### Work Energy and Power - Revision Notes

CBSE Class XI PHYSICS

Revision Notes
CHAPTER 6
WORK, ENERGY AND POWER

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

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.

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

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

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 $\theta$, where $\theta$ is the angle between A and B. It can bepositive, negative or zero depending upon the value of $\theta$. 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 :

Scalar products obey the commutative and the distributive laws.

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