What Is Work and Energy in Physics Class 9: Clear Definitions & Concepts

Definition of Work in Physics for Class 9

In physics, work is said to be done when a force applied on an object causes displacement in the direction of the force. The formula for work done ($W$) is:

$$W = F imes d imes \\cos \theta$$

Where:

• $F$ = magnitude of the force applied
• $d$ = displacement of the object
• $\theta$ = angle between force and displacement directions

Key points:

• If there is no displacement, no work is done.
• If force and displacement are perpendicular ($\theta = 90^\circ$), work done is zero.
• Work is a scalar quantity and can be positive, negative, or zero.

Example: If a force of 10 N moves a box 5 m in the same direction, work done is:

$$W = 10 \times 5 \times \cos 0^\circ = 50 \text{ Joules}$$

Understanding Energy: The Capacity to Do Work

Energy is defined as the capacity to do work. It exists in various forms, but in Class 9 NCERT, we focus mainly on:

• Kinetic Energy (KE): Energy possessed by a body due to its motion.
• Potential Energy (PE): Energy possessed due to position or configuration.

Formulas:

• Kinetic Energy:

$$KE = \frac{1}{2} m v^2$$

where $m$ is mass and $v$ is velocity.

• Potential Energy:

$$PE = m g h$$

where $m$ is mass, $g$ is acceleration due to gravity, and $h$ is height.

Energy is measured in Joules (J), the same unit as work.

Relationship Between Work and Energy

Work and energy are closely related. When work is done on an object, its energy changes. This relationship is the basis for the Work-Energy Theorem:

> The work done on an object is equal to the change in its kinetic energy.

Mathematically:

$$W = \Delta KE = KE_{final} - KE_{initial}$$

Example: If a force does 100 J of work on a stationary object, the object's kinetic energy increases by 100 J.

This theorem helps us understand how forces affect motion and energy in physical systems.

Law of Conservation of Energy Explained

The Law of Conservation of Energy states that energy can neither be created nor destroyed; it only changes from one form to another.

In practical terms:

• Total energy before an event = Total energy after the event
• For example, potential energy can convert into kinetic energy and vice versa.

Example: A pendulum at its highest point has maximum potential energy and zero kinetic energy. At the lowest point, potential energy is minimum, and kinetic energy is maximum. The total mechanical energy remains constant if no external forces like friction act.

This law is fundamental in solving many Class 9 physics problems.

Types of Work: Positive, Negative, and Zero Work

Work done can be classified based on the angle between force and displacement:

Example:

• Lifting a book upward: positive work
• Friction opposing motion: negative work
• Carrying a bag horizontally without moving it up or down: zero work by vertical force

Solved Example: Calculating Work Done

Problem: A person pushes a box with a force of 20 N at an angle of 60° to the horizontal. The box moves 3 m along the horizontal. Calculate the work done by the person.

Solution: Given:

• $F = 20$ N
• $d = 3$ m
• $\theta = 60^\circ$

Formula:

$$W = F \times d \times \cos \theta$$

Calculate:

$$W = 20 \times 3 \times \cos 60^\circ = 60 \times 0.5 = 30 \text{ Joules}$$

Answer: The work done is 30 Joules.

This example shows how to apply the work formula when force is applied at an angle.