NCERT Class 11 Physics Chapter 6 Work, Energy and Power Notes - Download PDF

Imagine waiting for a bus while standing still and carrying a bulky backpack. Your position is not changing. Even though the bag is heavy, in this case no work is being done on the bag even though you are applying force. This is a well-known example of a phenomenon that we discuss in Class 11 Physics—Work, Energy, and Power, Chapter 5.

These principles are crucial for preparing for competitive exams like JEE Main and NEET as well as other state-level engineering exams like WBJEE and BCECE.

The understandings provided in these Work, Energy, and Power notes are essential, regardless of your goals—getting high scores in examinations, class quizzes, assignments, or just wanting to learn more about the subject. The experts at Careers360 have carefully compiled comprehensive notes for CBSE Class 11 Physics Chapter 5, covering everything from everyday scenarios to more complex concepts.

Also, students can refer,

• NCERT Solutions for Class 11 Physics Chapter 5 Work, Energy, and Power.
• NCERT Exemplar Class 11 Physics Chapter 5 Solutions Work, Energy and Power

Introduction

The terms 'work', 'energy,' and 'power' appear in everyday conversations with different connotations. Consider a construction worker lifting heavy bricks or a student carrying a rucksack up a flight of stairs— both are examples of people putting in effort or doing work.

Now let's look at the concept of energy. Consider a tennis player serving a powerful shot. The player's ability to propel the ball from rest to rapid movement demonstrates the presence of energy. In this case, energy manifests as the ability to cause a change in the state of an object.

Moving on to power, imagine a sprinter accelerating quickly during a race. The sprinter's ability to cover a long distance in a short period of time demonstrates a high power output. In physics, power is precisely defined as the rate at which work is done or energy is transferred, with an emphasis on the speed at which these actions take place.

Work occurs when a force is applied to a body, causing it to move in the direction of the force.

Work Done by a Constant Force

If a constant force F is applied to a body at an angle θ with the horizontal, and the body is displaced through a distance ss, then the work done (Work) can be expressed using the formula:

Work (W) = F.S. cosθ

• Dimension of work: [ML²T^-2]
• Unit: The units of work are of two types (i) Absolute units and (ii) Gravitational units

(i) Absolute units: Joule [S.I.] and Erg [C.G.S.]

(ii) Gravitational units: kg-m [S.I.] and gm-cm [C.G.S.]

Nature of Work Done

1. Positive work: Positive work occurs when the force applied to an object is parallel to the direction of displacement. This collaboration between force and displacement is quantified as positive work, which indicates that the external force supports and promotes the object's motion. Examples of positive work include lifting a body against gravity or stretching a spring.

• Maximum work(W_max): FS [When cosθ is maximum, i.e. θ=0^o]

2. Negative work: Negative work occurs when a force is applied in the opposite direction of the displacement. This opposition between force and displacement produces negative work, indicating that the external force slows or opposes the object's motion. When a person lowers a body to the ground against gravity, they are performing negative work.

• Minimum work(W_min): -FS [When cosθ is -1, i.e. θ=180^o]

3. Zero work: Under the following three specific conditions, the work done becomes zero.

• If the force is perpendicular to the displacement.
• If there is no displacement, i.e. S=0
• If there is no force acting on the body, i.e. F=0

Work Done by a Variable Force

If the applied force (F) varies along the path, the work required to move a body from position A to B can be calculated by integrating the product of the force and differential displacement.

$W={\int }_A^B\overrightarrow{F}\cdot d\overrightarrow{s}={\int }_A^B(F\cos \theta )ds$

Work Done Calculation by Force Displacement Graph

The work done by a force on an object can be calculated using the area under the force-displacement graph.

$\begin{array}{rl}& dW=Fdx\\ & \therefore W={\int }_{x_i}^{x_f}dW={\int }_{x_i}^{x_f}\overrightarrow{F}dx\\ & \therefore W={\int }_{x_i}^{x_f}\text{ (strip area with width }dx\text{ ) }\\ & \therefore W=\text{ Area under curve Between }{x}_i\text{ and }{x}_f\end{array}$

Energy

The energy of a body is essentially its ability or capacity to get things done, or in other words, to do work.

• The SI unit of energy is the same as the work is Joule (J).

