Work Energy and Power- Topics, Notes, Books, FAQs

Important Topics of Work, Energy and Power

The important topics of the chapter Work, Energy and Power explain how energy is transferred, stored, and transformed in mechanical systems. These topics introduce the concepts of work done by forces, different forms of energy, and the rate at which work is done. They are used to comprehend the relationship between force, motion, and changes in energy. In order to solve numerical problems and real-life applications in mechanics, mastery of these topics is critical.

1. Work Done by a Force

The work is said to be done when the force exerted on a body causes displacement in the direction of the force. Work is mathematically defined as the product of force and displacement, i.e. F.d cos$\theta$. Positive, negative, or zero Work depends on the angle between force and displacement. This principle is used to examine the way forces cause energy to be transferred to or taken away from a body.

2. Kinetic Energy

Kinetic energy is the energy of the body because of its movement, and it is equal to K = 1/2 mv². It is dependent on the mass and velocity of the body. Due to its kinetic energy, a moving object is able to perform work. The speed change is directly proportional to the kinetic energy, and hence it is essential in collision and motion-related issues.

3. Work–Energy Theorem

According to the work-energy-theorem, the sum of all forces which act upon a body causes an increase or a decrease in its kinetic energy. This is the theorem that offers an effective alternative to Newton's laws in solving motion problems. It makes the calculations easy when the forces are dependent on position or in cases where motion is complicated. The theory is very common in mechanical problems.

4. Potential Energy

Potential energy is defined as the energy that a given body has because of its position or shape. In mechanics, the gravitational potential energy at the surface of the Earth is represented by U=mgh. Potential energy depends on the level of choice of the reference. It is a form of stored energy which may be transformed into kinetic energy when in motion.

5. Conservative Forces

A force is said to be conservative when the amount of work it does is determined by the initial and final positions of the point, but not the route taken. Examples of conservative forces are gravitational and elastic forces. In the case of such forces, potential energy can be defined. Energy conservation depends on the conservative forces.

6. Non-Conservative Forces

The non-conservative forces are those forces where the work done is dependent on the path taken. The most typical example is friction. These forces transform mechanical energy into other forms like heat and sound. Due to this reason, the mechanical energy is not conserved when there are non-conservative forces.

7. Mechanical Energy

The kinetic energy plus the potential energy of a system is referred to as mechanical energy, E=K+U. It is the sum of the energy that can be used to perform some mechanical work. The principle of mechanical energy assists in the examination of systems where energy is changed between kinetic and potential energy.

8. Law of Conservation of Mechanical Energy

According to the law of conservation of mechanical energy, the total mechanical energy of a system is constant when conservative forces are the only forces which act upon the system. This principle is used to explain several phenomena in nature, including falling objects, motion and oscillation on smooth surfaces. It is particularly helpful in solving those problems that do not make direct use of forces.

9. Power

Power is the rate of doing work:

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

Instantaneous Power:

$
P=\vec{F} \cdot \vec{v}
$

11. Collision

A collision is an encounter between two or more bodies over a brief period of time. The collisions may be elastic and inelastic. During the elastic collisions, all momentum and kinetic energy is conserved, whereas the momentum is conserved in inelastic collisions. Collision analysis has significance in particle motion and in real-life applications.
Elastic Collision: Both momentum and kinetic energy are conserved.
Inelastic Collision: Only momentum is conserved; kinetic energy is partly lost as heat, sound, or deformation.
Perfectly Inelastic Collision: Bodies stick together after a collision.

Important Formulas of Work, Energy and Power

The formulas in the chapter Work, Energy and Power describe how forces transfer energy, how energy is stored in different forms, and how fast work is done. These relations are essential for analysing mechanical systems and solving numerical problems accurately.

