Friction

Friction: Complete CBSE Class 8 Science Notes & Study Guide

Introduction to Friction

Friction is a fundamental force in physics that plays a crucial role in our daily lives. When any object in motion is left to itself on a surface, it eventually comes to rest after traveling some distance. This happens because of an opposing force that acts between the two surfaces in contact this force is called friction.

What is Friction?

Friction is the force that acts along the direction tangential to the surfaces in contact and opposes relative motion between two bodies. This force is always tangential to the contact surfaces and acts opposite to the direction of motion or intended motion.

Characteristics of friction:

• Acts parallel to the contact surface
• Opposes relative motion
• Exists even when bodies are at rest
• Depends on the nature of surfaces in contact
• Independent of the apparent area of contact (in most cases)

Causes of Friction

Understanding why friction occurs helps us comprehend its behavior and find ways to control it.

Surface Irregularities

When observed under a powerful microscope, every surface appears uneven with numerous depressions (valleys) and elevations (peaks). When two bodies come in contact:

1. Interlocking occurs: The elevations of one surface fit into the depressions of the other surface
2. Resistance develops: This interlocking creates an opposing force that resists motion
3. Shearing effect: When external force is applied, these irregularities must be sheared off for motion to occur

This mechanical interlocking and the subsequent shearing of surface irregularities are the primary causes of friction.

Additional Factors Contributing to Friction:

• Material properties: Different materials have different atomic structures affecting friction
• Normal force: The force pressing the surfaces together
• Surface conditions: Whether surfaces are dry, wet, rough, or smooth
• Molecular adhesion: Attractive forces between molecules of different surfaces

Types of Friction

Friction is classified into three main types based on the state of motion of the objects in contact.

1. Static Friction

Static friction is the opposing force that comes into play when one body tends to move over the surface of another, but actual motion has not yet started.

Key Properties:

• Self-adjusting force: Static friction adjusts itself to match the applied force
• Range: Varies from zero to a maximum value (limiting friction)
• Formula: F_s ≤ μ_s × R (where equality holds at limiting friction)
• Zero at rest: If no force is applied, static friction is zero

Example: When you try to push a heavy box, it doesn't move initially because static friction equals your applied force. As you push harder, static friction increases until it reaches its maximum value.

Limiting Friction

Limiting friction is the maximum value of static friction that develops when a body is just on the verge of sliding over another surface.

Law of Limiting Friction:

• The magnitude of limiting friction is directly proportional to the normal reaction
• F_L ∝ R or F_L = μ_s × R
• Direction: Always opposite to the direction of intended motion

2. Kinetic (Dynamic) Friction

Kinetic friction is the frictional force that comes into play after motion has started. It's the force required to keep a body moving with uniform velocity over another surface.

Properties:

• Constant magnitude: Remains relatively constant regardless of velocity
• Less than static friction: μ_k < μ_s (always)
• Formula: F_k = μ_k × R
• Independent of velocity: Doesn't change with speed of motion

Why is kinetic friction less than static friction?
Once motion starts, the irregularities of surfaces have less time to interlock completely. Inertia of rest has been overcome, so less force is needed to maintain motion than to start it.

Types of Kinetic Friction:

a) Sliding Friction

• Occurs when one body slides over another
• Example: A book sliding across a table, a sled moving on snow
• Relatively high compared to rolling friction

b) Rolling Friction

• Occurs when an object rolls over a surface
• Formula: F_rolling = μ_r × (R/r) where r is the radius of the rolling object
• Significantly less than sliding friction
• Examples: Ball bearings, wheels of vehicles, cylinders rolling on surfaces

Why is rolling friction less?

• Surfaces don't rub against each other
• Point of contact has zero velocity relative to the surface
• Less surface deformation
• Minimal interlocking of irregularities

3. Relationship Between Friction Types

Important Hierarchy:

Static Friction (Limiting) > Kinetic Friction (Sliding) > Rolling Friction
f_s > f_k > f_r
μ_s > μ_k > μ_r

This relationship explains why:

• It's harder to start pushing a heavy object than to keep it moving
• Wheels are used for transportation instead of dragging
• Ball bearings reduce friction in machinery

Coefficient of Friction

The coefficient of friction (μ) is a dimensionless number that represents the ratio of frictional force to the normal reaction between two surfaces.

