Laws of Motion Chapter Notes | Physics Class 9 ICSE PDF Download

Contact and Non-Contact Forces

Force

• Force is a physical cause that changes or tends to change the state of rest, motion, size, or shape of a body.
• Effects of force:
  • Changes the state of rest or motion (e.g., pushing a broom moves trash, kicking a ball sets it in motion).
  • Alters size or shape (e.g., stretching a spring increases its length, hammering silver makes a thin foil).
• For rigid objects, force causes motion without changing dimensions.
• For non-rigid objects, force can change dimensions and cause motion.
• Forces are classified into:
  • Contact forces: Require physical contact.
  • Non-contact forces: Act without physical touch.

Contact Forces

Contact forces occur when bodies physically touch each other.

Examples:

• Frictional force: Opposes motion when a body slides or rolls on a rough surface (e.g., a book sliding on a table experiences friction acting opposite to its motion).
• Normal reaction force: Equal and opposite force exerted by a surface perpendicular to a body’s weight (e.g., a block on a palm is held by an upward force equal to its downward weight).
• Tension force: Force in a string pulling a suspended body upward, balancing its weight (e.g., a body hanging from a string experiences tension upward).
• Spring force: Restoring force opposite to displacement when a spring is stretched or compressed (e.g., a stretched spring pulls objects inward).
• Collision force: Equal and opposite forces during a collision (e.g., two bodies colliding push each other, causing them to move apart).

Example: When a book is pushed on a table, the frictional force opposes its motion, slowing it down. If the table exerts a normal reaction force equal to the book’s weight, the book stays in place vertically.

Non-Contact Forces

Non-contact forces act without physical contact, also called forces at a distance.

Examples:

• Gravitational force: Attractive force between masses (e.g., Earth pulls a ball downward, causing it to fall).
• Electrostatic force: Force between charged objects, attractive or repulsive (e.g., a charged comb attracts paper bits).
• Magnetic force: Force between magnetic poles, attractive or repulsive (e.g., a magnet attracts an iron nail).

Characteristics of non-contact forces:

• Gravitational force is always attractive; electrostatic and magnetic forces can be attractive or repulsive.
• Magnitude decreases with increased distance, inversely proportional to the square of the distance (doubling distance reduces force to one-fourth).

Example: When a ball rolls down a tilted table, the gravitational force pulls it downward, causing motion without physical contact.

Newton’s First Law of Motion and Inertia

Newton’s First Law of Motion

• Force is the cause of motion, required to start or change motion.
• Galileo’s findings: No force is needed to keep a body moving if friction is absent; a body continues in its state of rest or uniform motion unless acted upon by an external force.
• Newton’s First Law: A body remains at rest or in uniform motion in a straight line unless an external force acts on it.
• Qualitative aspects:
  • Defines inertia: A body resists changes to its state of rest or motion.
  • Defines force: An external cause that changes a body’s state of rest or motion.
• Example: A book on a table stays at rest due to inertia until pushed, demonstrating that it resists motion without an external force.

Mass and Inertia

• Inertia: Property of a body to resist changes in its state of rest or motion, dependent on mass.
• Greater mass means greater inertia, making it harder to move or stop a body.
• Examples:
  • A cricket ball (more mass) is harder to move or stop than a tennis ball (less mass) when equal force is applied.
  • A loaded trolley requires more force to start or stop than an unloaded one.

Kinds of Inertia and Its Examples as Illustration of First Law

Inertia types:

• Inertia of rest: A body at rest resists motion.
• Inertia of motion: A moving body resists changes to its motion.

Inertia of rest examples:

• Passenger falls backward when a train starts suddenly: Lower body moves with the train, upper body remains at rest due to inertia.
• Dust falls from a carpet when beaten: Carpet moves, dust stays at rest, falling due to gravity.
• Fruits fall when tree branches are shaken: Branches move, fruits remain at rest, detaching due to gravity.
• Lowest coin moves in a carrom pile when struck: Pile stays intact due to inertia of rest.
• Coin on a card falls into a tumbler when the card is flicked: Coin remains at rest, falling due to gravity.
• Sliding train doors open when the train starts: Frame moves, doors remain at rest, sliding open.

