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

Definition of Work in Physics for Class 11

Work in physics is done when a force causes displacement of an object in the direction of the force. The formula for work done is:

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

where:

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

Key points:

• Work is positive if force and displacement are in the same direction.
• Work is negative if force and displacement are in opposite directions.
• No work is done if there is no displacement or force is perpendicular to displacement.

Example: If a force of 10 N moves a box 5 m horizontally, and the force is applied horizontally, work done is:

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

Understanding Energy: Kinetic and Potential Energy Explained

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.

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

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

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

Mechanical Energy is the sum of kinetic and potential energy:

$$E_{mechanical} = KE + PE$$

In the absence of friction, mechanical energy is conserved.

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

$$KE = \frac{1}{2} \times 2 \times 3^2 = 9 \text{ J}$$

Power: Rate of Doing Work in Class 11 Physics

Power measures how fast work is done or energy is transferred. It is defined as:

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

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.

Horsepower (hp) is another unit of power, where:

$$1 \text{ hp} = 746 \text{ W}$$

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

Work, energy, and power are closely related concepts:

• Work done on an object changes its energy.
• Energy is the ability to do work.
• Power tells how quickly work or energy transfer happens.

Understanding these links helps solve many physics problems in Class 11 NCERT syllabus.

Law of Conservation of Energy in Class 11 Physics

The law of conservation of energy states that energy can neither be created nor destroyed, only transformed from one form to another.

In mechanical systems without friction:

$$\text{Total Mechanical Energy} = KE + PE = \text{constant}$$

For example, a pendulum converts potential energy to kinetic energy and back, but total energy remains constant.

This principle is fundamental in solving problems related to motion and energy in Class 11 NCERT Physics.

Worked Example: Calculating Work and Power

Problem: A person pushes a cart with a force of 50 N at an angle of 60° to the horizontal. The cart moves 10 m horizontally in 4 seconds. Calculate:

1. Work done by the person 2. Power developed

Solution:

1. Work done:

$$W = F \times d \times \cos\theta = 50 \times 10 \times \cos 60^\circ = 50 \times 10 \times 0.5 = 250 \text{ J}$$

2. Power:

$$P = \frac{W}{t} = \frac{250}{4} = 62.5 \text{ W}$$

Thus, the work done is 250 joules and power developed is 62.5 watts.