Definition and Formula

μ = F/R

Where:

• F = Frictional force
• R = Normal reaction force
• μ = Coefficient of friction (no unit)

Types of Coefficients:

1. Coefficient of Static Friction (μ_s)
   • μ_s = F_L / R (at limiting friction)
   • Always the highest value

2. Coefficient of Kinetic Friction (μ_k)
   • μ_k = F_k / R
   • Less than μ_s

3. Coefficient of Rolling Friction (μ_r)
   • Has dimensions of length (measured in meters)
   • Smallest among all three

Factors Affecting Coefficient of Friction:

• Materials in contact: Steel on steel differs from rubber on concrete
• Nature of surfaces: Rough, smooth, polished, or lubricated
• Surface conditions: Dry or wet

Does NOT depend on:

• Apparent area of contact
• Magnitude of normal force
• Velocity of motion (for kinetic friction)

How is Coefficient of Friction Measured?

Experimental Method - Inclined Plane:

1. Setup: Place an object on an adjustable inclined plane
2. Procedure: Gradually increase the angle of inclination
3. Observation: Note the angle (θ) at which the object just begins to slide
4. Calculation: At this critical angle, μ_s = tan(θ)

Derivation:

• Forces parallel to plane: mg sin θ (down) = f_s (up)
• Forces perpendicular to plane: R = mg cos θ
• At limiting friction: mg sin θ = μ_s × mg cos θ
• Therefore: μ_s = tan θ

Alternative Methods:

Horizontal Surface Method:

• Apply horizontal force using spring balance
• Measure force at which object starts moving (F_L)
• Measure weight (mg) which equals R on horizontal surface
• Calculate μ_s = F_L / R

Kinetic Friction Measurement:

• Measure force required to maintain constant velocity
• Calculate μ_k = F_k / R

Laws of Friction

1. Law of Limiting Friction

• Limiting friction is directly proportional to normal reaction
• F_L = μ_s × R

2. Direction Law

• Friction always acts opposite to the direction of motion or intended motion
• Acts tangentially to the contact surface

3. Independence from Area

• Friction is independent of the apparent area of contact (for most practical cases)

4. Material Dependence

• Coefficient of friction depends on materials and surface conditions
• Independent of normal force magnitude

Graph: Applied Force vs Force of Friction

Understanding the relationship between applied force and friction helps visualize how friction behaves.

Regions of the Graph:

Region OA (Static Friction):

• Linear relationship: F_friction = F_applied
• Friction increases proportionally with applied force
• Body remains at rest
• Self-adjusting nature of static friction

Point A (Limiting Friction):

• Maximum static friction reached
• Body is on the verge of motion
• Critical point where static becomes kinetic friction

Region BC (Kinetic Friction):

• Horizontal line: friction remains constant
• F_k is independent of applied force
• F_k < F_L (kinetic friction is always less than limiting friction)
• Body is in motion

Observations:

• Static friction can vary from 0 to F_L
• There's a slight drop from point A to B when motion begins
• Kinetic friction remains constant regardless of how much extra force is applied

How Surface Roughness Affects Friction

Surface roughness plays a crucial but nuanced role in friction behavior.

Effect on Static Friction:

Rough Surfaces:

• Increased interlocking: More and deeper irregularities
• Higher μ_s: Greater resistance to initial motion
• More force needed: Harder to start motion
• Example: Rubber on concrete (μ_s ≈ 0.7-1.0)

Smooth Surfaces:

• Less interlocking: Fewer and shallower irregularities
• Lower μ_s: Less resistance to initial motion
• Example: Ice on ice (μ_s ≈ 0.02-0.05)

Effect on Kinetic Friction:

Rough Surfaces:

• Continuous shearing: Irregularities constantly break and reform
• Higher μ_k: More resistance during motion
• More heat generation

