CBSE Class 9 Science Chapter 11: Work and Energy Notes

Key Concepts & Formulas (Must Remember)

• Work Done (W): Product of force (F) and displacement (s) in the direction of force. Formula: W = F × s (if force and displacement are in same direction).
• SI Unit of Work: Joule (J). 1 Joule = 1 Newton-metre (Nm).
• Conditions for Work: A force must act on an object, and the object must be displaced from its position.
• Energy: The capacity of a body to do work. SI Unit: Joule (J).
• Kinetic Energy (KE): Energy possessed by a body due to its motion. Formula: KE = ½ mv² (where m = mass, v = velocity).
• Potential Energy (PE): Energy possessed by a body due to its position or change in shape. Formula: PE = mgh (where m = mass, g = acceleration due to gravity, h = height).
• Power: The rate at which work is done or energy is transferred. Formula: P = W/t or P = E/t (where W = work, E = energy, t = time).
• SI Unit of Power: Watt (W). 1 Watt = 1 Joule/second (J/s).
• Law of Conservation of Energy: 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.
• Commercial Unit of Energy: Kilowatt-hour (kWh). 1 kWh = 3.6 × 10⁶ J.

Essential Definitions

Work

Work is said to be done when a force causes a displacement of an object in the direction of the applied force.

Joule (J)

The SI unit of work and energy. One joule is the amount of work done when a force of one Newton displaces an object by one meter along the line of action of the force.

Energy

The capacity of a body to do work. It exists in various forms like kinetic, potential, heat, light, sound, electrical, and chemical energy.

Kinetic Energy

The energy possessed by an object due to its motion. Any object that is moving has kinetic energy.

Potential Energy

The energy stored in an object due to its position (e.g., gravitational potential energy) or configuration (e.g., elastic potential energy in a spring).

Power

The rate at which work is done or energy is transferred. It quantifies how fast energy is used or work is accomplished.

Watt (W)

The SI unit of power. One watt is defined as the rate of energy consumption or work done at one joule per second.

Law of Conservation of Energy

A fundamental principle stating that in an isolated system, the total amount of energy remains constant. It can only change from one form to another, but is neither created nor destroyed.

Understanding Work Done

In physics, the term work has a very specific meaning. For work to be done, two conditions must be fulfilled:

1. A force must act on an object.
2. The object must undergo displacement (change in position) in the direction of or opposite to the force.

If either of these conditions is not met, no work is considered to be done, even if effort is expended. For example, pushing against a wall that doesn't move results in zero work done, because there is no displacement. Similarly, holding a heavy book stationery above the ground does not involve work done on the book (relative to the ground) because there is no displacement of the book, although your muscles might feel fatigued.

The formula for work done when the force is applied in the direction of displacement is given by: W = F × s, where W is work, F is the applied force, and s is the displacement. The SI unit of work is Joule (J), with 1 Joule being equal to 1 Newton-metre (1 N·m).

Work can be positive, negative, or zero:

• Positive Work: Occurs when the force and displacement are in the same direction. For instance, when you push a trolley forward, the force you apply and the trolley's displacement are in the same direction. Here, work is done on the object.
• Negative Work: Occurs when the force and displacement are in opposite directions. For example, when an object is slowing down, the force of friction acts opposite to the direction of motion, thus friction does negative work. Work is done by the object against the force.
• Zero Work: Occurs in two main scenarios:

1. When there is no displacement (s = 0), despite a force being applied (e.g., pushing a stationary wall).
2. When the force is perpendicular to the displacement (angle = 90°). For example, a person carrying a load on their head and walking horizontally performs zero work against gravity because the gravitational force acts vertically downwards, perpendicular to the horizontal displacement.

Forms of Energy and the Law of Conservation of Energy

Energy is the fundamental ability to do work. It exists in various forms, including mechanical energy, which is the sum of kinetic energy and potential energy. Understanding these forms and how they transform is key to mastering this chapter.

Kinetic Energy (KE) is the energy possessed by an object due to its motion. Any object moving with a certain velocity has kinetic energy. The faster an object moves, or the greater its mass, the more kinetic energy it possesses. The formula for kinetic energy is: KE = ½ mv², where 'm' is the mass of the object and 'v' is its velocity. This formula highlights that kinetic energy is directly proportional to mass and to the square of velocity, meaning a small change in velocity has a significant impact on KE.

