Work Energy and Power- Topics, Notes, Books, FAQs
You must have heard these terms work, energy, and power very frequently in your day to day life, like a barber cutting hair, a laborer lifting bricks and transporting them and a student studying are all said to be working. But here in physics, work is defined using very specific words and it has a very precise meaning. Similarly, a gymnast who can do a lot number of pull-ups we say that he/she has very good stamina or in other words, he/she has a good amount of energy. This means energy is something which tells about the capacity to do the work.
This Story also Contains
- Work Energy and Power Class 11th Topics (NCERT Syllabus)
- Important Formulas - Work, Energy and Power
- Real-Life Applications of Work, Energy, and Power
- Exam-wise Weightage of Work, Energy and Power Class 11
- How to prepare Work Energy and Power
- Work Energy and Power- Books
In physics as well energy is related to work similarly but as already mentioned the definition of the word Work is very precise itself in Physics hence the definition of energy as well. We often come across the word Power as well, for example, the bodybuilder hit the punching bag with huge power, so in a very crude way, we could say that the rate of doing work is power. We could loosely correlate the physical definitions and physiological pictures. In this chapter, we would go in depth of the definitions and relations between these three physical quantities.
Work Energy and Power Class 11th Topics (NCERT Syllabus)
1. Introduction
In our daily lives, we come across terms like work, energy, and power. Physics gives these words a specific meaning. Work is said to be done when a force is applied on an object and the object gets displaced. Energy is the capacity to do work, and power is the rate at which work is done. This chapter builds the connection between force, motion, work, and energy through mathematical laws.
2. Notions of Work and Kinetic Energy: The Work-Energy Theorem
Work: The product of force and displacement in the direction of force.
Kinetic Energy: The energy possessed by a body due to its motion.
Work-Energy Theorem: The net work done on a body by all the forces acting on it is equal to the change in its kinetic energy.
$
W=\Delta K E=K E_f-K E_i
$
This theorem provides a powerful link between dynamics and energy.
3. Work
Work is defined mathematically as:
$
W=\vec{F} \cdot \vec{d}=F d \cos \theta
$
Where $F$ is the magnitude of force, $d$ is the displacement, and $\theta$ is the angle between force and displacement.
Work is positive when force has a component in the direction of displacement, and negative when opposite.
4. Kinetic Energy
The kinetic energy of an object of mass $m$ moving with velocity $v$ is given by:
$
K E=\frac{1}{2} m v^2
$
It is a scalar quantity and depends only on the speed (not direction).
5. Work Done by a Variable Force
When force is not constant, work is calculated by integration:
$
W=\int_{x_i}^{x_f} F(x) d x
$For example, in the case of a spring, force varies with extension or compression.
6. The Work-Energy Theorem for a Variable Force
Even for variable forces, the work-energy theorem holds true:
$
\Delta K E=\int_{x_i}^{x_f} F(x) d x
$
This means that the change in kinetic energy of the particle equals the work done by the net force, whether the force is constant or variable.
7. The Concept of Potential Energy
Potential energy is the energy stored in a body due to its position or configuration.
For a body of mass $m$ at height $h$ :
$
P E=m g h
$
Potential energy is relative and depends on the choice of reference level.
8. The Conservation of Mechanical Energy
For conservative forces (like gravity, spring force):
$
K E+P E=\text { Constant }
$
That is, the total mechanical energy of a system remains constant if only conservative forces act.
9. The Potential Energy of a Spring
For a spring stretched or compressed by a distance $x$ :
$
P E=\frac{1}{2} k x^2
$
where $k$ is the spring constant. This comes from the work done against the restoring spring force.
10. Power
Power is the rate of doing work:
$
P=\frac{W}{t}
$
Instantaneous Power:
$
P=\vec{F} \cdot \vec{v}
$
SI unit: Watt (W).
11. Collisions
A collision is an interaction between two bodies for a short time during which they exert large forces on each other.
