Class 9 Notes

Class 9 Science Notes Chapter 9 (Chapter 9) – Examplar Problem (English) Book

Philoid

Philoid

— 7 min read

Examplar Problem (English)
Alright class, let's focus on Chapter 9: Force and Laws of Motion from your NCERT Exemplar. This is a fundamental chapter, crucial not just for your Class 9 understanding but also as a base for many concepts tested in government exams. Pay close attention as we break it down.

Chapter 9: Force and Laws of Motion - Detailed Notes for Exam Preparation

1. Force

  • Definition: A push or a pull on an object that results from the object's interaction with another object. Force is required to change the state of motion or the shape/size of an object.
  • 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 a moving 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) is zero. Balanced forces do not cause a change in the state of rest or uniform motion. They can, however, change the shape or size (e.g., squeezing a balloon).
    • Unbalanced Forces: When the net effect of all forces acting on an object is not zero. An unbalanced force is required to change the state of motion (i.e., accelerate the object) or direction.
  • Unit of Force:
    • SI Unit: Newton (N). One Newton is defined as the force required to accelerate a mass of 1 kg by 1 m/s². (1 N = 1 kg m/s²)
    • CGS Unit: Dyne. (1 N = 10⁵ Dyne)
  • Force is a Vector Quantity: It has both magnitude (strength) and direction.

2. Newton's Laws of Motion

These three laws form the bedrock of classical mechanics.

  • 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 any change in its state of rest or uniform motion.
      • Inertia is directly proportional to the mass of the object. Heavier objects have more inertia.
      • Types of Inertia:
        • Inertia of Rest: Tendency to resist changes from a state of rest. (Example: Passengers jerk backward when a bus starts suddenly; dust particles fall off a carpet when beaten).
        • Inertia of Motion: Tendency to resist changes from a state of uniform motion. (Example: Passengers jerk forward when a moving bus stops suddenly; an athlete runs some distance before taking a long jump).
        • Inertia of Direction: Tendency to resist changes in the direction of motion. (Example: Mud flying off a rotating wheel tangentially; sparks from a grinding stone).
  • Newton's Second Law of Motion (Law of Momentum):
    • Momentum (p): The quantity of motion possessed by a body. It is the product of the object's mass (m) and its velocity (v).
      • Formula: p = mv
      • SI Unit: kg m/s
      • Momentum is a vector quantity, having the same direction as the velocity.
    • Statement: The rate of change of momentum of an object is directly proportional to the applied unbalanced force and takes place in the direction in which the force acts.
    • Mathematical Formulation:
      • Initial momentum (p₁) = mu (where u = initial velocity)
      • Final momentum (p₂) = mv (where v = final velocity)
      • Change in momentum (Δp) = p₂ - p₁ = mv - mu = m(v - u)
      • Time taken = t
      • Rate of change of momentum = Δp / t = m(v - u) / t
      • According to the law, Force (F) ∝ Rate of change of momentum
      • F ∝ m(v - u) / t
      • Since acceleration (a) = (v - u) / t, we have F ∝ ma
      • Introducing a constant of proportionality, k: F = kma
      • The units of force, mass, and acceleration are chosen such that k = 1.
      • Therefore, F = ma (This is the common form, derived from the momentum definition).
    • Definition of 1 Newton: From F=ma, if m=1 kg and a=1 m/s², then F = 1 N.
    • Applications:
      • Catching a cricket ball: The fielder increases the time (t) duration of the impact by pulling hands back, reducing the rate of change of momentum (Δp/t), and hence reducing the force (F) exerted by the ball on the hands.
      • High jump/Long jump: Athletes land on cushioned beds or sand pits to increase the time of impact, reducing the force experienced.
      • Seat belts: Increase the time taken for the passenger's momentum to reduce to zero during a collision, reducing the force exerted on the passenger.
    • Impulse (J): The change in momentum produced by a force acting for a short duration. Impulse = Force × Time = Change in Momentum (J = FΔt = Δp). Unit: Ns or kg m/s.
  • Newton's Third Law of Motion (Law of Action-Reaction):
    • Statement: To every action, there is always an equal and opposite reaction.
    • Key Characteristics:
      • Forces always occur in pairs (Action and Reaction).
      • These two forces are equal in magnitude.
      • These two forces act in opposite directions.
      • Crucially, these two forces act on different objects. (This is why they don't cancel each other out in terms of causing motion for a single object).
      • Action and reaction occur simultaneously.
    • Examples:
      • Walking: We push the ground backward (action), the ground pushes us forward (reaction).
      • Rocket Propulsion: Hot gases expelled downwards (action), rocket moves upwards (reaction).
      • Recoil of a Gun: Gun exerts a forward force on the bullet (action), bullet exerts an equal backward force on the gun (reaction - recoil).
      • Boat and Shore: When jumping off a boat, you push the boat backward (action), the boat pushes you forward (reaction).

