Physics Mechanics

Master mechanics concepts for RRB exam preparation with comprehensive coverage of forces, motion, energy, and their practical applications.

What is Mechanics?

Definition

Mechanics is the branch of physics that deals with the behavior of physical bodies when subjected to forces or displacements, and the subsequent effects of the bodies on their environment.

Importance in RRB Exams

• Fundamental Concepts: Basic physics principles
• Practical Applications: Real-world examples in railways
• Problem Solving: Numerical problems and calculations
• Technical Knowledge: Essential for technical posts

Kinematics

Motion and Rest

Basic Concepts

• Motion: Change in position of an object with time
• Rest: Object remains at same position relative to reference
• Reference Point: Fixed point for observing motion
• Path Length: Actual distance traveled by object
• Displacement: Shortest distance between initial and final positions

Types of Motion

Translational Motion

• Linear Motion: Motion in straight line
• Curvilinear Motion: Motion in curved path
• Random Motion: Irregular motion pattern

Rotational Motion

• Circular Motion: Motion in circular path
• Spinning Motion: Rotation about own axis
• Orbital Motion: Revolution around another object

Oscillatory Motion

• Periodic Motion: Repeated motion at regular intervals
• Simple Harmonic Motion: Special type of periodic motion
• Vibratory Motion: Back and forth motion

Motion in One Dimension

Speed and Velocity

Speed

• Definition: Distance traveled per unit time
• Formula: Speed = Distance/Time
• Units: m/s, km/h
• Scalar Quantity: Only magnitude, no direction

Velocity

• Definition: Displacement per unit time
• Formula: Velocity = Displacement/Time
• Units: m/s, km/h
• Vector Quantity: Both magnitude and direction

Average Speed and Velocity

• Average Speed: Total distance/Total time
• Average Velocity: Total displacement/Total time
• Instantaneous Speed: Speed at particular instant
• Instantaneous Velocity: Velocity at particular instant

Acceleration

Definition

• Acceleration: Rate of change of velocity
• Formula: a = (v-u)/t
• Units: m/s²
• Vector Quantity: Has both magnitude and direction

Types of Acceleration

• Positive Acceleration: Speeding up
• Negative Acceleration (Retardation): Slowing down
• Zero Acceleration: Constant velocity
• Uniform Acceleration: Equal changes in equal times

Equations of Motion

Uniform Acceleration Equations

First Equation: v = u + at

• v: Final velocity
• u: Initial velocity
• a: Acceleration
• t: Time

Second Equation: s = ut + (1/2)at²

• s: Displacement
• u: Initial velocity
• t: Time
• a: Acceleration

Third Equation: v² = u² + 2as

• v: Final velocity
• u: Initial velocity
• a: Acceleration
• s: Displacement

Fourth Equation: s = vt - (1/2)at²

• s: Displacement
• v: Final velocity
• t: Time
• a: Acceleration

Free Fall

Gravitational Acceleration

• g: 9.8 m/s² (approximated as 10 m/s² in exams)
• Direction: Always toward Earth’s center
• Independence: Same for all objects (neglecting air resistance)

Free Fall Equations

• v = gt (for free fall from rest)
• h = (1/2)gt² (height fallen)
• v² = 2gh (final velocity)

Dynamics

Force and Motion

What is Force?

Definition

• Force: Push or pull that changes or tends to change state of motion
• Effect: Can cause motion, stop motion, or change direction
• Units: Newton (N)
• Vector Quantity: Has both magnitude and direction

Effects of Force

• Motion: Can set stationary object into motion
• Stop: Can stop moving object
• Change Direction: Can change direction of moving object
• Deformation: Can change shape of object
• Rotation: Can cause rotational motion

Types of Forces

Contact Forces

• Applied Force: Force applied by direct contact
• Normal Force: Support force perpendicular to surface
• Friction Force: Force opposing relative motion
• Tension Force: Force in strings, ropes, cables
• Air Resistance: Force opposing motion through air

Non-Contact Forces

• Gravitational Force: Force of attraction between masses
• Magnetic Force: Force between magnetic poles
• Electrostatic Force: Force between charged particles
• Nuclear Force: Force holding nucleus together

Newton’s Laws of Motion

First Law (Law of Inertia)

Statement

• Object at rest: Remains at rest unless acted upon by unbalanced force
• Object in motion: Continues in motion with constant velocity unless acted upon by unbalanced force

Inertia

• Definition: Property of matter to resist change in state of motion
• Mass: Measure of inertia
• Examples: Passenger leans forward when bus stops, dust removed from carpet

Second Law (F = ma)

Statement

• Force: Equals mass times acceleration
• Direction: Force and acceleration are in same direction
• Proportionality: Acceleration is directly proportional to force and inversely proportional to mass

Mathematical Form

• F = ma: Force = mass × acceleration
• a = F/m: Acceleration = force/mass
• m = F/a: Mass = force/acceleration

Applications

• Rocket Propulsion: Newton’s third law in action
• Vehicle Motion: Engine force causes acceleration
• Braking: Friction force causes deceleration

Third Law (Action-Reaction)

Statement

• Action Force: Every action has equal and opposite reaction
• Equal Magnitude: Forces are equal in magnitude
• Opposite Direction: Forces are opposite in direction
• Different Bodies: Forces act on different bodies

Examples

• Walking: Foot pushes ground backward, ground pushes foot forward
• Rocket: Hot gases pushed down, rocket pushed up
• Swimming: Water pushed backward, swimmer moves forward

Friction

What is Friction?

