Class 9 Notes

Class 9 Science Notes Chapter 9 (Force and Laws of Motion) – Science Book

Philoid

Philoid

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Science
Alright class, let's focus on Chapter 9: Force and Laws of Motion. This is a fundamental chapter, not just for your Class 9 understanding, but its concepts frequently appear in various government examinations. Pay close attention to the definitions, laws, and their applications.

Chapter 9: Force and Laws of Motion - Detailed Notes

1. Force

  • Definition: A push or a pull on an object that tends to change its state of rest or of uniform motion, its direction of motion, or its shape and size.
  • Effects of Force:
    • Can start motion in a stationary object.
    • Can stop a moving object.
    • Can change the speed of a moving object.
    • Can change the direction of motion of an object.
    • Can change the shape and/or size of an object.
  • Types of Forces:
    • Balanced Forces:
      • When two or more forces acting on an object are such that their net effect (resultant force) is zero.
      • They do not cause a change in the state of rest or of uniform motion.
      • They can, however, change the shape or size of the object.
      • Example: In a tug-of-war, if both teams pull with equal force, the rope doesn't move (state of motion unchanged). A balloon pressed equally from opposite sides changes shape.
    • Unbalanced Forces:
      • When the net effect (resultant force) of all forces acting on an object is not zero.
      • They always cause a change in the state of motion (i.e., produce acceleration) or change the direction.
      • Example: Pushing a box across the floor requires an unbalanced force to overcome friction and start motion. Kicking a football changes its state from rest to motion.

2. Newton's Laws of Motion

These laws describe the relationship between force, mass, and motion.

  • Newton's First Law of Motion (Law of Inertia):

    • Statement: An object remains in its state of rest or of uniform motion in a straight line unless compelled to change that state by an applied external unbalanced force.
    • Inertia: The natural tendency of an object to resist a change in its state of rest or of uniform motion.
      • It's an inherent property of all objects.
      • Inertia depends on Mass: More massive objects have greater inertia (harder to start moving or stop once moving). Less massive objects have less inertia.
      • Mass is a quantitative measure of inertia.
    • Examples:
      • Feeling a jerk forward when a moving bus stops suddenly (your body tends to continue moving due to inertia of motion).
      • Feeling a jerk backward when a stationary bus starts suddenly (your body tends to remain at rest due to inertia of rest).
      • Dust particles falling off a carpet when it's beaten (carpet moves, dust tends to stay at rest).
      • Leaves falling from a tree when its branch is shaken vigorously.

  • Newton's Second Law of Motion:

    • Statement: The rate of change of momentum of an object is directly proportional to the applied unbalanced force in the direction of the force.
    • Momentum (p): A measure of the quantity of motion possessed by a moving body.
      • Definition: Product of mass (m) and velocity (v).
      • Formula: p = mv
      • It's a vector quantity (has both magnitude and direction, same as velocity).
      • SI Unit: kilogram-metre per second (kg m/s).
    • Mathematical Formulation:
      • Initial momentum = mu (where u is initial velocity)
      • Final momentum = mv (where v is final velocity)
      • Change in momentum = mv - mu = m(v - u)
      • Time taken = t
      • Rate of change of momentum = m(v - u) / t
      • From the statement, Force (F) ∝ Rate of change of momentum
      • F ∝ m(v - u) / t
      • We know acceleration a = (v - u) / t
      • So, F ∝ ma
      • Introducing a constant of proportionality, k: F = kma
      • The SI unit of force (Newton) is defined such that k=1.
      • Therefore, F = ma
    • Force (F): Product of mass (m) and acceleration (a).
    • SI Unit of Force: Newton (N).
      • Definition of 1 Newton: The force required to produce an acceleration of 1 m/s² in an object of mass 1 kg. (1 N = 1 kg m/s²)
    • Applications:
      • A cricketer lowers his hands while catching a fast-moving ball: This increases the time (t) over which the momentum changes to zero. Since F ∝ 1/t (for a given change in momentum), increasing the time decreases the force exerted on the hands.
      • High jumpers land on cushioned beds or sand: Increases the time taken to stop, reducing the impact force.
      • Seat belts in cars: Increase the time taken for the passenger's body to stop during a collision, reducing the force experienced.

  • Newton's Third Law of Motion:

    • Statement: To every action, there is always an equal and opposite reaction.
    • Explanation:
      • Forces always occur in pairs (action-reaction pair).
      • These two forces are always equal in magnitude.
      • These two forces are always opposite in direction.
      • Crucially, these two forces act on different objects. (Therefore, they never cancel each other out).
    • Examples:
      • Walking: We push the ground backward (action), the ground pushes us forward (reaction).
      • Recoil of a Gun: The gun exerts a forward force on the bullet (action), the bullet exerts an equal backward force on the gun (reaction/recoil).
      • Rocket Propulsion: Hot gases expelled downwards (action), rocket moves upwards (reaction).
      • Boat moving away from the shore: When you jump off a boat to the shore, you push the boat backward (action), the boat pushes you forward (reaction).