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 collision.
Important Formulas - Work, Energy and Power
Work
$
W=\vec{F} \cdot \vec{d}=F d \cos \theta
$
Work done by a variable force:
$
W=\int_{x_i}^{x_f} F(x) d x
$
Kinetic Energy (KE)
$
K E=\frac{1}{2} m v^2
$
Work-Energy Theorem
$
W_{n e t}=\Delta K E=K E_f-K E_i
$
Potential Energy (PE)
- Gravitational:$P E=m g h$
- Spring potential energy:$P E=\frac{1}{2} k x^2$
Conservation of Mechanical Energy
$
K E+P E=\mathrm{constant} \quad(\text { for conservative forces })
$
Power
- Average Power:$P=\frac{W}{t}$
- Instantaneous Power:$P=\vec{F} \cdot \vec{v}$
Collisions
Law of Conservation of Momentum:
$
m_1 u_1+m_2 u_2=m_1 v_1+m_2 v_2
$
Elastic Collision in One Dimension:
$
u_1-u_2=-\left(v_1-v_2\right)
$
(Momentum and KE conserved)
Perfectly Inelastic Collision:
$
v=\frac{m_1 u_1+m_2 u_2}{m_1+m_2}
$
Real-Life Applications of Work, Energy, and Power
- Lifting a bag involves work against gravity, storing energy as gravitational potential energy.
- A moving vehicle uses the engine’s power to increase its kinetic energy.
- In hydroelectric dams, water’s potential energy converts into kinetic energy and then into electricity.
- Compressed springs in toys store potential energy and release it as motion.
- In sports, kinetic energy of players is transferred to the ball while hitting or kicking it.
- Household appliances like fans, mixers, and washing machines show power as the rate of doing work.
Exam-wise Weightage of Work, Energy and Power Class 11
| Exam | Weightage | Remarks |
|---|---|---|
| JEE Main | Usually 1–2 questions | Mostly numerical or conceptual problems on work, energy, power, and conservation laws. |
| JEE Advanced | 1–2 Questions | Often, multi-concept problems combining work-energy theorem, conservation of energy, and power. |
| NEET (Physics) | 1 Question | mostly conceptual or formula-based on work, energy, and power. |
How to prepare Work Energy and Power
It is one of the basic and important chapters in mechanics because with the help of the concept used in this chapter you will be able to solve questions from other mechanics chapters as well. So for preparing this chapter, you need to remember the concept from laws of motion and you should be able to understand what kind of forces are acting on the particle. You should also understand how scalar product of the two vectors is operated and what is the significance of scalar product. Because work, energy, and power all are a scalar quantity.
Work Energy and Power- Books
For this chapter, we would recommend you to first go through NCERT book and your Lab manual and solve questions from those chapters. Then you should solve questions from NCERT Exemplar book for a good hold on this chapter. If you want to test yourself for competitive exams, then you should read Understanding Physics by D.C. Pandey.
NCERT Notes Subject Wise Link:
- NCERT notes Class 11 Maths
- NCERT notes Class 11 Physics
- NCERT notes Class 11 Chemistry
- NCERT notes Class 11 Biology
NCERT Solutions Subject wise link:
- NCERT solutions for class 11 Physics.
- NCERT solutions for class 11 Chemistry.
- NCERT solutions for class 11 Mathematics.
- NCERT solutions for class 11 Biology.
NCERT Exemplar Solutions Subject wise link:
Frequently Asked Questions (FAQs)
In an elastic collision, both momentum and kinetic energy are conserved.
Work is the total energy transferred, while power is the rate at which work is done.
The net work done on a body by all the forces acting on it is equal to the change in its kinetic energy.
Kinetic energy is the energy possessed by a body due to motion, while potential energy is the energy possessed due to position or configuration.
Work is done only when a force is applied on a body and the body gets displaced in the direction of the force.