# Work, Energy, And Power NCERT Textbook PDF

### Chapter 6: Work, Energy, and Power

#### 6.1 Introduction

The terms ‘work’, ‘energy’, and ‘power’ are frequently used in everyday language.

A farmer ploughing the field, a construction worker carrying bricks, a student studying for a competitive examination, an artist painting a beautiful landscape, all are said to be working.

In physics, however, the word ‘Work’ covers a definite and precise meaning.

Somebody who has the capacity to work for 14-16 hours a day is said to have large stamina or energy. We admire a long-distance runner for her stamina and energy.

Energy is thus our capacity to do work. In Physics too, the term ‘energy’ is related to work in this sense, but as said above the term ‘work’ itself is defined much more precisely. The word ‘power’ is used in everyday life with different shades of meaning.

In karate or boxing, we talk of ‘powerful’ punches. These are delivered at a great speed. This shade of meaning is close to the meaning of the word ‘power’ used in physics.

We shall find that there is at best a loose correlation between the physical definitions and the physiological pictures these terms generate in our minds.

The aim of this chapter is to develop an understanding of these three physical quantities. Before we proceed with this task, we need to develop a mathematical prerequisite, namely the scalar product of two vectors.

#### 6.1.1 The Scalar Product

We have learned about vectors and their use in Chapter 4. Physical quantities like displacement, velocity, acceleration, force, etc. are vectors.

We have also learned how vectors are added or subtracted. We now need to know how vectors are multiplied.

There are two ways of multiplying vectors we shall come across: one way known as the scalar product gives a scalar from two vectors and the other known as the vector product produces a new vector from two vectors.

We shall look at the vector product in Chapter 7. Here we take up the scalar product of two vectors. The scalar product or dot product of any two vectors A and B denoted as A.B (read

A dot B) is defined as A.B = A B cos θ

#### 6.7 The Concept of Potential Energy

The word potential suggests possibility or capacity for action. The term potential energy
brings to one’s mind ‘stored’ energy.

A stretched bow string possesses potential energy. When it is released, the arrow flies off at a great speed.

The earth’s crust is not uniform but has discontinuities and dislocations that are called fault lines. These fault lines in the earth’s crust are like ‘compressed springs’. They possess a large amount of potential energy.

An earthquake results when these fault lines readjust. Thus, potential energy is the ‘stored energy’ by virtue of the position or configuration of a body.

The body left to itself releases this stored energy in the form of kinetic energy. Let us make our notion of potential energy more concrete.

### NCERT Solutions Class 11 Physics Chapter 6 Work, Energy, and Power

Que.1.The sign of work done by a force on a body is important to understand. State carefully if the following quantities are positive or negative:

(a) work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket.
(b) work done by the gravitational force in the above case,
(c) work done by friction on a body sliding down an inclined plane,
(d) work done by an applied force on a body moving on a rough horizontal plane with uniform
velocity,
(e) work done by the resistive force of air on a vibrating pendulum in bringing it to rest

Ans.

(a) It is clear that the direction of both the force and the displacement is the same and thus the work done on it is positive.

(b) It can be noted that the displacement of the object is in an upward direction whereas, the force due to gravity is in a downward direction. Hence, the work done is negative.

(c) It can be observed that the direction of motion of the object is opposite to the direction of the frictional force. So, the work done is negative.

(d) The object which is moving in a rough horizontal plane faces the frictional force which is opposite to the direction of the motion. To maintain a uniform velocity, a uniform force is applied to the object. So, the motion of the object and the applied force are in the same direction. Thus, the work done is positive.

(e) It is noted that the direction of the bob and the resistive force of air which is acting on it are in opposite directions. Thus, the work done is negative.

Que.2. A body is initially at rest. It undergoes one-dimensional motion with constant acceleration. The power delivered to it at time t is proportional to

(i) t^{\frac{1}{2}}t21​

(ii) t^{\frac{3}{2}}t23​

(iii) t2

(iv) t

Ans. body mass = m

Acceleration = a

According to Newton’s second law of motion:

F = ma (constant)

We know that a = \frac{dv}{dt}dtdv​ = constant

dv = dt x constant

On integrating

v = \alphaαt \rightarrow→ 1

Where, \alphaα is also a constant

v \propto∝ t \rightarrow→ 2

The relation of power is given by:

P = F.v

From equation 1 & 2

P \propto∝ t

Thus, from the above, we conclude that power is proportional to time.