What is Work, Energy and Power Class 11: Complete NCERT Guide

Definition and Concept of Work in Physics

In Class 11 NCERT Physics, work is defined as the product of the force applied on an object and the displacement produced in the direction of the force. Mathematically, work done $W$ is expressed as:

$$ W = extbf{F} imes extbf{d} imes \\cos\theta $$

where:

• $\textbf{F}$ = magnitude of the force applied
• $\textbf{d}$ = displacement of the object
• $\theta$ = angle between force and displacement vectors

Key points about work:

• Work is done only if the object moves.
• If $\theta = 90^\circ$, work done is zero (force perpendicular to displacement).
• Work can be positive, negative, or zero depending on the direction of force.

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

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

Understanding Energy: Forms and Principles

Energy is the capacity to do work. In Class 11 Physics, energy mainly appears in two forms:

• Kinetic Energy (KE): Energy possessed by a body due to its motion.

$$KE = \frac{1}{2} m v^2$$ where $m$ is mass and $v$ is velocity.

• Potential Energy (PE): Energy possessed due to position or configuration.

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

Law of Conservation of Energy: Energy can neither be created nor destroyed; it only transforms from one form to another.

Example: A ball of mass 2 kg is lifted to a height of 3 m. Its potential energy is:

$$PE = 2 \times 9.8 \times 3 = 58.8 \text{ J}$$

Power: Definition and Calculation

Power is the rate at which work is done or energy is transferred. It tells us how quickly work is completed.

The formula for power $P$ is:

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

where:

• $W$ = work done (in joules)
• $t$ = time taken (in seconds)

The SI unit of power is the watt (W), where 1 watt = 1 joule/second.

Horsepower (hp): Another unit of power commonly used is horsepower.

Example: If 100 J of work is done in 5 seconds, power is:

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

Relationship Between Work, Energy, and Power

These three concepts are closely related:

• Work and Energy: Work done on an object changes its energy. For example, doing work to lift an object increases its potential energy.
• Energy and Power: Power measures how fast energy is used or work is done.

Understanding these relations helps solve many physics problems involving motion and forces.

Work Done by Variable Forces and Work-Energy Theorem

When force varies with displacement, work done is calculated by integrating the force over the path:

$$ W = \int \textbf{F} \cdot d\textbf{x} $$

The Work-Energy Theorem states:

> The net work done on an object equals the change in its kinetic energy.

Mathematically:

$$ W_{net} = \Delta KE = KE_{final} - KE_{initial} $$

Example: A 3 kg object accelerates from 2 m/s to 6 m/s. Change in kinetic energy:

$$ \Delta KE = \frac{1}{2} \times 3 \times (6^2 - 2^2) = \frac{3}{2} \times (36 - 4) = 48 \text{ J} $$

So, net work done is 48 J.

Power in Daily Life and Its Applications

Power is an important concept in real life, especially in machines and engines.

• Electric appliances: Power rating (in watts) indicates energy consumption.
• Vehicles: Engine power affects speed and acceleration.
• Human body: Power output during activities like running or lifting weights.

Example: A motor with power 1000 W does work for 10 seconds. Total work done:

$$ W = P \times t = 1000 \times 10 = 10,000 \text{ J} $$

Knowing power helps in selecting appropriate machines and understanding energy efficiency.