StudyNotesHub

Chapter 8: Force and Laws of Motion

Explore Science with Fun & Easy Notes for Class 9!

1. Balanced and Unbalanced Forces

  • Force Definition: A push, pull, or hit that changes an object’s state of motion, velocity, or shape (Fig. 8.1, 8.2).
  • Balanced Forces:
    • Equal forces in opposite directions (e.g., pulling block with strings X and Y equally, Fig. 8.3).
    • Result: No change in motion or rest state.
  • Unbalanced Forces:
    • Unequal forces cause motion in the direction of the greater force (e.g., block moves if string X pulls harder).
    • Example: Pushing a box on a rough floor (Fig. 8.4):
      • Small push: Friction balances, no motion.
      • Larger push: Friction still balances, no motion.
      • Hard push: Unbalanced force, box moves.
  • Friction: Opposes motion between surfaces (e.g., box on floor, bicycle slowing when pedaling stops).
  • Motion and Force:
    • Uniform motion: Balanced forces (no net force).
    • Accelerated motion: Unbalanced force required.
    • No force: Object maintains velocity (or rest).

Activity: Try pushing a book on a table with varying force!

2. First Law of Motion

  • Statement: An object remains at rest or in uniform motion unless acted upon by an unbalanced force.
  • Inertia: Tendency to resist change in motion state (also called Law of Inertia).
  • Galileo’s Observations (Fig. 8.5):
    • Marble on inclined plane: Velocity increases downhill, decreases uphill.
    • Frictionless plane: Marble travels forever at constant speed if slope is zero.
    • Conclusion: No net force needed for uniform motion; unbalanced force changes motion.
  • Examples:
    • Braking car: Body moves forward due to inertia; safety belts reduce impact.
    • Bus starting: Body falls backward as feet move with bus, but upper body resists.
    • Car turning: Body slips sideways due to inertia.
  • Activities:
    • Activity 8.1: Hit bottom carom coin (Fig. 8.6); others fall vertically due to inertia.
    • Activity 8.2: Flick card under coin (Fig. 8.7); coin falls into glass due to inertia.
    • Activity 8.3: Spin with water-filled tumbler; water spills due to inertia.

Activity: Flick a card under a coin and watch inertia in action!

3. Inertia and Mass

  • Inertia: Resistance to change in motion state; depends on mass.
  • Mass: Measure of inertia; heavier objects have more inertia (SI unit: kg).
  • Examples:
    • Easier to push empty box than full one.
    • Football flies farther than a stone when kicked.
    • Activity 8.2: Five-rupee coin needs more force than one-rupee coin.
  • Questions:
    • More Inertia:
      • Stone > rubber ball (stone is denser).
      • Train > bicycle (train is heavier).
      • Five-rupee coin > one-rupee coin (heavier).
    • Football Example: Velocity changes 4 times (kick, kick, catch, kick); agents are players’ feet and goalkeeper’s hands.
    • Leaves Detach: Shaking tree; leaves’ inertia resists motion, detaching them.
    • Bus Motion: Forward fall (braking) due to inertia; backward fall (acceleration) as body resists motion.

Activity: Compare pushing a light vs. heavy object!

4. Second Law of Motion

  • Statement: Rate of change of momentum is proportional to the applied unbalanced force, in the direction of the force.
  • Momentum:
    • Definition: Product of mass and velocity (\( p = mv \)); vector, same direction as velocity.
    • SI Unit: kg·m/s.
  • Mathematical Formulation:
    • Force: \( F = ma \), where \( a = \frac{v - u}{t} \) (m = mass, v = final velocity, u = initial velocity, t = time).
    • Unit: Newton (N) = kg·m/s²; 1 N gives 1 m/s² to 1 kg.
    • Derivation: \( F = \frac{m(v - u)}{t} \); if F = 0, v = u (first law).
  • Examples:
    • Cricket ball hurts more than table tennis ball due to higher momentum.
    • Fielder pulls hands back to reduce force by increasing stopping time (Fig. 8.8).
    • High jump: Cushioned bed reduces force by increasing stopping time.
  • Worked Examples:
    • Example 8.1: 5 kg, 3 m/s to 7 m/s in 2 s; F = 10 N; for 5 s, v = 13 m/s.
    • Example 8.2: 2 kg at 5 m/s² (F = 10 N) > 4 kg at 2 m/s² (F = 8 N).
    • Example 8.3: Car 1000 kg, 108 km/h to 0 in 4 s; F = -7500 N.
    • Example 8.4: 5 N gives 10 m/s² to m₁ (0.5 kg), 20 m/s² to m₂ (0.25 kg); combined, a = 6.67 m/s².
    • Example 8.5: Ball 20 g, 20 cm/s to 0 in 10 s; F = -0.0004 N (friction).

