Class 9 Notes

Class 9 Science Notes Chapter 11 (Work and Energy) – Science Book

Philoid

Philoid

— 7 min read

Science
Alright class, let's focus on Chapter 11: Work and Energy. This is a fundamental chapter in Physics, and understanding these concepts clearly is crucial for your government exam preparations. Pay close attention to the definitions, formulas, units, and the underlying principles.

Chapter 11: Work and Energy - Detailed Notes

1. Work

  • Scientific Conception of Work: In physics, work is done only when a force applied to an object causes a displacement of that object in the direction of the force. Just applying force (like pushing a wall) or just displacement without force is not considered work.
  • Conditions for Work Done:
    1. A force must act on the object.
    2. The object must be displaced.
    3. There must be a component of the force along the direction of the displacement.
  • Formula for Work Done:
    • When force (F) acts along the direction of displacement (s):
      W = F × s
    • When force (F) acts at an angle (θ) to the direction of displacement (s):
      W = F × s × cos θ
      (Note: cos θ is a trigonometric function. For Class 9 level, focus on specific cases):
      • If F and s are in the same direction, θ = 0°, cos 0° = 1, so W = Fs (Maximum positive work)
      • If F and s are in opposite directions, θ = 180°, cos 180° = -1, so W = -Fs (Negative work)
      • If F and s are perpendicular, θ = 90°, cos 90° = 0, so W = 0 (Zero work)
  • Unit of Work:
    • The SI unit of work is the Joule (J).
    • Definition of 1 Joule: 1 Joule is the amount of work done on an object when a force of 1 Newton displaces it by 1 meter along the line of action of the force.
      1 J = 1 N × 1 m
  • Types of Work:
    • Positive Work: Work done is positive when the force applied is in the direction of the object's displacement (e.g., lifting an object upwards, pulling a cart). Angle θ is acute (0° ≤ θ < 90°).
    • Negative Work: Work done is negative when the force applied is in the direction opposite to the object's displacement (e.g., work done by friction on a moving object, work done by gravity on an object lifted upwards). Angle θ is obtuse (90° < θ ≤ 180°).
    • Zero Work: Work done is zero when:
      • There is no displacement (s = 0), e.g., pushing a stationary wall.
      • The force is perpendicular to the displacement (θ = 90°), e.g., a coolie carrying a load on his head and walking horizontally (work done by gravity is zero), the Moon revolving around the Earth (gravitational force is perpendicular to instantaneous displacement).

2. Energy

  • Definition: Energy is defined as the capacity or ability to do work. An object possessing energy can exert a force on another object to cause displacement.
  • Unit of Energy:
    • The SI unit of energy is the Joule (J), the same as the unit of work.
    • Larger unit: kilojoule (kJ), 1 kJ = 1000 J.
  • Forms of Energy: Energy exists in various forms, including:
    • Mechanical Energy (Kinetic + Potential)
    • Heat Energy
    • Light Energy
    • Sound Energy
    • Chemical Energy
    • Electrical Energy
    • Nuclear Energy
    • (This chapter primarily focuses on Mechanical Energy).

3. Mechanical Energy

  • The sum of kinetic energy and potential energy of an object is called its mechanical energy.

4. Kinetic Energy (KE)

  • Definition: The energy possessed by an object by virtue of its motion is called kinetic energy. Every moving object possesses kinetic energy.
  • Factors Affecting KE: Kinetic energy depends on the mass (m) and the velocity (v) of the object.
  • Formula:
    KE = ½ mv²
  • Derivation:
    Consider an object of mass 'm' starting from rest (u=0) and reaching velocity 'v' after displacement 's' under a constant force 'F'.
    Work done, W = F × s
    From Newton's second law, F = ma
    So, W = (ma) × s = m(as)
    From the third equation of motion, v² - u² = 2as. Since u=0, v² = 2as, or as = v²/2.
    Substituting 'as' in the work equation: W = m (v²/2) = ½ mv²
    This work done on the object to change its velocity is stored as its kinetic energy.
    Therefore, KE = ½ mv².
  • Characteristics:
    • KE is always positive (mass is positive, v² is positive).
    • KE is directly proportional to the mass.
    • KE is directly proportional to the square of the velocity (doubling velocity quadruples KE).

5. Potential Energy (PE)

  • Definition: The energy possessed by an object by virtue of its position or configuration (shape/size) is called potential energy.
  • Types:
    • Gravitational Potential Energy (GPE): Energy stored due to an object's position (height) above the Earth's surface (or a reference level).
    • Elastic Potential Energy: Energy stored due to a change in the shape or size of an object (e.g., stretched rubber band, compressed spring). (GPE is the main focus here).
  • Gravitational Potential Energy (GPE):
    • Formula:
      PE = mgh
      where, m = mass of the object, g = acceleration due to gravity, h = height of the object above the reference level.
    • Derivation:
      Consider lifting an object of mass 'm' vertically upwards to a height 'h' against gravity.
      Minimum force required to lift = Weight of the object = mg.
      Displacement = h.
      Work done (W) = Force × Displacement = (mg) × h = mgh.
      This work done against gravity is stored in the object as its gravitational potential energy.
      Therefore, PE = mgh.
  • Characteristics:
    • GPE depends on the chosen reference level (usually the ground).
    • GPE can be positive (above reference level), zero (at reference level), or negative (below reference level, e.g., in a mine).