Inertia of motion examples:

• Bicycle continues moving after pedaling stops: Motion persists until friction stops it.
• Passenger falls forward when jumping from a moving train: Upper body continues moving due to inertia, causing a fall.
• Passenger leans forward when a car stops suddenly: Upper body remains in motion.
• Athlete runs before a long jump: Body in motion aids the jump.
• Ball thrown upward in a moving train returns to the thrower: Ball maintains forward motion due to inertia.

Linear Momentum and Newton’s Second Law of Motion

Linear Momentum (p = m v)

• Linear momentum: Product of a body’s mass and velocity, denoted by p.
• Formula: p = m v
• Vector quantity, direction same as velocity.
• Units:
  • S.I.: kg m s^-1
  • C.G.S.: g cm s^-1
• Example: A 5 kg ball moving at 2 m s^-1 has momentum p = 5 × 2 = 10 kg m s^-1, indicating the force needed to stop it depends on both mass and velocity.

Change in Momentum (Δp = m Δv)

• Change in momentum: Δp = Δ(m v)
• If mass is constant, Δp = m Δv, where Δv is the change in velocity.
• Valid when velocity is much less than the speed of light (v << c), as mass may increase at high velocities.

Rate of Change of Momentum

• Rate of change of momentum: (m(v - u))/t, where u is initial velocity, v is final velocity, t is time.
• Since acceleration a = (v - u)/t, rate of change of momentum = m a (if mass is constant).
• Alternative: Δp/Δt = m (Δv/Δt) = m a

Newton’s Second Law of Motion (Derivation of F = m a)

• Newton’s Second Law: Force is proportional to the rate of change of momentum, in the direction of the force.
• Acceleration (a) is directly proportional to force (F) for constant mass: a ∝ F
• Force is proportional to mass (m) for constant acceleration: F ∝ m
• Combining: F = K m a, where K = 1 when units are chosen such that 1 unit force produces 1 unit acceleration in 1 unit mass.
• Final form: F = m a
• For constant force, a ∝ 1/m (acceleration inversely proportional to mass).
• Example: A 15 N force on a 2 kg body produces a = F/m = 15/2 = 7.5 m s^-2, showing force causes acceleration proportional to mass.

C.G.S. and S.I. Units of Force

• Force: F = m a
• S.I. unit: Newton (N), 1 N = 1 kg × 1 m s^-2
• C.G.S. unit: Dyne, 1 dyne = 1 g × 1 cm s^-2
• Relation: 1 N = 10⁵ dyne

Newton’s Second Law in Terms of Rate of Change of Momentum

• Force equals rate of change of momentum: F = Δp/Δt = Δ(m v)/Δt
• If mass is constant: F = m (Δv/Δt) = m a
• Conditions for F = m a:
  • Velocity much less than speed of light (v << c).
  • Mass remains constant.
    
• Examples:
  • Catching a ball: Pulling hands back increases stopping time, reducing force (F = Δp/Δt).
  • Athlete landing on sand: Longer stopping time reduces force on feet.
  • Glass breaking on hard floor: Short stopping time increases force, causing breakage; carpet increases time, reducing force.

Newton’s Third Law of Motion

Newton’s Third Law of Motion

• Statement: To every action, there is an equal and opposite reaction.
• Action and reaction act on different bodies, are equal in magnitude, opposite in direction, and occur simultaneously (F_AB = -F_BA).
• Examples:
  • Book on table: Book’s weight (action) downward, table’s reaction upward.
  • Pushing a wall: Hand’s force (action) on wall, wall’s force (reaction) on hand.
  • Boat moving: Boatman pushes water backward (action), water pushes boat forward (reaction).
  • Firing a bullet: Gun exerts force on bullet (action), bullet causes gun recoil (reaction).
  • Rocket motion: Rocket expels gases backward (action), gases push rocket forward (reaction).
  • Walking: Foot pushes ground backward (action), ground pushes foot forward (reaction).
  • Stepping off a boat: Foot pushes boat (action), boat moves away (reaction).
  • Catching a ball: Ball exerts force on hand (action), hand exerts force on ball (reaction).
• Example: When firing a gun, the bullet moves forward (action), and the gun recoils backward (reaction), illustrating equal and opposite forces on different bodies.

