Class 9 Science Notes Chapter 11 (Chapter 11) – Examplar Problem (English) Book

Alright class, let's focus on Chapter 11: Work and Energy. This is a fundamental chapter in Physics, and concepts from here are crucial not just for your Class 9 exams but also form the base for higher studies and competitive government exams. Pay close attention to the definitions, formulas, and the underlying principles.

Chapter 11: Work and Energy - Detailed Notes

1. Work

• Scientific Definition: Work is said to be done by a force only when the force applied on an object causes the object to move (displace) in the direction of the force (or a component of the force).
• Conditions for Work Done:
  • A force must act on the object.
  • The object must be displaced.
  • There must be a component of the force along the direction of displacement.
• Formula:
  • If a constant force F acts on an object, and the object is displaced by a distance 's' in the direction of the force, then work done W is:
    W = F × s
  • If the force F acts at an angle θ to the direction of displacement s, then work done is the product of the displacement and the component of the force in the direction of displacement (F cos θ):
    W = (F cos θ) × s = Fs cos θ
• Units:
  • SI unit: Joule (J)
  • Definition of 1 Joule: Work done is 1 Joule when a force of 1 Newton displaces an object by 1 metre in the direction of the force.
    1 J = 1 N × 1 m
• Nature of Work: Work is a scalar quantity (it has magnitude but no direction).

2. Types of Work Done

Based on the angle (θ) between the force vector and the displacement vector:

• Positive Work (θ < 90°, typically θ = 0°):
  • When the force and displacement are in the same direction (or the component of force is in the direction of displacement).
  • Example: Lifting an object upwards (work done by lifting force), pushing a box along the floor.
  • Formula: W = Fs (when θ = 0°, cos 0° = 1)
• Negative Work (90° < θ ≤ 180°, typically θ = 180°):
  • When the force acts opposite to the direction of displacement.
  • Example: Work done by friction on a moving object, work done by gravity when an object is lifted upwards.
  • Formula: W = -Fs (when θ = 180°, cos 180° = -1)
• Zero Work (θ = 90° or F=0 or s=0):
  • When the force is perpendicular to the displacement. Example: Work done by gravity on an object moving horizontally, work done by a coolie carrying a load on his head and walking horizontally (work done by the force supporting the load against gravity).
  • When there is no displacement (s=0). Example: Pushing a rigid wall.
  • When no force is applied (F=0).
  • Formula: W = 0 (when θ = 90°, cos 90° = 0)

3. 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.
• Relation with Work: The energy possessed by an object is measured in terms of the amount of work it can do. Work done on an object changes its energy.
• Units:
  • SI unit: Joule (J) (Same as work)
  • Other units: calorie (cal), kilocalorie (kcal). 1 cal ≈ 4.184 J.
• Nature of Energy: Energy is a scalar quantity.

4. Forms of Energy

Energy exists in various forms: Mechanical Energy (Kinetic + Potential), Heat Energy, Light Energy, Sound Energy, Chemical Energy, Electrical Energy, Nuclear Energy, etc. In this chapter, we focus on Mechanical Energy.

5. Mechanical Energy

The sum of kinetic and potential energy of an object.

• a) Kinetic Energy (KE)

  • Definition: The energy possessed by an object by virtue of its motion. All moving objects possess kinetic energy.
  • Factors: Depends on the mass (m) and 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 being displaced by 's' under a constant force 'F'.
    Work done, W = F × s
    From Newton's second law, F = ma
    So, W = (ma) × s = mas
    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 bring it to velocity 'v' is stored as its kinetic energy.
    Therefore, KE = ½ mv²
  • KE is always positive as mass (m) is positive and v² is positive.
  • Work-Energy Theorem (Concept): The work done by the net force on an object is equal to the change in its kinetic energy. W_net = ΔKE = KE_final - KE_initial

• b) Potential Energy (PE)

  • Definition: The energy possessed by an object by virtue of its position or configuration (shape/size). It is the stored energy that can be converted into other forms of energy (like kinetic energy).

  • Types:

    • Gravitational Potential Energy: Energy due to position above the Earth's surface.
    • Elastic Potential Energy: Energy stored due to deformation (stretching or compressing) of an object. Example: Stretched rubber band, compressed spring, bent bow.

  • Gravitational Potential Energy (PE_g)

    • Definition: Work done in lifting an object of mass 'm' against gravity to a height 'h' above a reference level (usually the ground).
    • Formula: PE = mgh
    • Derivation:
      To lift an object of mass 'm' vertically upwards to height 'h', a minimum force equal to its weight (mg) must be applied in the upward direction.
      Force (F) = mg
      Displacement (s) = 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
    • Depends on mass (m), acceleration due to gravity (g), and height (h) relative to a reference level.
    • The choice of reference level (where h=0) is arbitrary, so PE can be positive, negative, or zero depending on the reference.

