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Forces, Energy, and Motion

Motion and Forces​

1. Speed and Velocity​

Speed (गति):

  • Scalar (magnitude only)
  • Distance/time
  • Example: 50 km/h

Velocity (वेग):

  • Vector (magnitude + direction)
  • Displacement/time
  • Example: 50 km/h north
  • Can be negative (change in direction)

Acceleration (त्वरण):

  • Rate of change of velocity
  • Vector quantity
  • a = (v - u) ÷ t
  • Units: m/s²
  • Positive: Speeding up
  • Negative: Slowing down (deceleration)

2. Newton's Laws of Motion​

First Law (जड़त्व नियम):

  • Object at rest stays at rest
  • Moving object continues motion
  • Unless acted by unbalanced force
  • Property: Inertia (mass)
  • More mass = greater inertia

Second Law (बल नियम):

  • F = ma
  • Force causes acceleration
  • Greater force = greater acceleration
  • Greater mass = less acceleration for same force
  • Units: F in Newtons (N)

Third Law (क्रिया-प्रतिक्रिया नियम):

  • For every action, equal and opposite reaction
  • Forces occur in pairs
  • On different objects
  • Example: Walking (push back, ground pushes forward)

3. Types of Forces​

Weight (भार):

  • Gravitational force on object
  • W = mg
  • Acts downward
  • Example: 60 kg person weighs 600 N (using g = 10 m/s²)

Normal Force:

  • Perpendicular force from surface
  • Reaction to weight on horizontal
  • Equals weight on horizontal surface
  • Less than weight on incline

Friction (घर्षण):

  • Opposes motion between surfaces
  • F = μN (μ = coefficient of friction, N = normal force)
  • Static friction: Before motion (higher)
  • Kinetic friction: During motion (lower)
  • Direction opposite to motion

Tension:

  • Force in ropes, cables
  • Acts along rope
  • Same throughout rope (if massless)
  • Supporting weight creates tension

Air Resistance:

  • Friction from air
  • Increases with speed
  • Terminal velocity: Maximum speed when air resistance = weight

4. Hooke's Law​

Spring Force:

  • F = kx
  • k = spring constant (stiffness)
  • x = extension/compression
  • Restoring force (returns to original)
  • Linear relationship

Work and Energy​

1. Work (कार्य)​

Definition:

  • W = Fs cos(θ)
  • Force applied × distance in direction of force
  • Units: Joules (J) = Newton·meter
  • No work if no displacement
  • No work if force perpendicular to motion

Example:

  • Lifting weight vertically: Work = Force × Distance
  • Pushing object horizontally: Work = Force × Distance
  • Holding weight still: No work (no motion)

2. Energy (ऊर्जा)​

Definition:

  • Capacity to do work
  • Many forms

Kinetic Energy (गतिज):

  • Energy of moving object
  • KE = ½mv²
  • Increases with speed squared
  • Use work-energy theorem to calculate

Gravitational Potential Energy:

  • Energy due to height
  • PE = mgh (near Earth)
  • h = height above reference
  • Increases with height

Elastic Potential Energy:

  • Energy stored in springs
  • EPE = ½kx²
  • Stored when compressed/extended
  • Released when returns to original

Internal/Thermal Energy:

  • Random motion of particles
  • Increasing temperature

Energy Conservation:

  • Total energy stays constant
  • Converts between forms
  • Dissipated as heat through friction

3. Work-Energy Theorem​

Definition:

  • Work done = Change in kinetic energy
  • W = ΔKE = ½mvf² - ½mvi²
  • Relates force, displacement, velocity

4. Power (शक्ति)​

Definition:

  • P = W ÷ t
  • Rate of doing work
  • Units: Watts (W) = Joules/second
  • Also: P = Fv (force × velocity)

Example:

  • Same work in less time = more power
  • Climbing stairs quickly = high power
  • Climbing slowly = low power

Momentum​

1. Momentum (संवेग)​

Definition:

  • p = mv
  • Mass × Velocity
  • Vector quantity
  • Units: kg·m/s
  • Larger mass or faster = greater momentum

Newton's Second Law (Alternative Form):

  • F = Δp ÷ t
  • Rate of change of momentum
  • Impulse: FΔt = Δp
  • Force × time = change in momentum

2. Conservation of Momentum​

Principle:

  • Total momentum before = Total momentum after
  • In closed system (no external forces)
  • Applies to collisions and explosions

Example - Collision:

  • Two cars collide:
    • Before: m₁v₁ + m₂v₂
    • After: (m₁ + m₂)v
    • Total momentum conserved

Types of Collisions:

Elastic Collision:

  • Kinetic energy conserved
  • Objects bounce apart
  • Momentum conserved
  • Example: Billiard balls

Inelastic Collision:

  • Kinetic energy not conserved
  • Objects may stick
  • Momentum still conserved
  • Energy lost as heat, sound, deformation

Simple Machines​

1. Levers​

Classes:

  • Class 1: Fulcrum between effort and load (seesaw)

    • Effort can be less than load
    • Example: Crowbar

  • Class 2: Load between fulcrum and effort (wheelbarrow)

    • Effort always less than load
    • Mechanical advantage > 1

  • Class 3: Effort between fulcrum and load (tweezers)

    • Effort greater than load
    • Large movement for small effort

Mechanical Advantage:

  • MA = Load ÷ Effort
  • = Effort arm length ÷ Load arm length
  • MA > 1: Advantage in force
  • MA < 1: Advantage in distance/speed

2. Other Simple Machines​

Inclined Plane:

  • Reduces effort needed
  • Trade-off: Distance longer
  • Example: Ramp

Pulley:

  • Changes direction of force
  • Movable pulley reduces force needed
  • Number of supporting ropes = MA
  • Example: Lifting weight

Wheel and Axle:

  • Wheel is large lever
  • Turning outer wheel moves axle
  • MA = radius of wheel ÷ radius of axle
  • Example: Steering wheel

Screw:

  • Inclined plane wrapped around cylinder
  • Small rotation creates large linear movement
  • Mechanical advantage high but velocity advantage low

Wedge:

  • Converts downward force to sideways force
  • Sharpness affects effectiveness
  • Example: Axe, knife

Pressure and Density​

1. Pressure (दाब)​

Definition:

  • P = F ÷ A
  • Force per unit area
  • Units: Pascals (Pa) = N/m²
  • Also: Atmospheres, psi, bars

Example:

  • Needle (small area) = high pressure
  • Flat shoe (large area) = low pressure
  • Same force, different pressure

Pressure in Fluids:

  • Acts in all directions
  • Increases with depth
  • P = ρgh (at depth h)
  • ρ = density, g = 9.8 m/s², h = depth

2. Density (घनत्व)​

Definition:

  • ρ = m ÷ V
  • Mass per unit volume
  • Units: kg/m³
  • Constant for substance at given conditions

Buoyancy:

  • Upward force on submerged object
  • Buoyant force = weight of fluid displaced
  • Object floats if density < fluid density
  • Object sinks if density > fluid density

Summary​

Forces and energy explain:

  • Motion: How objects move under forces
  • Work and Energy: Transformations and conservation
  • Momentum: Conservation in collisions
  • Simple Machines: How to reduce effort needed
  • Pressure: Force distributed over area
  • Density: Mass per volume

These concepts explain everything from vehicle motion to planetary orbits.