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Chapter 10: Work and Energy

Explore Science with Fun & Easy Notes for Class 9!

1. Work

  • Scientific Definition: Work is done when a force causes displacement. Conditions: (i) Force acts, (ii) Object moves (Fig. 10.1).
  • Daily vs. Scientific: Studying or holding a load involves effort but no work if no displacement occurs.
  • Activities:
    • 10.1: Analyze daily tasks (e.g., pushing rock, climbing stairs) to identify force, object, and displacement.
    • 10.2: List daily work scenarios (e.g., pulling a cart).
    • 10.3: Identify cases with force but no displacement (e.g., pushing a wall) or displacement without force (e.g., coasting bike).
    • 10.4: Lift an object; your force does positive work (same direction as displacement), gravity does negative work (opposite direction).
  • Work by Constant Force:
    • Formula: \( W = F \times s \) (force × displacement in force’s direction).
    • Unit: Joule (J)
    • Positive Work: Force and displacement in same direction (e.g., pulling a trolley, Fig. 10.4).
    • Negative Work: Force opposes displacement (e.g., retarding force).
    • Zero Work: If \( F = 0 \) or \( s = 0 \).
  • Questions:
    • 1. Work is done when force causes displacement.
    • 2. Expression: \( W = F \times s \).
    • 3. 1 J: Work when 1 N displaces 1 m.

Activity: Push an object to see if it moves!

2. Energy

  • Definition: Capacity to do work; unit: Joule (J)
  • Sources: Sun, nuclear, geothermal, tides; Sun drives most (e.g., fossil fuels, wind).
  • Forms of Energy: Kinetic, potential, heat, chemical, electrical, light.
  • Energy Transfer: Object with energy exerts force, transfers energy to another object, enabling work.

Activity: Identify energy sources around you!

3. Kinetic Energy

  • Definition: Energy due to motion; increases with speed.
  • Formula: \( E_k = \frac{1}{2} m v^2 \); derived from work done to change velocity.
  • Questions:
    • 1. Kinetic Energy: Energy due to motion.
    • 2. Expression: \( E_k = \frac{1}{2} m v^2 \).
    • 3. Mass \( m \); doubled velocity

Activity: Drop a ball to see kinetic energy!

4. Potential Energy

  • Definition: Energy due to position or configuration.
  • Activities:
    • 10.8: Stretch rubber band; stores energy, released when let go.
    • 10.9: Stretch/compress slinky; stores energy in configuration.
    • 10.10: Wind toy car; spring stores potential energy.
    • 10.11: Lift object; gains potential energy to do work when dropped.
    • 10.12: Stretch bow (Fig. 10.6); potential energy converts to kinetic energy of arrow.
  • Gravitational Potential Energy:
    • Formula: \( E_p = m g h \) (Fig. 10.7).
    • Depends on height and reference level (Fig. 10.8).
  • Examples:
    • 10.5: \( 10 \, \text{kg}, 6 \, \text{m}, g = 9.8 \, \text{m/s}^2 \); \( E_p = 588 \, \text{J} \).
    • 10.6: \( 12 \, \text{kg}, E_p = 480 \, \text{J}, g = 10 \, \text{m/s}^2 \); \( h = 4 \, \text{m} \).

Activity: Stretch a rubber band to feel potential energy!

5. Conservation of Energy

  • Law: Energy transforms but total remains constant; cannot be created or destroyed.
  • Activities:
    • 10.13: Discuss energy conversions (e.g., photosynthesis: light to chemical; water cycle: solar to kinetic).
    • 10.14: List gadgets (e.g., bulb: electrical to light; fan: electrical to kinetic).
    • 10.15: Object (\( 20 \, \text{kg}, 4 \, \text{m}, g = 10 \, \text{m/s}^2 \)):
      • 4 m: \( E_p = 800 \, \text{J}, E_k = 0, \text{Total} = 800 \, \text{J} \)
      • 3 m: \( E_p = 600 \, \text{J}, E_k = 200 \, \text{J}, \text{Total} = 800 \, \text{J} \)
      • 2 m: \( E_p = 400 \, \text{J}, E_k = 400 \, \text{J}, \text{Total} = 800 \, \text{J} \)
      • 1 m: \( E_p = 200 \, \text{J}, E_k = 600 \, \text{J}, \text{Total} = 800 \, \text{J} \)
      • 0 m: \( E_p = 0, E_k = 800 \, \text{J}, \text{Total} = 800 \, \text{J} \)
  • Free Fall: \( E_p + E_k = m g h + \frac{1}{2} m v^2 = \text{constant} \); potential energy converts to kinetic energy.