Gravitation

Universal Law of Gravitation

• Gravitational force: Attractive force between two masses due to their mass.
• Newton’s Law of Gravitation: Force is directly proportional to the product of masses and inversely proportional to the square of the distance between them.
• Formula: F = G (m₁ m₂ / r²)
• G: Universal gravitational constant, G = 6.67 × 10^-11 N m² kg^-2.
• Force is along the line joining the masses, equal in magnitude, opposite in direction (F₁₂ = -F₂₁).
• Characteristics:
  • Always attractive.
  • Proportional to m₁ m₂.
  • Inversely proportional to r² (doubling distance reduces force to one-fourth).
  • Significant for heavenly bodies, negligible for ordinary objects.
• Importance: Explains planetary motion, moon’s orbit, and free fall.
• Example: The gravitational force between two 1 kg masses 1 m apart is F = (6.67 × 10^-11) × 1 × 1 / 1² = 6.67 × 10^-11 N, showing its small magnitude for ordinary objects.

Force Due to Gravity

• Force due to gravity: Earth’s attractive force on a body, acting downward at the body’s center of gravity.
• Formula: F = G (M m / R²), where M is Earth’s mass, R is Earth’s radius.
• Example: For m = 1 kg, F = (6.67 × 10^-11 × 5.96 × 10²⁴ × 1) / (6.37 × 10⁶)² = 9.8 N.
• Earth attracts objects, but its large inertia prevents noticeable movement toward the object.

Acceleration Due to Gravity

• Acceleration due to gravity (g): Rate of velocity increase in a freely falling body due to Earth’s gravitational pull.
• Vector quantity, directed downward, S.I. unit: m s^-2.
• Galileo’s findings: All bodies fall with the same acceleration in a vacuum, regardless of mass, size, or shape.
• Average value: g = 9.8 m s^-2 on Earth’s surface, varies by location (less at equator, more at poles).
• Relation: g = G M / R²
• Example: On Earth, g = (6.67 × 10^-11 × 5.96 × 10²⁴) / (6.37 × 10⁶)² = 9.8 m s^-2; on Moon, g = 1.6 m s^-2 (1/6th of Earth’s).

Free Fall

• Free fall: Motion under gravity, e.g., falling from a height or thrown upward.
• Equations for free fall (u = 0, a = g):
  • v = g t
  • h = (1/2) g t²
  • v² = 2 g h
• With initial velocity u:
  • v = u + g t
  • h = u t + (1/2) g t²
  • v² = u² + 2 g h
• Thrown upward (a = -g):
  • v = u - g t
  • h = u t - (1/2) g t²
  • v² = u² - 2 g h
• At highest point (v = 0): h_max = u² / 2 g, time to highest point t = u / g, total time = 2 u / g.
• Example: A stone dropped from 78.4 m takes t = √(78.4 / 4.9) = 4 s to reach the ground, with velocity v = 9.8 × 4 = 39.2 m s^-1.

Mass and Weight

• Mass: Quantity of matter in a body, scalar, S.I. unit: kg, constant, measured by a physical balance.
• Weight: Force of Earth’s gravity on a body, vector, downward, S.I. unit: N.
• Relation: W = m g
• Weight varies with g, mass remains constant.
• Comparison:
  • Mass: Measures matter, scalar, kg, constant, measured by physical balance HXbalance.
  • Weight: Force of gravity, vector, N, varies with g, measured by spring balance.
• Example: A 10 kg body on Earth (g = 9.8 m s^-2) weighs W = 10 × 9.8 = 98 N; on the Moon (g = 1.6 m s^-2), W = 16 N.

Gravitational Units of Force

• M.K.S. unit: Kilogram force (kgf), 1 kgf = 9.8 N (force on 1 kg mass).
• C.G.S. unit: Gram force (gf), 1 gf = 980 dyne.
• Approximation: 1 kgf ≈ 10 N, 1 N ≈ 0.1 kgf or 100 gf.
• Example: Holding 100 g feels like 1 N force (100 g × 9.8 m s^-2).