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

Definition of Work in Physics for Class 9

Work in physics is done when a force causes displacement of an object in the direction of the force. Mathematically, work is defined as:

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

where:

• $W$ = work done (in joules, J)
• $F$ = magnitude of force applied (in newtons, N)
• $d$ = displacement of the object (in metres, m)
• $\theta$ = angle between force and displacement direction

If the force and displacement are in the same direction, $\theta = 0^\circ$ and $\cos 0^\circ = 1$, so work done is simply $W = F \times d$.

Important points:

• No displacement means no work done.
• If force is perpendicular to displacement ($\theta = 90^\circ$), work done is zero.
• Work can be positive, negative, or zero depending on $\theta$.

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

$$W = 10 \times 5 \times \cos 0^\circ = 50\, J$$

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 Science, we focus mainly on mechanical energy.

Types of mechanical energy:

• Kinetic Energy (K.E.): Energy possessed by a body due to its motion.
• Potential Energy (P.E.): Energy possessed by a body due to its position or configuration.

Formulas:

• Kinetic Energy:

$$K.E. = \frac{1}{2} m v^2$$

where $m$ is mass (kg) and $v$ is velocity (m/s).

• Potential Energy:

$$P.E. = mgh$$

where $m$ is mass (kg), $g$ is acceleration due to gravity (9.8 m/s²), and $h$ is height (m).

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

Example: A 2 kg ball moving at 3 m/s has kinetic energy:

$$K.E. = \frac{1}{2} \times 2 \times 3^2 = 9\, J$$

Relation Between Work and Energy

Work and energy are closely related. When work is done on an object, its energy changes.

• Work-Energy Theorem: The net work done on an object equals the change in its kinetic energy.

Mathematically:

$$W_{net} = \Delta K.E. = K.E._{final} - K.E._{initial}$$

This means:

• If positive work is done, kinetic energy increases.
• If negative work is done, kinetic energy decreases.

Example: If a force does 20 J of work on a stationary object, the object’s kinetic energy increases by 20 J.

This theorem helps explain how forces affect the motion and energy of objects.

Law of Conservation of Energy Explained

The law of conservation of energy states:

> Energy can neither be created nor destroyed; it can only be transformed from one form to another.

In practical terms, the total mechanical energy (sum of kinetic and potential energy) of an isolated system remains constant if only conservative forces act.

Example: A pendulum swinging converts potential energy to kinetic energy and back, but the total mechanical energy remains the same (ignoring air resistance).

Understanding this law is important for solving problems related to energy transformations.

Calculating Work Done: Step-by-Step Example

Let’s solve a typical Class 9 NCERT problem on work:

Problem: A person pushes a box with a force of 15 N at an angle of 60° to the horizontal. The box moves 4 m along the horizontal. Calculate the work done by the person.

Solution:

Given:

• Force, $F = 15$ N
• Displacement, $d = 4$ m
• Angle, $\theta = 60^\circ$

Formula:

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

Calculate $\cos 60^\circ = 0.5$:

$$W = 15 \times 4 \times 0.5 = 30\, J$$

Answer: Work done by the person is 30 joules.

This example shows how to apply the formula when force is not along displacement.

Comparing Work and Energy: Key Differences

It’s helpful to understand how work and energy differ and relate:

Remember, work is a process of energy transfer, while energy is a property of a system.