Potential Energy (PE) is the energy stored in an object due to its position or configuration. For objects near the Earth's surface, the most common type is gravitational potential energy, which depends on an object's height above a reference point. The formula for gravitational potential energy is: PE = mgh, where 'm' is the mass, 'g' is the acceleration due to gravity (approximately 9.8 m/s²), and 'h' is the height. An object held at a certain height has the potential to do work when released.

The Law of Conservation of Energy is a cornerstone of physics, stating that energy can neither be created nor destroyed; it can only be transformed from one form to another. The total energy in an isolated system remains constant. For example, when a ball is dropped from a height, its potential energy is maximum at the top and gradually converts into kinetic energy as it falls. Just before hitting the ground, its potential energy is minimal (assuming ground level as zero 'h') and its kinetic energy is maximum. The sum of kinetic and potential energy (mechanical energy) at any point during its fall remains constant, ignoring air resistance.

Worked Examples

• {"title":"Example 1: Calculating Work Done","bodyMarkdown":"Problem: A force of 10 N acts on an object. The object is displaced through 5 m in the direction of the force. Calculate the work done.\nSolution:\nGiven: Force (F) = 10 N, Displacement (s) = 5 m\nFormula: W = F × s\nW = 10 N × 5 m\nW = 50 J\nAnswer: The work done is 50 Joules."}
• {"title":"Example 2: Calculating Kinetic Energy","bodyMarkdown":"Problem: A car of mass 1000 kg is moving with a velocity of 20 m/s. Calculate its kinetic energy.\nSolution:\nGiven: Mass (m) = 1000 kg, Velocity (v) = 20 m/s\nFormula: KE = ½ mv²\nKE = ½ × 1000 kg × (20 m/s)²\nKE = 500 kg × 400 m²/s²\nKE = 200,000 J or 200 kJ\nAnswer: The kinetic energy of the car is 200,000 Joules."}
• {"title":"Example 3: Calculating Potential Energy","bodyMarkdown":"Problem: An object of mass 5 kg is raised to a height of 10 m. Calculate its potential energy (take g = 9.8 m/s²).\nSolution:\nGiven: Mass (m) = 5 kg, Height (h) = 10 m, Acceleration due to gravity (g) = 9.8 m/s²\nFormula: PE = mgh\nPE = 5 kg × 9.8 m/s² × 10 m\nPE = 490 J\nAnswer: The potential energy of the object is 490 Joules."}

Exam Tips: Common Mistakes & Scoring Cues

1. Units are Crucial: Always include the correct SI units (Joule, Watt, Newton, meter, second, kg) in your final answers. Marks are often awarded for correct units.
2. Direction Matters for Work: Remember that work done is zero if force and displacement are perpendicular (e.g., satellite orbiting Earth, man walking horizontally with load on head against gravity). Also, work can be negative if force opposes displacement.
3. Square the Velocity for KE: A common error is forgetting to square the velocity (v²) in the kinetic energy formula (½ mv²). Double-check this during calculations.
4. Gravitational Potential Energy Reference: Potential energy is relative to a reference level. Clearly define your 'h=0' point (usually the ground or starting point) when solving problems involving PE.
5. Distinguish Work and Power: Work is the total energy transferred, while power is the rate of energy transfer. Don't confuse their formulas or units.
6. Conservation of Energy: When applying the Law of Conservation of Energy, ensure you account for all forms of energy transformation within the system.

Practice Questions with Solutions

• Q: Under what conditions is the work done by a force on an object considered zero? A: Work done is zero if (a) there is no displacement, or (b) the force applied is perpendicular to the direction of displacement.
• Q: What is the SI unit of power, and how is it related to work and time? A: The SI unit of power is Watt (W). It is defined as the rate of doing work, so Power = Work / Time (P = W/t).
• Q: State the Law of Conservation of Energy. A: The Law of Conservation of Energy states that 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.
• Q: A body of mass 'm' is moving with velocity 'v'. What is its kinetic energy? If its velocity doubles, how does its kinetic energy change? A: Its kinetic energy is given by KE = ½ mv². If its velocity doubles (2v), its new kinetic energy will be ½ m(2v)² = ½ m(4v²) = 4 × (½ mv²). So, its kinetic energy will become four times the original.

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