Smooth Surfaces:

• Less shearing: Minimal irregularity interaction
• Lower μ_k: Smoother motion
• Less heat generation

The Polishing Paradox:

Interestingly, excessive polishing can sometimes increase friction because:

• Surfaces come into extremely close contact
• Molecular adhesion becomes significant
• Surface molecules attract each other strongly
• This is why perfectly smooth surfaces can sometimes "stick" together

Practical Implications:

Surface Condition	Static Friction	Kinetic Friction	Application
Very rough	Very high	High	Non-slip surfaces, tire treads
Moderately rough	High	Moderate	Walking surfaces, brake pads
Smooth	Moderate	Low	Sliding surfaces, low-wear parts
Polished	Low to Moderate	Very low	Bearings, precision machinery
Lubricated smooth	Very low	Very low	Engine parts, hinges

Friction on Inclined Planes

Inclined plane problems are common in physics and involve analyzing friction forces in two dimensions.

Forces on an Inclined Plane:

When an object rests on an inclined plane at angle θ:

1. Weight (mg): Acts vertically downward
   • Component parallel to plane: mg sin θ (down the plane)
   • Component perpendicular to plane: mg cos θ (into the plane)

2. Normal Reaction (R): Acts perpendicular to plane surface
   • R = mg cos θ (for object at rest or constant velocity)

3. Friction (f): Acts parallel to plane
   • Direction: Opposes motion or intended motion

Case 1: Object at Rest on Inclined Plane

Condition for rest: f_s ≤ μ_s × R

Equilibrium conditions:

• Perpendicular to plane: R = mg cos θ
• Parallel to plane: f_s = mg sin θ

Critical angle (angle of repose): When object just begins to slide:

• mg sin θ = μ_s × mg cos θ
• μ_s = tan θ

Case 2: Object Sliding Down (Acceleration)

Net force down the plane:

• F_net = mg sin θ - f_k
• F_net = mg sin θ - μ_k × mg cos θ
• Acceleration: a = g(sin θ - μ_k cos θ)

Case 3: Object Pushed Up the Plane

Force required to push up with constant velocity:

• F = mg sin θ + f_k
• F = mg sin θ + μ_k × mg cos θ
• F = mg(sin θ + μ_k cos θ)

Solving Inclined Plane Problems - Step by Step:

Step 1: Draw free body diagram
Step 2: Resolve weight into components
Step 3: Identify normal reaction: R = mg cos θ
Step 4: Calculate friction: f = μ × R
Step 5: Apply Newton's laws parallel to plane
Step 6: Solve for unknown quantity

Example Problem:

Question: A block of mass 4 kg slides down a 30° incline. If it covers 8 m in 2 seconds starting from rest, find the coefficient of kinetic friction.

Solution: Given: m = 4 kg, θ = 30°, s = 8 m, t = 2 s, u = 0

Using s = ut + ½at²:

• 8 = 0 + ½ × a × 4
• a = 4 m/s²

Net force equation:

• ma = mg sin 30° - μ_k × mg cos 30°
• 4 = g(sin 30° - μ_k cos 30°)
• 4 = 10(0.5 - μ_k × 0.866)
• 4 = 5 - 8.66μ_k
• μ_k = 1/(8.66) ≈ 0.115

Friction as a Cause of Motion

While friction is often seen as opposing motion, it's actually essential for causing and controlling motion in many scenarios.

1. Walking and Running

How friction enables walking:

• Backward push: Your foot pushes the ground backward (action)
• Forward reaction: Ground pushes your foot forward due to friction (reaction)
• Result: You move forward

Three positions of foot during walking:

1. Position 1: Friction acts forward (driving force) - foot pushes back
2. Position 2: No friction - foot directly under body
3. Position 3: Friction acts backward (decelerating force) - foot pushes forward to slow down

Without friction:

• You would slip without moving forward
• Like walking on extremely slippery ice

2. Cycling

Rear wheel (driving wheel):