3. Law of Conservation of Momentum

  • Statement: In an isolated system (i.e., when no external unbalanced force acts on the system), the total linear momentum of the system remains constant or conserved.
  • Explanation: Consider two objects (A and B) with masses m₁ and m₂ moving with initial velocities u₁ and u₂. They collide for a time t and their final velocities become v₁ and v₂.
    • During collision, A exerts force F₁₂ on B (Action). B exerts force F₂₁ on A (Reaction).
    • By Newton's Third Law: F₁₂ = - F₂₁
    • Using Newton's Second Law (F = ma = m(v-u)/t):
      • F₁₂ = m₂(v₂ - u₂) / t
      • F₂₁ = m₁(v₁ - u₁) / t
    • Substituting into the Third Law equation: m₂(v₂ - u₂) / t = - [m₁(v₁ - u₁) / t]
    • Cancelling 't': m₂(v₂ - u₂) = - m₁(v₁ - u₁)
    • m₂v₂ - m₂u₂ = - m₁v₁ + m₁u₁
    • Rearranging: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
    • Total initial momentum = Total final momentum
  • Applications: Collisions, explosions (like firing a bullet from a gun), rocket propulsion. It helps calculate velocities after interactions.

Key Takeaways for Exams:

  • Clearly distinguish between balanced and unbalanced forces and their effects.
  • Understand inertia and its direct relationship with mass. Be ready with examples for different types of inertia.
  • Memorize the precise statements of all three laws.
  • Understand the concept of momentum (p=mv) and its vector nature.
  • Be able to derive F=ma from the second law's momentum statement.
  • Know the applications of the second law (increasing time to reduce force).
  • Crucially understand that action-reaction forces act on different bodies.
  • Memorize the statement and formula for the conservation of momentum and know the condition (no external unbalanced force).
  • Be comfortable with units (N, kg m/s).
  • Practice numerical problems based on F=ma and conservation of momentum.

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) Accelerated
    (b) Uniform
    (c) Retarded
    (d) Along circular tracks

  2. An object of mass 2 kg is sliding with a constant velocity of 4 m/s on a frictionless horizontal table. The force required to keep the object moving with the same velocity is:
    (a) 32 N
    (b) 0 N
    (c) 2 N
    (d) 8 N

  3. According to Newton's third law of motion, action and reaction:
    (a) always act on the same body
    (b) always act on different bodies in opposite directions
    (c) have same magnitude and directions
    (d) act on either body at normal to each other

  4. 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) Reduce the force exerted by the ball on hands
    (c) Increase the rate of change of momentum
    (d) Decrease the impulse experienced

  5. The inertia of an object tends to cause the object to:
    (a) increase its speed
    (b) decrease its speed
    (c) resist any change in its state of motion
    (d) decelerate due to friction

  6. A water tanker filled up to 2/3 of its height is moving with a uniform speed. On sudden application of the brake, the water in the tank would:
    (a) Move backward
    (b) Move forward
    (c) Be unaffected
    (d) Rise upwards

  7. What is the momentum of an object of mass 'm' moving with a velocity 'v'?
    (a) (mv)²
    (b) mv²
    (c) ½ mv²
    (d) mv

  8. A rifle of mass 4 kg recoils with a velocity of 5 m/s when a bullet of mass 20 g is fired from it. What is the initial velocity of the bullet (muzzle velocity)?
    (a) 100 m/s
    (b) 500 m/s
    (c) 1000 m/s
    (d) 2000 m/s

  9. Which of the following has the largest inertia?
    (a) A pin
    (b) An ink pot
    (c) Your physics book
    (d) Your school bag (assuming it's full)

  10. The SI unit of force is Newton (N). It is equivalent to:
    (a) kg m/s
    (b) kg m²/s²
    (c) kg m/s²
    (d) kg/m s

Answers to MCQs:

  1. (a) Accelerated (If the train accelerates, the passenger moves forward with the train, but the coin, once tossed, continues its horizontal velocity from the moment it was tossed. Since the train speeds up, it moves further ahead, making the coin appear to fall behind relative to the passenger).
  2. (b) 0 N (According to Newton's First Law, if an object is moving with constant velocity (uniform motion) and there's no friction, no net force is required to maintain that state).
  3. (b) always act on different bodies in opposite directions
  4. (b) Reduce the force exerted by the ball on hands (By increasing the time interval over which the momentum changes, F = Δp/Δt).
  5. (c) resist any change in its state of motion
  6. (b) Move forward (Due to inertia of motion, the water tends to continue moving forward when the tanker stops).
  7. (d) mv
  8. (c) 1000 m/s (Using conservation of momentum: M_rifle * V_rifle + m_bullet * v_bullet = 0 (initial momentum is zero). Note: recoil velocity is opposite, so use -5 m/s or assign opposite signs. Mass of bullet = 0.02 kg. (4 kg * (-5 m/s)) + (0.02 kg * v_bullet) = 0 => -20 + 0.02 * v_bullet = 0 => v_bullet = 20 / 0.02 = 1000 m/s).
  9. (d) Your school bag (assuming it's full) (Inertia depends on mass; the school bag likely has the largest mass among the options).
  10. (c) kg m/s² (From F=ma, unit of F = unit of m × unit of a = kg × m/s²).

Study these notes thoroughly. Understand the concepts behind the laws and their applications. Practice solving problems based on the formulas. Good luck!

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