Kinetic Energy

Kinetic energy is the energy possessed by an object due to its motion.

$$\text{ Kinetic Energy }(\mathrm{KE})=\frac{1}{2}m{v}^2$$

Where: KE is the kinetic energy, m is the mass of the object and v is its velocity.

Relation of kinetic energy with linear momentum

$\begin{array}{rl}& \mathrm{KE}(\mathrm{E})=\frac{1}{2}m{v}^2=\frac{1}{2}\left[\frac{p}{v}\right]v^2\{\text{ from }\mathrm{p}=\mathrm{mv}\}\\ & \Rightarrow \mathrm{E}=\frac{1}{2}pv\\ & \mathrm{E}=\frac{p^2}{2m}\{\text{ from }\mathrm{v}=\mathrm{p}/\mathrm{m}\}\\ & \text{ And Momentum }(\mathrm{P})=\sqrt{2mE}\end{array}$

Potential Energy

Potential energy is the energy that an object has because of its position or state.

Types of Potential Energy

Gravitational Potential Energy (GPE): It is the energy associated with an object's height in a gravitational field.

$$\text{ Potential Energy }(U)=\mathrm{mgh}$$

Where, U is the potential energy, m is the mass of the object, g is the acceleration due to gravity and h is the height of the object above a reference point.

Elastic Potential Energy: For objects like springs or rubber bands, the potential energy is associated with how much the material is stretched or compressed.

When an elastic spring is compressed (or strained) by a distance x from its equilibrium state, its elastic potential energy is represented by:

$$U=\frac{1}{2}k{x}^2$$

Where, k is the force constant of a given spring.

Work-Energy Theorem

It states that the work done on an object is equal to the change in its kinetic energy. Mathematically, it is expressed as:

W= Change in K. E. of a body =Δ KE

Or,

$\begin{array}{rl}& W=\frac{1}{2}m{v}^2-\frac{1}{2}m{v}_0^2\\ & W=k_f-k_i\end{array}$

Where, v_o is initial velocity and v is final velocity

Law of Conservation of Energy

The Law of Conservation of Energy asserts that energy is neither created nor destroyed; it merely changes from one form to another.

1. Conservation of Mechanical Energy: In systems where only conservative forces are at play, the total mechanical energy (sum of kinetic and potential energy) remains constant. This principle is expressed as K + U = E, where K is the kinetic energy, U is the potential energy, and E is the total mechanical energy. The conservation of mechanical energy implies that in the absence of non-conservative forces like friction or air resistance, the total energy within the system remains unchanged.
2. Law of Conservation of Total Energy: This law states that while energy may transform from one type to another, the total energy within an isolated system remains constant. In other words, energy cannot be created or destroyed; it can only change forms. This principle is a fundamental concept in physics and holds true for various physical processes.

Power

The power (P) of a body is defined as the rate at which the body can do work. Mathematically, power is expressed as the amount of work done (W) divided by the time (t) taken to do that work. The formula for power is:

Average $Power\left(P_{\text{avg }}\right)=\frac{\mathrm{\Delta }w}{\mathrm{\Delta }t}=\frac{{\int }_0^{t}p\cdot dt}{{\int }_0^{t}dt}$
Instantaneous $Power(P)=\frac{dw}{dt}=P=\overrightarrow{F}\cdot \overrightarrow{v}$

• Dimension of power: [ML²T^-3]
• Unit of power: Watt or Joule/sec [S.I.], Erg/sec [C.G.S.]
• Practical unit: Kilowatt (kW), Megawatt (MW) and Horsepower (hp)

Collision

A collision occurs when two or more objects come into contact for a short period, during which they exert forces on each other. These forces can cause changes in the motion of the objects involved. Collisions are important because they help us understand how momentum and kinetic energy are transferred and conserved.

Types of collision

On the basis of conservation of kinetic energy, there are mainly three types of collision

• Perfectly Elastic Collision: In a perfectly elastic collision, the system's kinetic energy is conserved, which means that the total kinetic energy before and after the collision is the same. There is no net loss or gain in kinetic energy, and the objects involved bounce off each other without deforming or losing energy to other forms.
• Inelastic collision: In an inelastic collision, the system's kinetic energy is not conserved; that is, the kinetic energy after the collision differs from the kinetic energy before the collision. Some of the initial kinetic energy is converted into different forms, such as internal energy, heat, or deformation.
• Perfectly inelastic collision: Inelastic collisions occur when the kinetic energy after the collision is less than the kinetic energy before the collision. In inelastic collisions, some of the initial kinetic energy is converted into other forms, while the total kinetic energy is not conserved.