• Pedaling applies force making wheel push ground backward
• Friction acts forward on rear wheel (propels bicycle)
• Cause of motion

Front wheel (driven wheel):

• Moves by itself due to bicycle's motion
• Friction acts backward (opposes motion)
• Resistance to motion

When pedaling stops:

• Both wheels become driven wheels
• Friction acts backward on both
• Bicycle slows down and stops

3. Vehicle Acceleration

When a person stands in an accelerating vehicle:

• Without friction: Person would remain stationary (inertia) while vehicle moves forward
• With friction: Friction force = ma provides the acceleration to the person
• Condition: Friction must be sufficient, i.e., μ_s mg ≥ ma

4. Vehicles and Tires

Tire treads increase friction by:

• Increasing effective surface roughness
• Providing channels for water drainage
• Increasing contact area through deformation

Starting a car:

• Wheels push road backward
• Friction pushes car forward
• Greater friction = better acceleration

Fluid Friction (Drag)

When solid objects move through fluids (liquids or gases), they experience fluid friction, also called drag.

Characteristics of Fluid Friction:

1. Hierarchy: f_solid > f_liquid > f_gas
2. Velocity dependent: Unlike solid friction, drag increases with velocity
3. Shape dependent: Streamlined shapes experience less drag

Streamlining

Streamlined shape: A body shape around which fluid can flow easily with minimum friction.

Examples:

• Aeroplanes (reduce air resistance)
• Submarines (reduce water resistance)
• Rockets (reduce atmospheric drag)
• Fish (natural streamlining)
• Racing cars (aerodynamic design)

Benefits:

• Reduced energy consumption
• Higher speeds possible
• Better fuel efficiency
• Less turbulence

Practical Applications:

In air:

• Aircraft design
• High-speed trains
• Cycling helmets
• Automotive design

In water:

• Ship hulls
• Submarine design
• Swimsuit design
• Torpedo shape

Ways to Reduce Friction

Reducing friction is crucial for increasing efficiency, reducing wear, and saving energy.

1. Polishing and Smoothing Surfaces

Method: Make surfaces smoother through polishing
Effect: Reduces irregularities, decreasing interlocking
Application: Machinery parts, sliding surfaces
Limitation: Excessive polishing may increase molecular adhesion

2. Lubrication

Lubricants: Substances applied between surfaces to reduce friction

Common lubricants:

• Oils (engine oil, machine oil)
• Grease (thick oil-based lubricant)
• Graphite powder (dry lubricant)
• Teflon coating

How lubricants work:

• Create thin film between surfaces
• Prevent direct contact
• Convert solid friction to fluid friction
• Fill in surface irregularities

Applications:

• Engine parts
• Door hinges
• Bicycle chains
• Industrial machinery

3. Ball Bearings

Principle: Convert sliding friction to rolling friction

Structure:

• Inner ring (attached to rotating shaft)
• Outer ring (attached to stationary housing)
• Rolling balls or rollers between rings

Advantages:

• Dramatically reduces friction (rolling << sliding)
• Reduces wear and tear
• Allows smooth rotation
• Increases efficiency

Applications:

• Wheels and axles
• Electric motors
• Hard disk drives
• Skateboard wheels

4. Using Wheels

Principle: Rolling friction instead of sliding friction

Benefits:

• f_rolling << f_sliding
• Easier to move heavy loads
• Less energy required
• Reduced wear

Applications:

• All vehicles (cars, trains, bicycles)
• Carts and trolleys
• Rolling luggage
• Industrial transport

5. Streamlining

For fluid friction:

• Reduces drag force
• Allows smoother flow of fluid around object
• Minimizes turbulence

6. Air Cushioning

Hovercraft principle:

• Creates air layer between surface and object
• Eliminates direct contact
• Extremely low friction

Applications:

• Hovercraft vehicles
• Air hockey tables
• Some high-speed trains (magnetic levitation)

7. Material Selection

Choose materials with low coefficient of friction:

• Teflon on metal (μ ≈ 0.04)
• Graphite as dry lubricant
• Synthetic materials for reduced friction

Ways to Increase Friction

In many situations, we actually want more friction for safety and functionality.