1. Work:

$
W=\vec{F} \cdot \vec{d}=F d \cos \theta
$

2. Work done by a variable force:

$
W=\int_{x_i}^{x_f} F(x) d x
$

3. Kinetic Energy (KE):

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

4. Work-Energy Theorem:

$
W_{n e t}=\Delta K E=K E_f-K E_i
$

5. Potential Energy (PE):

• Gravitational:$P E=m g h$
• Spring potential energy:$P E=\frac{1}{2} k x^2$

6. Conservation of Mechanical Energy

$
K E+P E=\mathrm{constant} \quad(\text { for conservative forces })
$

7. Power

• Average Power:$P=\frac{W}{t}$
• Instantaneous Power:$P=\vec{F} \cdot \vec{v}$

8. Law of Conservation of Momentum:

$
m_1 u_1+m_2 u_2=m_1 v_1+m_2 v_2
$

9. Collisions:

• Elastic Collision in One Dimension:

Conservation of momentum:

$
m_1 u_1+m_2 u_2=m_1 v_1+m_2 v_2
$
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
$

• Perfectly Inelastic Collision:

$
v=\frac{m_1 u_1+m_2 u_2}{m_1+m_2}
$

10. Coefficient of Restitution:

$e=\frac{\text { relative speed of separation }}{\text { relative speed of approach }}$

Work, Energy and Power: Previous Year Questions

Previous year questions from the chapter Work, Energy and Power mainly focus on the application of energy concepts, work–energy theorem, power, and conservation of mechanical energy. These questions help students understand the exam pattern and identify frequently tested formulas and problem types. Practising them improves numerical-solving skills, accuracy, and conceptual clarity. This section is highly useful for effective revision and exam-oriented preparation.

Question 1:

Two blocks $\mathrm{M}_1$ and $\mathrm{M}_2$ having equal mass are free to move on a horizontal frictionless surface. $\mathrm{M}_2$ is attached to a massless spring as shown in the figure. Iniially $\mathrm{M}_2$ is at rest and $\mathrm{M}_1$ is moving toward $\mathrm{M}_2$ with speed v and collides head-on with $\mathrm{M}_2$.

a. While spring is fully compressed all the KE of $\mathrm{M}_1$ is stored as PE of spring.
b. While spring is fully compressed the system momentum is not conserved, though final momentum is equal to initial momentum.
c. If spring is massless, the final state of the $\mathrm{M}_1$ is state of rest.
d. If the surface on which blocks are moving has friction, then collision cannot be elastic.

Solution:

If it is not specified we always consider the collision elastic.
When two bodies of equal masses collide elastically, their velocities are interchanged in these types of collision.
Kinetic energy and linear momentum remain conserved.
According to the above diagram, when $\mathrm{m}_1$ comes in contact with the spring, $\mathrm{m}_1$ is retarded by the spring force, and $\mathrm{m}_2$ is accelerated by the spring force.
a. The spring will continue to compress until the two blocks acquire a common velocity. So some of the kinetic energy of block $\mathrm{M}_{\mathrm{x}}$ is stored in P.E, and some part of it is stored in K.E of block $\mathrm{M}_2$. So option (a) is incorrect.
b. As surfaces are frictionless momentum of the system will be conserved. So option (b) is also incorrect.
c. The two bodies of equal mass exchange their velocities in a head-on elastic collision between them. So, if spring is massless, the final state of the $M_1$ is a state of rest.
d. Since there is a loss of K.E when the blocks collide on the rough surface. Hence, the collision is inelastic.

