pairs

Newton’s Third Law (Formal Statement)

• This is often summarized as:

  For every action, there is an equal and opposite reaction.

Action–Reaction Forces

• Action and reaction forces:

  • Are equal in magnitude

  • Are opposite in direction

  • Act on different objects

  • Occur simultaneously

Horse and Wagon Example

• The horse pulls the wagon using a harness.

• When the horse pulls forward on the wagon:

  • The wagon pulls backward on the horse.

• This backward pull is:

  • A force exerted by the wagon on the horse

  • Equal in size to the force the horse exerts on the wagon

Key Clarification

• The force the horse exerts on the wagon and the force the wagon exerts on the horse:

  • Do not cancel each other out

  • Because they act on different objects

Big Takeaway

• Newton’s Third Law explains force interactions, not motion by itself.

• Motion depends on the net force on each individual object, not on action–reaction pairs.

Newton’s Third Law — Horse and Wagon Analysis

Action–Reaction Forces

• In every interaction, two forces act simultaneously:

  • One is the action

  • The other is the reaction

• These forces:

  • Are equal in magnitude

  • Are opposite in direction

  • Do not act on the same object

Forces Acting on the Horse

Because motion is horizontal, only horizontal forces are considered.

Two main forces act on the horse:

1. Force the horse exerts on the ground

   • The horse pushes backward on the ground.

2. Force the wagon exerts on the horse

   • The wagon pulls backward on the horse through the harness.

Forces Acting on the Wagon

The wagon experiences:

1. Force the horse exerts on the wagon

   • The horse pulls the wagon forward.

2. Force of friction between the wagon’s wheels and the ground

   • Friction acts opposite the motion.

Key Clarification About Action–Reaction

• The force of the horse on the wagon and

• The force of the wagon on the horse:

  • Are an action–reaction pair

  • Act on different objects

• Because they act on different bodies, they do not cancel.

Net Force on the System

• The net force on the system (horse + wagon) is:

  • Not necessarily zero

• Therefore:

  • The system is not always in equilibrium

  • The horse and wagon can:

    • Accelerate from rest

    • Move at constant speed

    • Slow down or stop

Big Takeaway

• Newton’s Third Law explains force pairs, not equilibrium.

• Motion depends on the net external forces acting on each object or on the system as a whole.

Situation

• A flower pot (plant) is resting on a table.

• The object is stationary (not moving).

Static Equilibrium

• According to Newton’s First Law:

  • An object is in static equilibrium if:

    • It is at rest

    • The net force = 0

Key Clarifications

• The normal force is not automatically equal to the weight.

  • It is equal only because the plant is in equilibrium.

• The forces are:

  • Equal in magnitude

  • Opposite in direction

  • Acting on the same object (the plant)

Big Takeaway

• A stationary object on a surface is held in place because:

  • Gravity pulls it down

  • The surface pushes it up

• When these forces are equal:

  • Net force = 0

  • The object remains at rest

Key Principle (Newton’s Third Law)

• Action and reaction forces always act on different objects.

• They are:

  • Equal in magnitude

  • Opposite in direction

  • Simultaneous

  • Never cancel each other, because they act on different bodies.

Plant–Earth Interaction

• The Earth pulls the plant downward with gravitational force (Fg).

• At the same time:

  • The plant pulls the Earth upward with an equal gravitational force.

• This is an action–reaction pair:

  • Earth on plant

  • Plant on Earth

Table–Floor Interaction

• The table pushes down on the floor with a force equal to:

  • The table’s weight plus

  • The plant’s weight

• The floor pushes up on the table with a normal force of equal magnitude.

This forms another action–reaction pair:

• Table on floor

• Floor on table

Static Equilibrium Reminder

• An object is in static equilibrium when:

  • It is at rest

  • The net force on that object is zero

• Even though many forces exist in the system:

  • Each object individually can still have zero net force

Big Takeaway

• Action–reaction forces:

  • Do not cancel because they act on different objects

• Equilibrium depends on:

  • The net force on a single object, not on force pairs across objects

• This explains why stacked systems (plant → table → floor) remain at rest without collapsing

Friction — Notes

What Is Friction?

• Friction is a contact force.

• It occurs when two objects in physical contact:

  • Are moving relative to each other, or

  • Are trying to move relative to each other.

• Friction always opposes motion (or attempted motion).

Friction in the Horse and Wagon

• While the wagon moves:

  • Friction between the horse’s hooves and the ground acts on the horse.

  • Friction between the wagon’s wheels and the ground acts on the wagon.

• These frictional forces resist forward motion.

Why Friction Exists (Microscopic View)

• Surfaces are not perfectly smooth.

• They have tiny bumps and irregularities.

• When surfaces touch:

  • Atoms come very close

  • Weak electrical bonds can form

• These bonds must be broken for motion to occur.

• Breaking them requires force → this resistance is friction.

Direction of Friction

• Friction always acts:

  • Opposite the direction of motion

  • Or opposite the attempted motion

• Example:

  • If an object slides right, friction acts left.

Friction and Motion

• Friction:

  • Slows moving objects

  • Can stop objects

  • Makes it harder to start moving an object

• Without friction:

  • Objects would keep moving once pushed (Newton’s First Law)

Friction and Mass (Preview)

• Heavier objects press down more on surfaces.

• This increases contact at the microscopic level.

• Result:

  • Greater mass → greater frictional force

• This relationship will be analyzed more formally later.