Definition

• Friction: Force that opposes relative motion between surfaces in contact
• Nature: Always opposes motion or tendency of motion
• Dependence: Depends on nature of surfaces and normal force

Types of Friction

Static Friction

• Definition: Friction when object is at rest
• Maximum: Has maximum value (limiting friction)
• Self-adjusting: Adjusts to applied force up to maximum

Kinetic Friction

• Definition: Friction when object is in motion
• Constant: Remains constant for given surfaces
• Less than Static: Usually less than static friction

Rolling Friction

• Definition: Friction when object rolls over surface
• Minimum: Minimum type of friction
• Applications: Ball bearings, wheels

Factors Affecting Friction

Surface Nature

• Roughness: Rougher surfaces have more friction
• Materials: Different materials have different friction
• Lubrication: Reduces friction between surfaces

Normal Force

• Directly Proportional: Friction increases with normal force
• Weight: Heavier objects have more friction
• Surface Pressure: Pressure affects friction

Methods to Reduce Friction

Lubrication

• Oil/Grease: Reduces direct contact
• Ball Bearings: Convert sliding to rolling
• Air Cushion: Separates surfaces with air

Surface Treatment

• Polishing: Makes surfaces smoother
• Coating: Applies low-friction materials
• Streamlining: Reduces air resistance

Work and Energy

Work

Definition

• Work: Force × displacement in direction of force
• Formula: W = F × s × cosθ
• Units: Joule (J) = Newton × meter (N·m)
• Scalar Quantity: Only magnitude, no direction

Conditions for Work

1. Force must act on object
2. Object must be displaced
3. Force must have component in direction of displacement

Types of Work

Positive Work

• Angle: 0° ≤ θ < 90°
• Direction: Force and displacement in same direction
• Examples: Pushing object forward, lifting object upward

Negative Work

• Angle: 90° < θ ≤ 180°
• Direction: Force and displacement in opposite directions
• Examples: Friction, braking, lowering object

Zero Work

• Angle: θ = 90°
• Direction: Force perpendicular to displacement
• Examples: Carrying load horizontally, satellite in circular orbit

Energy

What is Energy?

Definition

• Energy: Capacity to do work
• Units: Joule (J)
• Scalar Quantity: Only magnitude
• Conservation: Energy cannot be created or destroyed

Forms of Energy

Kinetic Energy

• Definition: Energy possessed by moving object
• Formula: KE = (1/2)mv²
• Factors: Depends on mass and velocity
• Work-Energy Theorem: Work done = change in kinetic energy

Potential Energy

• Definition: Energy possessed by object due to position or configuration
• Gravitational PE: PE = mgh
• Elastic PE: Energy in stretched/compressed springs
• Factors: Depends on mass, height, and gravity

Mechanical Energy

• Definition: Sum of kinetic and potential energy
• Formula: ME = KE + PE
• Conservation: Remains constant if no non-conservative forces

Power

Definition

• Power: Rate of doing work or rate of energy transfer
• Formula: P = W/t = F×v
• Units: Watt (W) = Joule/second (J/s)
• Average Power: Total work/Total time

Momentum

Linear Momentum

Definition

• Momentum: Product of mass and velocity
• Formula: p = mv
• Units: kg·m/s
• Vector Quantity: Has both magnitude and direction

Properties

• Conservation: Total momentum remains constant in isolated system
• Additivity: Momenta add vectorially
• Relation to Force: Force = rate of change of momentum

Conservation of Momentum

Law of Conservation

• Statement: Total momentum of isolated system remains constant
• Condition: No external unbalanced force acts on system
• Applications: Collisions, explosions, rocket propulsion

Collisions

Elastic Collisions

• Definition: Both momentum and kinetic energy conserved
• Examples: Billiard balls, atomic collisions
• Characteristics: No energy loss, perfect rebound

Inelastic Collisions

• Definition: Only momentum conserved, kinetic energy not conserved
• Examples: Car crashes, lump of clay hitting wall
• Energy Loss: Converted to heat, sound, deformation

Perfectly Inelastic Collisions

• Definition: Objects stick together after collision
• Maximum Energy Loss: Maximum kinetic energy loss
• Examples: Two cars sticking together after crash

Circular Motion

Uniform Circular Motion

Characteristics

• Speed: Constant speed
• Velocity: Changing direction
• Acceleration: Centripetal acceleration toward center
• Force: Centripetal force toward center

Centripetal Force

• Definition: Force toward center of circular path
• Formula: F = mv²/r
• Direction: Always toward center
• Examples: Tension in string, gravitational force