Question 2:

A cricket ball of mass 150 g moving with a speed of 126 km/h hits at the middle of the bat, held firmly at its position by the batsman. The ball moves straight back to the bowler after hitting the bat. Assuming that collision between ball and bat is completely elastic and the two remain in contact for 0.001s, the force that the batsman had to apply to hold the bat firmly at its place would be

Solution:

momentum $=m(v-u)=\frac{3}{20}(-70)=\frac{-21}{2}$
Force $
=\frac{\frac{-21}{2}}{0.001}=-1.05 \times 10^4 \mathrm{~N}
$
The negative sign indicates the opposite direction of the force. Hence the force exerted by batman should be

$
1.05 \times 10^4 \mathrm{~N}
$

Quetion 3:

In a shotput event, an athlete throws the shotput of mass 10 kg with an initial speed of $1 \mathrm{~m} \mathrm{~s}^{-1}$ at $45^{\circ}$ from a height 1.5 m above ground. Assuming air resistance to be negligible and acceleration due to gravity to be $10 \mathrm{~m} \mathrm{~s}^{-2}$, the kinetic energy of the shotput when it just reaches the ground will be

Solution:

K E=m g h+\frac{1}{2} m v^2 \\
& =10 \times 10 \times 1.5+\frac{1}{2} \times 10 \times 1=155 J
\end{aligned}
$
From the law of conservation of energy, we can write that, $(P E+K E)$ initial $=(P E+K E)$ final.

Hence, the final kinetic energy of the shotput: KE final $+0=155 \mathrm{~J}$
Hence the answer is 155 J.

Work, Energy and Power in Different Exams

Work, Energy and Power chapter is a good and scoring chapter in a number of school-level and competitive examinations because of its solid concept foundation and problems with formulas. This chapter is assessed by different exams using numerical questions, conceptual issues, and reasoning on energy. Proper understanding of work-energy relations, energy conservation, power is beneficial to enable students to solve questions of different levels of difficulty. The chapter is important in developing problem solving abilities in mechanics in board and competitive examination.

Important Books and Resources for Class 11 Work, Energy and Power

In order to master the chapter Work, Energy and Power, students are expected to consult quality textbooks, reference guides, and practice materials, which describe basic concepts, and numerical applications of work, energy, power and collisions. These materials aid in the development of good conceptual understanding and problem-solving abilities that one requires in school examinations and also competitiveness exams such as JEE Main, JEE Advanced and NEET.

NCERT Resources for Work, Energy and Power

NCERT resources for Work, Energy and Power are the most reliable and exam-oriented materials for mastering this chapter as per the Class 11 Physics syllabus. The NCERT textbook as well as exemplar problems covers the fundamental concepts of work done by forces, kinetic energy, potential energy, power, work-energy theorem and conservation of energy in an easy to understand theory, diagrams and numerical examples. Proper preparation by NCERT is the key to successfully scoring a good score in Class 11 exams and even in competitive exams such as NEET and JEE Main because a large number of questions are specifically tied to NCERT concepts and examples.

• NCERT solutions for Class 11 Physics Chapter 5 Work, Energy and Power
• NCERT notes Class 11 Physics Chapter 5 Work, Energy and Power
• NCERT Exemplar Class 11 Physics Solutions Chapter 6

NCERT Subject-Wise Resources

NCERT subject-wise materials are organised and syllabus-based learning content on various subjects, which assists students in developing a good conceptual basis. They consist of textbooks, exemplar problems, and solutions and can thus be very helpful in the preparation for the board exams and even competitive exams such as JEE and NEET.

Practice Questions based on Work, Energy and Power

Practice questions from the chapter Work, Energy and Power help students strengthen their understanding of energy concepts and their applications in mechanics. Work-energy theorem, conservation of energy, calculation of power and collision analysis are used in the answers of these questions. Practice enhances numerical-solving proficiency, clarity of concepts and speed. The answers to such questions are critical to succeeding in school tests and competitive tests such as JEE Main and NEET.

Conclusion

Work, Energy and Power chapter gives a solid conceptual base to the understanding of energy transfer and transformation in a mechanical system. Students can also possess effective analytical and numerical solving skills by reviewing the main concepts, essential formulas and principles including the work-energy theorem, conservation of energy and power. The approach of systematic and consistent practice will contribute to the development of confidence and accuracy. It is a very efficient preparation towards giving exams in Class 11 and also in competitive exams like JEE Main and NEET.