Activity: Drop an object to see energy conversion!

6. Power

  • Definition: Rate of doing work or energy transfer; \( P = \frac{W}{t} \).
  • Unit: Watt (W); \( 1 \, \text{W} = 1 \, \text{J/s} \); \( 1 \, \text{kW} = 1000 \, \text{W} \).
  • Average Power: Total energy ÷ total time.
  • Activity 10.16: Two children climb 8 m; A (15 s, 160 W), B (20 s, 64 W); same work, different power.
  • Activity 10.17: Monitor electric meter; calculate daily/nightly units; compare with bill.
  • Examples:
    • 10.7: Girls, 400 N, 8 m; A (20 s): 160 W; B (50 s): 64 W.
    • 10.8: Boy, 50 kg, 6.75 m, 9 s; \( P = 375 \, \text{W} \).
  • Questions:
    • 1. Power: Rate of doing work.
    • 2. 1 W: 1 J/s.
    • 3. Lamp: \( 1000 \, \text{J} / 10 \, \text{s} = 100 \, \text{W} \).
    • 4. Average Power: Total energy ÷ total time.

Activity: Time yourself climbing stairs!

7. Exercises

  • Exercise Questions:
    • 1. Work or Not:
      • Suma swimming: Work (force moves body).
      • Donkey carrying: No work (no displacement in force direction).
      • Windmill lifting: Work (water displaced).
      • Photosynthesis: No work (no displacement).
      • Engine pulling: Work (train moves).
      • Grains drying: No work (no force-displacement).
      • Sailboat moving: Work (wind force moves boat).
    • 2. Gravity on projectile: Zero work (force perpendicular to horizontal displacement).
    • 3. Battery to bulb: Chemical → electrical → light/heat.
    • 4. \( 20 \, \text{kg}, 5 \, \text{m/s} \to 2 \, \text{m/s} \): Work = \( -270 \, \text{J} \).
    • 5. Horizontal move: Zero work (gravity perpendicular to displacement).
    • 6. Falling object: No violation; potential energy → kinetic energy.
    • 7. Bicycle: Chemical (muscles) → kinetic (motion) → heat (friction).
    • 8. Pushing rock: No work; energy → internal (muscles, heat).
    • 9. 250 units: \( 250 \times 3.6 \times 10^6 = 9 \times 10^8 \, \text{J} \).
    • 10. \( 40 \, \text{kg}, 5 \, \text{m}, g = 10 \, \text{m/s}^2 \): \( E_p = 2000 \, \text{J} \); halfway (\( 2.5 \, \text{m} \)): \( E_k = 1000 \, \text{J} \).
    • 11. Satellite: Zero work (gravity perpendicular to circular path).
    • 12. Displacement without force: Yes (e.g., coasting object).
    • 13. Holding hay: No work (no displacement).
    • 14. Heater 1500 W, 10 h: \( 1500 \times 10 \times 3600 = 5.4 \times 10^7 \, \text{J} \).
    • 15. Pendulum: Potential → kinetic; stops due to air resistance/friction; energy → heat, not violated.
    • 16. Stop object: Work = \( -\frac{1}{2} m v^2 \).
    • 17. Car 1500 kg, 60 km/h: Work = \( -208333.33 \, \text{J} \).
    • 18. Work: (a) Zero (perpendicular), (b) Positive (same direction), (c) Negative (opposite direction).
    • 19. Zero acceleration: Yes, forces balance (e.g., object at rest).
    • 20. Four 500 W devices, 10 h: \( 4 \times 500 \times 10 \times 3600 = 7.2 \times 10^7 \, \text{J} \).
    • 21. Falling object: Kinetic energy → heat/sound on impact.

Activity: Solve a work-energy problem!

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