Centripetal Acceleration

• Definition: Acceleration toward center of circular path
• Formula: a = v²/r = ω²r
• Direction: Always toward center
• Effect: Changes direction of velocity

Applications of Circular Motion

Railway Curves

• Banking: Tracks tilted to provide centripetal force
• Speed Limit: Maximum safe speed for given radius
• Superelevation: Height difference between inner and outer rails

Satellites

• Orbital Motion: Balance between gravity and inertia
• Orbital Velocity: Required speed for circular orbit
• Geostationary: Matches Earth’s rotation

Gravitation

Universal Law of Gravitation

Statement

• Force: Proportional to product of masses
• Inverse Square: Inversely proportional to square of distance
• Formula: F = G(m₁m₂)/r²
• G: Universal gravitational constant (6.67×10⁻¹¹ N·m²/kg²)

Acceleration Due to Gravity

Variation of g

• Altitude: Decreases with height
• Depth: Decreases with depth (linearly)
• Latitude: Maximum at poles, minimum at equator
• Earth’s Rotation: Effective g reduced by centrifugal force

Escape Velocity

Definition

• Escape Velocity: Minimum velocity to escape gravitational field
• Formula: v = √(2GM/R)
• Earth: 11.2 km/s
• Factors: Depends on mass and radius of planet

Simple Machines

Types of Simple Machines

Lever

• Components: Fulcrum, effort, load
• Classes: First, second, third class
• Mechanical Advantage: Ratio of output force to input force
• Examples: Crowbar, scissors, seesaw

Pulley

• Types: Fixed, movable, compound
• Mechanical Advantage: Number of supporting ropes
• Applications: Lifts, cranes, elevators
• Advantage: Changes direction of force

Inclined Plane

• Purpose: Reduce effort required to raise object
• Mechanical Advantage: Length/Height
• Friction: Makes actual mechanical advantage less
• Examples: Ramps, roads, stairs

Wheel and Axle

• Components: Wheel attached to axle
• Mechanical Advantage: Radius of wheel/Radius of axle
• Applications: Steering wheel, door knob, screwdriver

Practice Questions

Question 1

A car accelerates from rest to 20 m/s in 5 seconds. Find its acceleration.

Question 2

A force of 10 N acts on a mass of 2 kg. Find the acceleration produced.

Question 3

A ball is thrown upward with velocity 20 m/s. Find maximum height reached.

Question 4

A 1000 kg car moving at 20 m/s stops in 5 seconds. Find the braking force.

Question 5

A satellite orbits Earth at altitude 400 km. If Earth’s radius is 6400 km, find orbital velocity.

Question 6

A person lifts a 10 kg box to height of 2 m. Find work done against gravity.

Question 7

A train moving at 30 m/s takes 20 seconds to stop. Find the braking distance.

Question 8

A 5 kg object moving at 4 m/s collides with 3 kg object at rest. Find velocity after collision (perfectly inelastic).

Question 9

A stone is thrown horizontally from cliff 20 m high with velocity 10 m/s. Find horizontal distance traveled.

Question 10

A simple machine has mechanical advantage 4. If effort force is 50 N, find load force.

Quick Reference

Important Formulas

Kinematics

• v = u + at
• s = ut + (1/2)at²
• v² = u² + 2as
• Average velocity = (u+v)/2

Dynamics

• F = ma
• Weight = mg
• Friction = μN
• Centripetal force = mv²/r

Work and Energy

• Work = F × s × cosθ
• KE = (1/2)mv²
• PE = mgh
• Power = W/t

Important Values

• g = 9.8 m/s² (≈ 10 m/s² for exams)
• G = 6.67 × 10⁻¹¹ N·m²/kg²
• 1 J = 1 N·m
• 1 W = 1 J/s

Common Conversions

• 1 km/h = 5/18 m/s
• 1 m/s = 18/5 km/h
• 1 kg = 1000 g
• 1 N = 1 kg·m/s²

Problem-Solving Tips

Strategy for Mechanics Problems

1. Draw Diagram: Visual representation of situation
2. Identify Given: Note all given quantities
3. Choose Formula: Select appropriate formula
4. Substitute Values: Replace variables with numbers
5. Calculate: Perform calculations carefully
6. Check Units: Ensure consistent units
7. Verify: Check if answer is reasonable

Common Mistakes to Avoid

1. Unit Mistakes: Use consistent units throughout
2. Sign Errors: Pay attention to positive/negative signs
3. Formula Selection: Use correct formula for situation
4. Vector Nature: Remember direction for vector quantities
5. Assumptions: State assumptions clearly

Railway Applications

Train Dynamics

• Traction Force: Force pulling train forward
• Braking Distance: Distance required to stop train
• Banking of Tracks: Angle for safe turning
• Coupling Forces: Forces between railway cars

Station Mechanics

• Escalators: Inclined plane applications
• Elevators: Pulley systems
• Automatic Doors: Hinge and lever mechanisms
• Signal Systems: Mechanical and electrical systems

Track Maintenance

• Track Alignment: Use of levers and rollers
• Bridge Mechanics: Load distribution principles
• Tunnel Construction: Support and arch principles

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