1. Making Surfaces Rough

Method: Add texture or roughness to surfaces
Effect: Increases interlocking, increases μ

Applications:

• Tire treads: Deep grooves for better road grip
• Shoe soles: Textured patterns for walking stability
• Sports equipment: Rough surfaces on tennis rackets, golf clubs
• Safety surfaces: Anti-slip flooring, stair treads

2. Adding Sand or Gravel

Application scenarios:

• Icy roads: Sand increases traction for vehicles
• Railway tracks: Sand on tracks in rainy/snowy conditions
• Slippery floors: Sand on wet marble floors prevents slipping

How it works:

• Particles fill gaps in ice or wet surface
• Increases effective roughness
• Provides mechanical interlocking

3. Using Rubber or High-Friction Materials

Rubber advantages:

• High coefficient of friction (μ ≈ 0.7-1.0)
• Deforms to increase contact area
• Works well on various surfaces

Applications:

• Vehicle tires: Especially important for braking
• Rubber mats: Anti-slip surfaces
• Shoe soles: Athletic and safety footwear
• Brake pads: Often contain rubber compounds

4. Increasing Normal Force

Principle: F = μR, so increasing R increases friction

Methods:

• Adding weight to increase normal force
• Pressing brake pads harder against rotating disc
• Increasing pressure in manufacturing processes

5. Brake Systems

Disc brakes:

• Friction pads press against rotating disc
• Higher friction material for better stopping
• Heat-resistant compounds

Drum brakes:

• Brake shoes press outward against drum
• Large surface area for friction

6. Grooves and Patterns

Tire design:

• Tread patterns for different conditions (rain, snow, off-road)
• Channels water away from contact patch
• Maximizes dry surface contact

Real-World Applications of Friction

Applications Where Friction is Beneficial:

Application	How Friction Helps	Consequence Without Friction
Walking	Enables forward motion	Slipping, no movement
Vehicle Braking	Stops moving vehicles	No stopping ability
Writing	Pencil/pen marks paper	No marks on paper
Climbing	Grip on surfaces	Cannot climb
Holding Objects	Grip prevents dropping	Objects slip from hands
Fasteners	Nails, screws stay in place	Fasteners fall out
Belt Drives	Transfers motion between pulleys	No power transmission
Matches	Creates fire through friction	Cannot light matches

Applications Where Friction is Reduced:

Application	Method of Reduction	Benefit
Engine Parts	Lubrication with oil	Reduced wear, increased efficiency
Bearings	Ball/roller bearings	Smooth rotation, less energy loss
Skiing	Smooth, waxed skis	Higher speed, easier gliding
Air/Water Vehicles	Streamlining	Less drag, better fuel economy
Machinery	Polishing and lubrication	Longer life, less maintenance
Ice Skating	Pressure melts ice forming water film	Easy gliding

Industry-Specific Applications:

Automotive Industry:

• High friction: Brake pads, tires, clutch plates
• Low friction: Engine components, transmission, wheel bearings

Construction:

• High friction: Foundation stability, bolt connections, worker safety (boots)
• Low friction: Sliding doors, window mechanisms

Sports:

• High friction: Rock climbing shoes, sports gloves, athletic footwear
• Low friction: Skis, ice skates, swimming suits

Manufacturing:

• High friction: Gripping mechanisms, fastening
• Low friction: Conveyor systems, robotic joints

Advantages of Friction

1. Enables Locomotion

• Essential for walking, running, and all forms of terrestrial movement
• Vehicles need friction between tires and road
• Without friction, all movement would be impossible

2. Allows Gripping and Holding

• Enables us to hold and manipulate objects
• Essential for using tools and equipment
• Prevents objects from slipping from our hands

3. Enables Braking and Stopping

• Critical for safety in vehicles
• Allows controlled deceleration
• Prevents accidents

4. Makes Writing Possible

• Pencil graphite adheres to paper through friction
• Chalk marks on board
• Pens work due to friction