Types of collision based on the direction of colliding bodies

• Head on or one dimensional collision: when the motion of colliding particles before and after the collision occurs along the same line, it is referred to as a "head-on" or "one-dimensional" collision. In such collisions, the initial and final velocities of the particles are aligned along a straight line, simplifying the analysis of the collision dynamics.

$$\begin{array}{rl}& \frac{1}{2}{m}_1{u}_1^2+\frac{1}{2}{m}_2{u}_2^2=\frac{1}{2}{m}_1{v}_1^2+\frac{1}{2}{m}_2{v}_2^2-(1)\\ & m_1{u}_1+m_2{u}_2=m_1{v}_1+m_2{v}_2-(2)\end{array}$$

$m_1,m_2$ : masses
$u_1,v_1$ : initial and final velocity of the mass $m_1$
$u_2,v_2$ : initial and final velocity of the mass $m_2$
From equation (1) and (2) We get,

$$u_1-u_2=v_2-v_1\dots \dots \text{ (3) }$$

From equations (1),(2), (3) We get

$$\begin{array}{rl}{v}_1& =\left(\frac{m_1-m_2}{m_1+m_2}\right)u_1+\frac{2m_2{u}_2}{m_1+m_2}\\ v_2& =\left(\frac{m_2-m_1}{m_1+m_2}\right)u_2+\frac{2m_1{u}_1}{m_1+m_2}\end{array}$$

• Perfectly Elastic Oblique Collision:

Let two bodies move as shown in the figure. By the law of conservation of momentum,

Along x-axis-

$$m_1{u}_1+m_2{u}_2=m_1{v}_1\cos \theta +m_2{v}_2\cos \varphi \dots -(1)$$

Along y-axis-

$$0=m_1{v}_1\sin \theta -m_2{v}_2\sin \varphi \dots -(2)$$

By the law of conservation of kinetic energy

$$\frac{1}{2}{m}_1{u}_1^2+\frac{1}{2}{m}_2{u}_2^2=\frac{1}{2}{m}_1{v}_1^2+\frac{1}{2}{m}_2{v}_2^2\dots -(3)$$

So along the line of impact (here along in the direction of ) We apply e $=1$

$$e=1=\frac{v_2-v_1\cos (\theta +\varphi )}{u_1\cos \varphi -u_2\cos \varphi }\dots$$

So we solve these equations $(1),(2),(3),(4)$ to get unknown.

• Perfectly Inelastic Collision

After a collision, two bodies stick together, resulting in a final common velocity.

• When the colliding bodies are moving in the same direction

$\begin{array}{rl}& m_1{u}_1+m_2(-u_2)=(m_1+m_2)v\\ & v=\frac{m_1{u}_1-m_2{u}_2}{m_1+m_2}\end{array}$

• When the colliding bodies are moving in the opposite direction

$\begin{array}{rl}& m_1{u}_1+m_2{u}_2=(m_1+m_2)v\\ & v=\frac{m_1{u}_1+m_2{u}_2}{(m_1+m_2)}\end{array}$

How to Use Physics Class 11 Chapter 5 Notes PDF Effectively?

Skim the Notes: Get an overview of the topics..

Focus on Key Concepts: Understand the core ideas like work, energy, and power

Read Actively: Highlight important points and formulas.

Take Notes: Write in your own words and make diagrams.

Solve Examples: Work through examples and practice problems.

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Clarify Doubts: Ask questions whenever needed.

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Importance of NCERT Class 11 Physics Chapter 5 Notes

Class 11 notes on work, energy, and power offer a comprehensive review of the chapter, improving understanding of fundamental concepts. These NCERT Class 11 Physics Chapter 5 notes are particularly useful for competitive exams like VITEEE, BITSAT, JEE Main, and NEET, as they cover key topics from the CBSE Physics syllabus. The availability of a PDF download provides the convenience of offline study.

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