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11 Physics notes Chapter 6 Work, Energy and Power

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CBSE Class XI PHYSICS
Revision Notes
CHAPTER 6
WORK, ENERGY AND POWER CLASS 11 NOTES

Notions of work, work-energy theorem, power
Kinetic energy
Potential energy
The conservation of Energy
Non-conservative forces-Motion in a vertical circle, Collisions

SUMMARY

1. The work-energy theorem states that the change in kinetic energy of a body is the workdone by the net force on the body.

${{\text{K}}_f}\; - {\text{ }}{{\text{K}}_i}\; = {\text{ }}{{\text{W}}_{net}}$

2. A force is conservative if (i) work done by it on an object is path independent anddepends only on the end points {xi, xj}, or (ii) the work done by the force is zero for anarbitrary closed path taken by the object such that it returns to its initial position.

3. For a conservative force in one dimension, we may define a potential energy function V(x)such that $\begin{gathered} {\text{F (x) = }}\frac{{dV(x)}}{{dx}} \hfill \\ {\text{ or }}{{\text{V}}_1}{\text{ }}{{\text{V}}_j}{\text{ = }}\int_{{x_i}}^{{x_f}} {F(x)dx} \hfill \\\end{gathered}$

4. The principle of conservation of mechanical energy states that the total mechanicalenergy of a body remains constant if the only forces that act on the body are conservative.

5. The gravitational potential energy of a particle of mass m at a height x about the earth’s surface is V(x) = m g x

where the variation of g with height is ignored.

6. The elastic potential energy of a spring of force constant k and extension x is ${\text{V x = }}\frac{1}{2}\;\;{\text{k }}{{\text{x}}^2}$

7. The scalar or dot product of two vectors A and B is written as A. B and is a scalar quantity given by : A.B = AB cos $\theta$ , where $\theta$ is the angle between A and B. It can be positive, negative or zero depending upon the value of $\theta$ . The scalar product of two vectors can be interpreted as the product of magnitude of one vector and component of the other vector along the first vector. For unit vectors :

${\text{ }}\widehat {i.}\;\widehat i = \widehat j.\widehat j \\= \widehat k{\text{.}}\widehat k{\text{ = 1 and }}\widehat {i.}\;\widehat j \\= \widehat j.\widehat k = \widehat k{\text{.}}\widehat i{\text{ = }}0$

Scalar products obey the commutative and the distributive laws.

Physical Quality	Symbol	Dimensions	units	Remarks
Work	W	$[M{L^2}{T^{ - 2}}]$	J	W=F.d.
Kinetic Energy	K	$[M{L^2}{T^{ - 2}}]$	J	$K = \frac{1}{2}m{\nu ^2}$
Potential energy	V(x)	$[M{L^2}{T^{ - 2}}]$	J	$F(x) = \frac{{dv(x)}}{{dx}}$
Mechanical energy	E	$[M{L^2}{T^{ - 2}}]$	J	E= K+V
Spring Constant	K	${T^{ - 2}}$	$[N{m^{ - 1}}]$	$\begin{gathered} {text{F}} = - {\text{kx}} \hfill \\{\text{V}}\left( {\text{x}} \right) = \frac{1}{2}k{x^2} \hfill \\\end{gathered}$
Power	P	$[M{L^2}{T^{ - 3}}]$	W	P=F.v ${\text{P}} = \frac{{dw}}{{dt}}$

Work, Energy and Power class 11 Notes

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Work, Energy and Power class 11 Notes. CBSE quick revision note for class-11 Physics, Chemistry, Maths, Biology and other subject are very helpful to revise the whole syllabus during exam days. The revision notes covers all important formulas and concepts given in the chapter. Even if you wish to have an overview of a chapter, quick revision notes are here to do if for you. These notes will certainly save your time during stressful exam days.

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