5. Fastening Mechanisms

• Nails and screws remain fixed due to friction
• Knots stay tied
• Connections remain stable

6. Power Transmission

• Belt drives transfer power through friction
• Clutches engage/disengage through friction
• Friction wheels in some machinery

7. Heat Generation

• Controlled use generates heat (matches, fire-starting)
• Friction welding in manufacturing
• Warming hands by rubbing

8. Sound Production

• Musical instruments like violin use friction
• Rubbing creates sound vibrations

Disadvantages of Friction

1. Opposes Motion

• Extra energy required to overcome friction
• Reduces efficiency of mechanical systems
• Increases fuel consumption in vehicles

2. Causes Wear and Tear

• Surfaces in contact gradually wear down
• Shortens lifespan of machinery parts
• Increases maintenance costs
• Examples: Tire wear, brake pad wear, engine component wear

3. Heat Generation (Unwanted)

• Friction generates heat which can:
  • Damage machinery components
  • Reduce efficiency (heat is wasted energy)
  • Cause warping or deformation
  • Lead to equipment failure
• Requires cooling systems (adding cost and complexity)

4. Energy Loss

• Kinetic energy converted to heat is lost
• Reduces mechanical efficiency
• More power input needed for same output
• Increases operational costs

5. Noise Production

• Friction creates unwanted noise in machinery
• Can be indication of excessive wear
• Requires sound dampening solutions

6. Maintenance Requirements

• Regular lubrication needed
• Parts need replacement
• Increases operational costs
• Requires downtime for maintenance

Key Formulas: Quick Reference Table

Formula Name	Mathematical Expression	Explanation	Variables
Static Friction	F_s ≤ μ_s × R	Static friction can range from zero up to limiting friction	F_s = static friction μ_s = coefficient of static friction R = normal reaction
Limiting Friction	F_L = μ_s × R	Maximum static friction when body is about to move	F_L = limiting friction μ_s = coefficient of static friction R = normal reaction
Kinetic Friction	F_k = μ_k × R	Friction force during motion	F_k = kinetic friction μ_k = coefficient of kinetic friction R = normal reaction
Rolling Friction	F_r = μ_r × (R/r)	Friction when object rolls on surface	F_r = rolling friction μ_r = coefficient of rolling friction R = normal reaction r = radius of rolling object
Coefficient of Friction	μ = F/R	Ratio of frictional force to normal reaction	μ = coefficient of friction F = frictional force R = normal reaction
Angle of Repose	μ_s = tan θ	Coefficient equals tangent of critical angle on incline	μ_s = coefficient of static friction θ = angle of incline
Normal Reaction (Horizontal)	R = mg	On horizontal surface	R = normal reaction m = mass g = acceleration due to gravity
Normal Reaction (Incline)	R = mg cos θ	Perpendicular component on inclined plane	R = normal reaction m = mass g = gravity θ = angle of incline
Force Down Incline	F = mg sin θ	Component of weight parallel to incline (down)	F = force m = mass g = gravity θ = angle
Acceleration Down Incline	a = g(sin θ - μ_k cos θ)	Net acceleration when sliding down with friction	a = acceleration g = gravity θ = angle μ_k = kinetic friction coefficient
Force to Push Up Incline	F = mg(sin θ + μ_k cos θ)	Force needed to move object up at constant velocity	F = applied force m = mass g = gravity θ = angle μ_k = kinetic friction coefficient

Important Relationships:

• μ_s > μ_k > μ_r (Static friction coefficient is always greatest)
• F_L > F_k > F_r (Limiting friction > Kinetic friction > Rolling friction)
• Coefficient of friction is dimensionless (except rolling friction coefficient which has dimension of length)
• Friction is independent of apparent area of contact
• Friction depends on materials, surface conditions, and normal force

Conclusion

Friction is a fundamental force that plays a dual role in our lives both enabling essential activities and creating challenges that require engineering solutions. Understanding the types, causes, and applications of friction is crucial not only for academic success in CBSE Class 8 Science notes but also for comprehending the physical world around us.