What is Work and Energy Class 9: Complete NCERT Guide

Definition of Work in Class 9 Science

In Class 9 NCERT Science, work is defined as done when a force is applied to an object and the object moves in the direction of the force. The formula for work is:

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

where:

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

Key points:

• If there is no displacement, no work is done.
• Work is positive if force and displacement are in the same direction.
• Work is negative if force and displacement are in opposite directions.

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

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

Understanding Energy: The Capacity to Do Work

Energy is defined as the capacity to do work. Without energy, no work can be performed. Energy exists in various forms, but in Class 9 Science, we mainly study:

• 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 (kg) and $v$ is velocity (m/s).

• Potential Energy:

$$PE = mgh$$

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

Energy can transform from one form to another but the total energy remains conserved.

Work Done by a Force: Positive, Negative, and Zero Work

Work done depends on the angle between force and displacement:

Examples:

• Lifting a book upward: positive work.
• Holding a book stationary: zero work (no displacement).
• Friction slowing a sliding object: negative work.

This helps understand energy transfer and forces acting in real life.

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.

For example, when you lift a ball, chemical energy in your muscles converts to potential energy. When you drop it, potential energy converts to kinetic energy.

This principle is crucial in solving problems related to work and energy in Class 9 Science.

Example: A ball of mass 2 kg is lifted to a height of 5 m. Potential energy gained:

$$PE = mgh = 2 \times 9.8 \times 5 = 98 \text{ J}$$

When dropped, this 98 J converts to kinetic energy just before hitting the ground.

Power: Rate of Doing Work

Power is defined as the rate at which work is done. It tells us how fast work is performed.

Formula:

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

where:

• $P$ = power (in watts, W)
• $W$ = work done (in joules, J)
• $t$ = time taken (in seconds, s)

One watt equals one joule per second.

Example: If a person does 100 J of work in 5 seconds, power is:

$$P = \frac{100}{5} = 20 \text{ W}$$

Power helps compare machines and human effort efficiency.

Worked Example: Calculating Work Done

Problem: A force of 15 N pulls a cart 8 m at an angle of 60° to the horizontal. Calculate the work done.

Solution:

Given:

• $F = 15$ N
• $d = 8$ m
• $\theta = 60^\circ$

Using formula:

$$W = F \times d \times \cos \theta = 15 \times 8 \times \cos 60^\circ$$

Since $\cos 60^\circ = 0.5$,

$$W = 15 \times 8 \times 0.5 = 60 \text{ J}$$

So, work done is 60 joules.