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 remains constant.
• Conservation of Mechanical Energy: In the absence of non-conservative forces like friction and air resistance, the total mechanical energy (KE + PE) of a system remains constant.
  KE_initial + PE_initial = KE_final + PE_final
(½ mv²)_initial + (mgh)_initial = (½ mv²)_final + (mgh)_final
• Examples:
  • Freely Falling Body: As a body falls, its PE decreases (height decreases) while its KE increases (velocity increases), but the sum (KE + PE) remains constant at all points (neglecting air resistance). At the highest point, energy is all PE. At the lowest point (just before hitting ground), energy is (almost) all KE.
  • Simple Pendulum: At extreme positions, energy is all PE. At the mean (lowest) position, energy is all KE. At intermediate positions, energy is partly KE and partly PE. The total mechanical energy remains constant (neglecting air resistance).
• Energy Transformation: Energy constantly changes form, e.g., electrical energy to light/heat in a bulb, chemical energy to heat/light during burning, electrical energy to mechanical energy in a fan.

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
• Units:
  • SI unit: Watt (W)
  • Definition of 1 Watt: Power is 1 Watt if 1 Joule of work is done in 1 second.
    1 W = 1 J / 1 s
  • Larger units: kilowatt (kW), megawatt (MW), gigawatt (GW).
    1 kW = 1000 W = 10³ W
1 MW = 1,000,000 W = 10⁶ W
  • Another common unit: horsepower (hp). 1 hp ≈ 746 W (Used often for engines/motors).
• Nature of Power: Power is a scalar quantity.

8. Commercial Unit of Energy

• The Joule is a very small unit for measuring energy consumption on a large scale (like in households, industries).
• Commercial Unit: kilowatt-hour (kWh), often called a 'unit' of electricity.
• Definition of 1 kWh: 1 kWh is the amount of 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 displacement s occurs perpendicular to the force, the work done is:
   (A) Fs
   (B) -Fs
   (C) Zero
   (D) F/s

2. An object of mass 10 kg is moving with a uniform velocity of 4 m/s. The kinetic energy possessed by the object is:
   (A) 40 J
   (B) 80 J
   (C) 160 J
   (D) 20 J

3. The potential energy of an object of mass 'm' raised to a height 'h' above the earth's surface is given by:
   (A) ½ mv²
   (B) mgh
   (C) Fs cos θ
   (D) W/t

4. 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 be transformed but the total energy remains constant.
   (D) Energy is always lost in transformations.

5. What is the commercial unit of electrical energy?
   (A) Joule (J)
   (B) Watt (W)
   (C) kilowatt-hour (kWh)
   (D) kilowatt (kW)

6. A coolie lifts a luggage of 15 kg from the ground and puts it on his head 1.5 m above the ground. Calculate the work done by him on the luggage (Take g = 10 m/s²).
   (A) 150 J
   (B) 22.5 J
   (C) 225 J
   (D) 1.5 J

7. Which of the following is NOT a unit of energy?
   (A) Joule
   (B) Newton-metre
   (C) kilowatt
   (D) kilowatt-hour

8. A body falling from a height 'h' possesses ______ energy at the maximum height (just before falling).
   (A) Only Kinetic Energy
   (B) Only Potential Energy
   (C) Both Kinetic and Potential Energy
   (D) Zero Energy

9. Power is defined as the rate of:
   (A) Change of velocity
   (B) Change of displacement
   (C) Doing work
   (D) Change of force

10. Two objects with masses in the ratio 1:4 are moving with equal kinetic energies. The ratio of their velocities is:
    (A) 1:2
    (B) 2:1
    (C) 1:16
    (D) 4:1

Answers to MCQs:

1. (C) Zero (Because cos 90° = 0)
2. (B) 80 J (KE = ½ mv² = ½ × 10 kg × (4 m/s)² = ½ × 10 × 16 = 80 J)
3. (B) mgh
4. (C) Energy can be transformed but the total energy remains constant.
5. (C) kilowatt-hour (kWh)
6. (C) 225 J (W = mgh = 15 kg × 10 m/s² × 1.5 m = 225 J)
7. (C) kilowatt (kilowatt is a unit of Power)
8. (B) Only Potential Energy (Velocity is zero initially)
9. (C) Doing work
10. (B) 2:1 (KE₁ = KE₂ => ½ m₁v₁² = ½ m₂v₂². Given m₁/m₂ = 1/4. So, (m₁/m₂) (v₁/v₂)² = 1 => (1/4) (v₁/v₂)² = 1 => (v₁/v₂)² = 4 => v₁/v₂ = 2/1 or 2:1)

Study these notes thoroughly. Understand the definitions, derivations, and applications of these concepts. Practice numerical problems based on the formulas. Good luck with your preparation!