3. Conservation of Momentum

  • Statement: In the absence of any external unbalanced force acting on a system of objects, the total momentum of the system remains constant (conserved).
  • Explanation: When two (or more) objects interact (e.g., collide), their individual momenta might change, but the total momentum of the system (sum of individual momenta) before the interaction is equal to the total momentum after the interaction, provided no external force acts.
  • Formula (for two objects colliding):
    • Let two objects A and B have masses m₁ and m₂, moving with initial velocities u₁ and u₂.
    • Let their velocities after collision be v₁ and v₂.
    • Total initial momentum = m₁u₁ + m₂u₂
    • Total final momentum = m₁v₁ + m₂v₂
    • According to the law of conservation of momentum:
      m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂ (provided no external force acts)
  • Derivation Hint: Can be derived from Newton's Third Law by considering the forces exerted by colliding bodies on each other during the collision time.
  • Applications: Collisions, explosions, recoil of guns, rocket propulsion.

Key Takeaways for Exams:

  • Know the precise statements of all three laws.
  • Understand the concept of inertia and its relation to mass.
  • Understand momentum (p=mv) and its unit.
  • Be able to apply F=ma to simple problems.
  • Know the unit of Force (Newton) and its definition.
  • Understand that action-reaction forces act on different bodies.
  • Know the statement and formula for the conservation of momentum and the condition under which it applies (no external force).
  • Be able to identify the law of motion being illustrated in various examples.

Multiple Choice Questions (MCQs)

  1. A passenger in a moving train tosses a coin which falls behind him. It implies that the motion of the train is:
    a) Uniform
    b) Accelerated
    c) Retarded
    d) Along circular tracks

  2. Inertia of an object depends upon its:
    a) Velocity
    b) Shape
    c) Mass
    d) Acceleration

  3. The SI unit of momentum is:
    a) kg m/s²
    b) Newton (N)
    c) Joule (J)
    d) kg m/s

  4. When a carpet is beaten with a stick, dust comes out of it. This phenomenon can be explained by:
    a) Newton's Second Law of Motion
    b) Newton's Third Law of Motion
    c) Newton's First Law of Motion (Inertia of Rest)
    d) Law of Conservation of Momentum

  5. According to Newton's Third Law of Motion, action and reaction:
    a) Act on the same body
    b) Act on different bodies in opposite directions
    c) Act on different bodies in the same direction
    d) May act on the same or different bodies depending on the situation

  6. A force of 10 N acts on an object of mass 2 kg. The acceleration produced in the object will be:
    a) 20 m/s²
    b) 5 m/s²
    c) 0.2 m/s²
    d) 12 m/s²

  7. A goalkeeper in a game of football pulls his hands backwards after holding the ball shot at the goal. This enables the goalkeeper to:
    a) Exert larger force on the ball
    b) Increase the rate of change of momentum
    c) Decrease the rate of change of momentum
    d) Keep the ball in hands firmly

  8. An object of mass 5 kg is moving with a velocity of 10 m/s. Its momentum is:
    a) 50 kg m/s
    b) 2 kg m/s
    c) 0.5 kg m/s
    d) 50 N

  9. The law of conservation of momentum states that the total momentum of a system remains conserved if:
    a) An external force acts on the system
    b) No external force acts on the system
    c) The objects collide elastically
    d) The objects are of equal mass

  10. A rocket works on the principle of:
    a) Conservation of Mass
    b) Conservation of Energy
    c) Conservation of Momentum (and Newton's Third Law)
    d) Newton's First Law

Answers to MCQs:

  1. b) Accelerated (The coin falls behind because the train is accelerating forward while the coin, once tossed, maintains the horizontal velocity it had at the moment of tossing. The train moves ahead faster.)
  2. c) Mass
  3. d) kg m/s
  4. c) Newton's First Law of Motion (Inertia of Rest)
  5. b) Act on different bodies in opposite directions
  6. b) 5 m/s² (Using F=ma, a = F/m = 10 N / 2 kg = 5 m/s²)
  7. c) Decrease the rate of change of momentum (By increasing the time taken to stop the ball, the force exerted is reduced)
  8. a) 50 kg m/s (Using p=mv, p = 5 kg * 10 m/s = 50 kg m/s)
  9. b) No external force acts on the system
  10. c) Conservation of Momentum (and Newton's Third Law)

Study these notes thoroughly. Understanding the core concepts and how they apply to real-world examples is key for your exams. Good luck!

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