Work, Energy And Power Class 11 Notes Physics Chapter 6 - CBSE

Chapter : 6

What Are Work, Energy And Power ?

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Work

Work is said to be done by a force acting on a body, provided the body is displaced actually in any direction except in a direction perpendicular to the direction of the force.

Work done is defined as:

$$\omega=\vec{\text{F}}.\vec{\text{s}}$$

Work done by a constant force:

$$\omega =\vec{\text{F}}.\vec{\text{s}}\\\text{or}\space\omega =\text{Fs cos}\theta$$

Dimension and units of work: Work = [M¹ L² T^–2] Joule is the SI unit of work.

Erg is the absolute unit of work in C.G.S system.

Positive work: As

$$\omega =\vec{\text{F}}.\vec{\text{s}} =\text{Fs cos}\space \theta$$

∴ When θ is acute (θ < 90°), cos q is positive.

Hence work done is positive.

Negative work: As

$$\omega =\vec{\text{F}}.\vec{\text{s}} =\text{Fs cos}\space \theta$$

∴ When θ is obtuse (θ> 90°), cos q is negative.

Zero work: When angle θ between

$$\vec{\text{F}}\space\text{and}\space\vec{\text{s}} =\text{Fs cos}\theta$$

cos θ = cos 90° = 0. Therefore work done is zero.

Work done by a variable force:

$$w=\int^{x_{B}}_{x_{A}}\text{F(dx)}$$

Conservative Force: A force is said to be conservative if work done by or against the force in moving a body depends only on the initial and final positions of the body and not on the nature of path followed between the initial and final position. If the force depends on the path followed, the force is said to be non conservative.

Power

Power of a body is defined as the rate of doing work.

$$\text{P} =\frac{\text{work}}{\text{time}} =\frac{\text{w}}{\text{t}}\\=\frac{\vec{\text{F}}.\vec{\text{s}}}{t}\\\therefore\space \text{P} =\vec{\text{F}}.\vec{\text{v}}$$

Dimension of power:

$$\text{P} =\frac{w}{t} =\frac{[\text{M}^{1}\text{L}^{2}\text{T}^{\normalsize-2}]}{[\text{T}]}\\=[\text{M}^{1}\text{L}^{2}\text{T}^{-3}]$$

The absolute unit of power in SI is watt.

1w = 1 Js^-1

1 horse power = 746 w

Energy

Energy of a body is defined as the capacity or ability of the body to do the work.
The kinetic energy of a body is the energy possessed by the body by virtue of its motion.

$$\text{K.E. of body =}\\\text{k =}\frac{1}{2}\text{mv}^{2}$$

Relation between K.E. and linear momentum

$$\because\space\text{p = mv}\\\text{K} =\frac{1}{2}\text{mv}^{2} =\frac{1}{2}(m^{2}v^{2})\\\text{K} =\frac{\text{p}^{2}}{\text{2m}}$$

Work energy theorem: According to this principle, work done by a force is equal to the change in K.E. of the body.
The potential energy of a body is defined as the energy possessed by the body by virtue of its positon or configuration in same field.
Gravitational P.E. of the body = U = mgh.
Potential energy of the spring is given by

$$\text{U} =\frac{1}{2}\text{kx}^{2}$$

k is called force constant of the spring

The mechanical energy (E) of a body is the sum of kinetic energy (K) and potential energy (U) of the body: E = K + U
Different forms of energy are:

(i) Heat energy

(ii) Internal energy

(iii) Electrical energy

(iv) Chemical energy

(v) Nuclear energy

Mass energy equivalanece: E = mc²

Principle Of Conservation Of Energy

According to the principle of conservation of energy, the total sum of energy in an isolated system remains
constant at all times.
A collision in which there is absolutely no loss of K.E. is called an elastic collision.
A collision in which there occurs some loss of K.E. is called an inelastic collision.
Coefficient of restitution is defined as the ratio of relative velocity of separation after collision to the
relative velocity of approach before collision.

$$e = \frac{v_{2}-v_{1}}{v_{2}-v_{1}}$$

For perfectly elastic collision: e = 1
For perfectly inelastic collision: e = 0
Elastic collision in one Dimension:

$$v_{1}=\frac{(m_{1}-m_{2})v_{1}}{m_{1} + m_{2}} + \frac{2m_{2}v_{2}}{m_{1} + m_{2}}\\v_{2}=\frac{2m_{1}v_{1}}{m_{1} + m_{2}} + \frac{(m_{2}-m_{1})v_{2}}{(m_{1} + m_{2})}$$