CBSE Class 9 Science Notes: Work and Energy

**Work and Work Done by a Force**

Let’s explore the fundamental concept of work in physics. Work, in a scientific sense, is done when a force causes an object to move a certain distance. It’s crucial to understand that not all applications of force result in work being done. For work to be done, the force must cause a displacement.

Definitions

• Work (W): The measure of energy transfer when an object is moved by an external force.
• Force (F): A push or pull that can change the motion of an object.
• Displacement (d): The change in position of an object.

Core Principles

Work is a scalar quantity, meaning it has magnitude but no direction. The amount of work done depends on the magnitude of the force applied, the distance the object moves, and the angle between the force and the displacement. Specifically, if the force and displacement are in the same direction, the work done is maximum.

Formulaes

The basic formula for work done is:

$W = F \cdot d \cdot cos(\theta)$

• W = Work done (measured in Joules, J)
• F = Magnitude of the force (measured in Newtons, N)
• d = Distance moved (measured in meters, m)
• θ = Angle between the force and the direction of displacement (in degrees). If the force is applied in the same direction as the displacement, then θ = 0.

Examples

• Lifting a book: When you lift a book, you apply a force against gravity, and move the book upwards, so work is done.
• Pushing a box: If you push a box across the floor, you are applying a force to overcome friction, and move it through a distance, so work is being done.
• Holding a book stationary: If you are holding a book in the air and not moving it, you are applying a force, but no work is being done because there is no displacement.

**Kinetic and Potential Energy**

Energy is the capacity to do work. There are several forms of energy, but in this chapter, we will focus on two major types: kinetic and potential energy.

Definitions

• Energy: The capacity to do work.
• Kinetic Energy (KE): The energy an object possesses due to its motion.
• Potential Energy (PE): The energy stored in an object due to its position or condition.

Core Principles

Kinetic energy is directly proportional to the mass and the square of the velocity of the object. Potential energy can be further categorized, with gravitational potential energy being the most common example we will explore, it depends on the height of an object relative to a reference point.

Formulaes

Kinetic Energy:

$KE = \frac{1}{2}mv^2$

• KE = Kinetic Energy (measured in Joules, J)
• m = mass of the object (measured in kilograms, kg)
• v = velocity of the object (measured in meters per second, m/s)

Gravitational Potential Energy:

$PE = mgh$

• PE = Potential Energy (measured in Joules, J)
• m = mass of the object (measured in kilograms, kg)
• g = acceleration due to gravity (approximately 9.8 m/s²)
• h = height of the object above a reference point (measured in meters, m)

Examples

• Kinetic Energy: A moving car, a falling ball, a flowing river.
• Potential Energy: A book held above the ground, water stored behind a dam, a stretched spring.

**Law of Conservation of Energy**

This is a cornerstone principle in physics. It states that energy cannot be created or destroyed, it can only be transformed from one form to another. The total energy in a closed system remains constant.

Core Principles

In an ideal scenario (without energy loss due to factors like friction and air resistance), the total mechanical energy (sum of potential and kinetic energy) of a system remains constant. This means if potential energy decreases, kinetic energy must increase, and vice-versa.

Examples

• Pendulum swinging: As the pendulum swings, the potential energy at the highest point is converted to kinetic energy at the lowest point, and back again.
• Free fall: A falling object converts its potential energy to kinetic energy as it falls. The total energy, however, remains constant, if we ignore air resistance.

Important Note: In real-world scenarios, some energy may be lost to other forms, like heat due to friction or sound. However, the law of conservation of energy still applies to the total energy of the system; it is just that not all of it might be easily observable as kinetic or potential energy.

**Power**

Power measures the rate at which work is done or energy is transferred or transformed. It’s a measure of how quickly work is completed.

Definitions

• Power (P): The rate at which work is done or energy is transformed.

Core Principles

A higher power indicates that work is done faster. Power is a scalar quantity.

Formulaes

The formula for power is:

$P = \frac{W}{t}$

• P = Power (measured in Watts, W)
• W = Work done (measured in Joules, J)
• t = Time taken (measured in seconds, s)

Alternatively, using energy transfer:

$P = \frac{E}{t}$

• E = Energy transferred or transformed (measured in Joules, J)

Examples

• Lifting a weight: If one person lifts a weight quickly and another lifts the same weight slowly, the person who lifts it faster has a higher power output.
• Electric appliance: A light bulb with a higher wattage rating consumes more energy per second, so has more power.