Big Takeaway

• Friction is:

  • A contact force

  • Caused by microscopic surface interactions

  • Always opposes motion

• It plays a crucial role in:

  • Walking

  • Driving

  • Pulling objects

  • Everyday motion

Dry Friction — Notes

Dry Friction

• Dry friction occurs between two non-lubricated (dry) surfaces in contact.

• It is divided into:

  • Static friction

  • Kinetic friction

Static Friction

Definition

• Static friction acts when an object is at rest and an attempt is made to move it, but it does not move.

• It acts parallel to the surfaces in contact.

• Its role is to prevent motion from starting.

Direction and Nature

• Static friction:

  • Acts opposite the applied force

  • Adjusts its magnitude to match the applied force

  • Exists only until motion begins

Everyday Example: Pushing a Table

• You push a study table lightly.

• The table does not move.

• According to Newton’s First Law:

  • If the table is at rest, the net force = 0

• This means:

  • Your applied force is balanced by an equal and opposite static friction force.

Overcoming Static Friction

• To make the table move:

  • You must increase your applied force

  • Motion begins only when the applied force exceeds the maximum static friction

• Once the table starts moving:

  • Static friction stops

  • Kinetic friction takes over

Key Takeaways

• Static friction:

  • Prevents motion

  • Acts on stationary objects

  • Balances applied forces up to a maximum value

• No motion occurs until static friction is overcome

Static Friction — Notes

What Happens When Motion Is About to Start

• The instant an object begins to move, the applied force has exceeded the maximum static friction.

• Before motion starts, static friction adjusts to oppose the applied force.

When Static Friction Exists

• Static friction:

  • Exists only when an applied force is present

  • Appears when one object attempts to move relative to another

• If there is no applied force:

  • No static friction acts

Key Takeaways

• Static friction:

  • Prevents motion from starting

  • Adjusts to match the applied force

  • Has a maximum value

• Motion starts when the applied force exceeds maximum static friction

• Once motion begins:

  • Static friction disappears

  • Kinetic friction takes over

Kinetic Friction — Notes

When Kinetic Friction Occurs

• Kinetic friction begins the instant an object starts moving.

• It replaces static friction once motion has started.

• Also called sliding friction.

Direction of Kinetic Friction

• Kinetic friction always acts:

  • Opposite the direction of the object’s velocity

• Example:

  • If the table slides to the right, kinetic friction acts to the left.

Keeping an Object Moving

• To keep an object moving at constant velocity:

  • You must apply an external force at least equal to the kinetic friction force.

• If applied force is:

  • Greater → object accelerates

  • Equal → constant speed

  • Less → object slows and stops

Dependence on Surfaces

• The magnitude of kinetic friction depends on:

  • The materials of the surfaces in contact

  • The roughness of those surfaces

Key Takeaways

• Kinetic friction:

  • Acts only when objects are sliding

  • Has a constant magnitude (for given surfaces and normal force)

  • Is proportional to the normal force

• Motion begins when static friction is overcome

• Motion continues only if kinetic friction is continuously overcome

Coefficient of Kinetic Friction (μₖ)

What μₖ Depends On

• The coefficient of kinetic friction (μₖ) depends on:

  • The materials of the two surfaces in contact

  • How smooth, rough, or dry the surfaces are

• Example:

  • Steel on steel (unlubricated) → μₖ ≈ 0.60

What μₖ Does Not Depend On

In most physics problems, μₖ:

• Does not depend on:

  • Surface area of contact

  • Sliding speed of the object

• These assumptions simplify real-world behavior for calculations.

Coefficients of Kinetic Friction (μₖ)

Interpreting the Table

• Lower μₖ → less friction → easier sliding

• Ice-related surfaces have very low friction

• Rough, dry metal surfaces have high friction

• Lubrication greatly reduces friction

Tension — Explanation & Notes

What Is Tension?

• Tension is a contact force.

• It is a pulling force (never a pushing force).

• Measured in newtons (N).

• Exerted by a string, rope, cable, or cord on the objects attached to its ends.

How Tension Acts

• Tension:

  • Acts along the length of the rope or cable

  • Is directed away from the object it acts on

  • Acts in both directions on the two objects connected by the rope

Example: Wrecking Ball and Cable

• A wrecking ball hangs from a cable.

• Forces on the wrecking ball:

  1. Weight (Fg) acting downward

  2. Tension (T) from the cable acting upward

• If the ball is at rest:

  T=Fg=mgT = F_g = mgT=Fg​=mg

• The ball is in static equilibrium (net force = 0).

Equal Tension Throughout the Cable

• Assuming the cable has negligible mass:

  • The tension is the same everywhere in the cable.

• The cable:

  • Pulls upward on the wrecking ball

  • Pulls downward on the crane or pulley

• These are Newton’s Third Law action–reaction pairs.

Direction of Tension

• Tension always:

  • Pulls away from the object

  • Acts parallel to the cable

• It never pushes or acts at an angle to the rope itself.

Real-World Importance

• Construction cranes:

  • Must stay below the maximum safe tension to avoid cable failure.

• Suspension bridges:

  • Cable tension is a major engineering design constraint.

• Elevators, pulleys, climbing gear:

  • All rely on correctly calculated tension forces.

Key Takeaways

• Tension is:

  • A contact, pulling force

  • Transmitted through ropes or cables

• In equilibrium:

  • Tension can equal weight

• With massless ropes:

  • Tension is the same throughout

• Understanding tension is critical for safety and structural design