Activity: Calculate force for a moving object!

5. Third Law of Motion

  • Statement: To every action, there is an equal and opposite reaction; forces act on different objects.
  • Examples:
    • Spring balances (Fig. 8.10): Equal readings for action (A pulls B) and reaction (B pulls A).
    • Gun recoil (Fig. 8.11): Bullet forward, gun backward.
    • Sailor jumping (Fig. 8.12): Sailor forward, boat backward.
    • Walking: Push ground backward, ground pushes feet forward.
  • Key Points:
    • Action and reaction are equal in magnitude, opposite in direction.
    • Act on different objects, so don’t cancel out.
    • Different masses cause different accelerations (e.g., gun vs. bullet).
  • Activity 8.4:
    • Children on carts throw sandbag; both experience equal, opposite forces.
    • Two vs. one child: Shows second law (same force, different accelerations).

Activity: Push against a wall and feel the reaction force!

6. Exercises

  • Exercise Questions:
    • 1. Non-zero velocity with zero force: Possible if no unbalanced force (uniform motion).
    • 2. Carpet beating: Dust’s inertia keeps it still; carpet moves, dust detaches.
    • 3. Luggage tie: Inertia causes luggage to slide during bus motion changes.
    • 4. Ball stops: (c) Friction opposes motion.
    • 5. Truck: 400 m in 20 s, m = 7000 kg; a = 2 m/s², F = 14000 N.
    • 6. Stone: 1 kg, 20 m/s to 0 in 50 m; F = -0.36 N (friction).
    • 7. Train: 8000 kg engine, 5×2000 kg wagons, F = 40000 N, friction = 5000 N; net F = 35000 N, a = 2.5 m/s².
    • 8. Vehicle: 1500 kg, a = -1.7 m/s²; F = -2550 N.
    • 9. Momentum: (d) \( p = mv \).
    • 10. Cabinet: 200 N friction (equals push for constant velocity).
    • 11. Truck: Action-reaction forces act on different objects; truck’s high inertia resists motion.
    • 12. Hockey ball: 200 g, 10 m/s to -5 m/s; change in momentum = -3 kg·m/s.
    • 13. Bullet: 10 g, 150 m/s, stops in 0.03 s; penetration = 2.25 m, F = -500 N.
    • 14. Collision: 1 kg at 10 m/s + 5 kg at 0; momentum = 10 kg·m/s (before/after), v = 1.67 m/s.
    • 15. Object: 100 kg, 5 m/s to 8 m/s in 6 s; p₁ = 500 kg·m/s, p₂ = 800 kg·m/s, F = 50 N.
    • 16. Insect vs. Car: Equal force and momentum change (third law); insect’s small mass causes larger velocity change.
    • 17. Dumb-bell: 10 kg, falls 80 cm, a = 10 m/s²; momentum = 40 kg·m/s.
  • Additional Exercises:
    • A1. Distance-time: Distances (0, 1, 8, 27, 64, 125, 216, 343 m); increasing acceleration (s = t³), unbalanced force.
    • A2. Car: 1200 kg, three push for 0.2 m/s²; each person’s force = 80 N.
    • A3. Hammer: 500 g, 50 m/s, stops in 0.01 s; F = -2500 N.
    • A4. Car: 1200 kg, 90 km/h to 18 km/h in 4 s; a = -5 m/s², Δp = -7200 kg·m/s, F = -1800 N.

Activity: Solve a momentum problem!

Next Chapter

  • Ready to dive deeper into science? Explore the next chapter to learn more exciting concepts!
Go to Chapter 9