Work Energy and Power - Revision Notes

 CBSE Class XI PHYSICS 

Revision Notes
CHAPTER 6
WORK, ENERGY AND POWER

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1. Notions of work, work-energy theorem, power
2. Kinetic energy
3. Potential energy
4. The conservation of Energy
5. Non-conservative forces-Motion in a vertical circle, Collisions

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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.

Kf− Ki= Wnet${\text{K}}_f-{\text{K}}_i={\text{W}}_{net}$

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 F (x) = dV(x)dx or V1 Vj = ∫xfxiF(x)dx$\begin{array}{c}\text{F (x) = }\frac{dV(x)}{dx}\\ \text{ or }{\text{V}}_1{\text{V}}_j\text{ = }{\int }_{x_i}^{x_f}F(x)dx\end{array}$

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 V x = 12k x2$\text{V x = }\frac{1}{2}\text{k }{\text{x}}^2$

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

 i.ˆiˆ=jˆ.jˆ=kˆ.kˆ = 1 and i.ˆjˆ=jˆ.kˆ=kˆ.iˆ = 0$$\begin{gathered} \widehat{i.}\hat{i}=\hat{j}.\hat{j} \\ =\hat{k}\text{.}\hat{k}\text{ = 1 and }\widehat{i.}\hat{j} \\ =\hat{j}.\hat{k}=\hat{k}\text{.}\hat{i}\text{ = }0 \end{gathered}$$

Scalar products obey the commutative and the distributive laws.

Physical Quality	Symbol	Dimensions	units	Remarks
Work	W	[ML2T−2]$[M{L}^2{T}^{-2}]$	J	W=F.d.
Kinetic Energy	K	[ML2T−2]$[M{L}^2{T}^{-2}]$	J	K=12mν2$K=\frac{1}{2}m{\nu }^2$
Potential energy	V(x)	[ML2T−2]$[M{L}^2{T}^{-2}]$	J	F(x)=dv(x)dx$F(x)=\frac{dv(x)}{dx}$
Mechanical energy	E	[ML2T−2]$[M{L}^2{T}^{-2}]$	J	E= K+V
Spring Constant	K	T−2$T^{-2}$	[Nm−1]$[N{m}^{-1}]$	textF=−kxV(x)=12kx2$\begin{array}{c}textF=-\text{kx}\\ \text{V}\left(\text{x}\right)=\frac{1}{2}k{x}^2\end{array}$
Power	P	[ML2T−3]$[M{L}^2{T}^{-3}]$	W	P=F.v P=dwdt