6. Law of Conservation of Energy

  • Statement: Energy can neither be created nor destroyed; it can only be transformed from one form to another. The total energy of an isolated system (where no external forces act) remains constant.
  • Mathematical Representation: Total Initial Energy = Total Final Energy.
  • For Mechanical Energy: In the absence of non-conservative forces like friction or air resistance, the total mechanical energy (KE + PE) of a system remains constant.
    KEᵢ + PEᵢ = KE<0xE1><0xB5><0xA7> + PE<0xE1><0xB5><0xA7>
  • Example: Freely Falling Body:
    • At maximum height (A): PE is maximum (mgh), KE is zero (v=0). Total Energy = mgh.
    • During fall (at height 'x' from ground, B): PE = mgx, KE = ½ mv². By conservation, mgh = mgx + ½ mv².
    • Just before hitting the ground (C): PE is zero (h=0), KE is maximum (½ mv²<0xE2><0x82><0x98>ₐₓ). By conservation, Total Energy = ½ mv²<0xE2><0x82><0x98>ₐₓ = mgh.
    • At all points A, B, and C, the total mechanical energy (PE + KE) remains constant (mgh), assuming no air resistance.

7. Power

  • Definition: Power is defined as the rate at which work is done or the rate at which energy is transferred or consumed. It measures how fast work is done.
  • Formula:
    Power (P) = Work Done (W) / Time Taken (t)
    P = W / t
    Since Work Done = Energy Transferred (E),
    P = E / t
  • Unit of Power:
    • The SI unit of power is the Watt (W).
    • Definition of 1 Watt: Power is said to be 1 Watt if 1 Joule of work is done in 1 second.
      1 W = 1 J / 1 s
  • Larger Units:
    • kilowatt (kW): 1 kW = 1000 W
    • megawatt (MW): 1 MW = 1,000,000 W
    • Horsepower (hp): An older unit, still sometimes used. 1 hp ≈ 746 W.
  • Average Power: Total work done divided by total time taken.

8. Commercial Unit of Energy

  • While Joule is the SI unit, it's too small for commercial purposes like electricity bills.
  • Commercial Unit: Kilowatt-hour (kWh), often simply called a 'unit'.
  • Definition of 1 kWh: 1 kilowatt-hour is the amount of electrical energy consumed when an electrical appliance having a power rating of 1 kilowatt is used for 1 hour.
  • Relation between kWh and Joule:
    1 kWh = 1 kilowatt × 1 hour
    1 kWh = 1000 Watt × (60 × 60 seconds)
    1 kWh = 1000 J/s × 3600 s
    1 kWh = 3,600,000 J = 3.6 × 10⁶ J

Multiple Choice Questions (MCQs)

  1. When a force F acts on an object and the object displaces by a distance s perpendicular to the direction of the force, the work done is:
    a) Fs
    b) -Fs
    c) F/s
    d) Zero

  2. The SI unit of energy is the same as the SI unit of:
    a) Power
    b) Force
    c) Work
    d) Momentum

  3. A body is falling from a height h. After it has fallen a height h/2, it will possess:
    a) Only potential energy
    b) Only kinetic energy
    c) Half potential and half kinetic energy
    d) More kinetic and less potential energy

  4. An object of mass 10 kg is moving with a uniform velocity of 4 m/s. What is the kinetic energy possessed by the object?
    a) 40 J
    b) 80 J
    c) 160 J
    d) 20 J

  5. Work done by the force of friction on a moving body is always:
    a) Positive
    b) Negative
    c) Zero
    d) Can be positive or negative

  6. The commercial unit of energy is:
    a) Joule (J)
    b) Watt (W)
    c) Kilowatt (kW)
    d) Kilowatt-hour (kWh)

  7. A girl weighing 400 N climbs a vertical ladder. If the value of g is 10 m/s², the work done by her after climbing 2 m will be:
    a) 200 J
    b) 800 J
    c) 8000 J
    d) 40 J

  8. Which of the following quantities is defined as the rate of doing work?
    a) Energy
    b) Power
    c) Force
    d) Momentum

  9. How much energy does a 100 W electric bulb transfer in 1 minute?
    a) 100 J
    b) 600 J
    c) 3600 J
    d) 6000 J

  10. The law of conservation of energy states that:
    a) Energy can be created but not destroyed.
    b) Energy can be destroyed but not created.
    c) Energy can neither be created nor destroyed, only transformed.
    d) The total energy in the universe is decreasing.

Answer Key for MCQs:

  1. d) Zero
  2. c) Work
  3. c) Half potential and half kinetic energy (Assuming starting from rest, at half height, PE = mg(h/2), and KE = Total Energy - PE = mgh - mg(h/2) = mg(h/2))
  4. b) 80 J (KE = ½ mv² = ½ * 10 * 4² = ½ * 10 * 16 = 80 J)
  5. b) Negative
  6. d) Kilowatt-hour (kWh)
  7. b) 800 J (Work = Force × Displacement = Weight × height = 400 N × 2 m = 800 J)
  8. b) Power
  9. d) 6000 J (Energy = Power × Time = 100 W × 60 s = 6000 J)
  10. c) Energy can neither be created nor destroyed, only transformed.

Revise these notes thoroughly. Understand the definitions, units, and how the formulas are applied. Practice numerical problems based on these concepts. Good luck with your preparation!

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