### Work Energy and Power - Revision Notes

CBSE Class XI PHYSICS

Revision Notes

CHAPTER 6

WORK, ENERGY AND POWER

- 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.

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 , where is the angle between A and B. It can bepositive, negative or zero depending upon the value of . 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 | J | W=F.d. | |

Kinetic Energy | K | J | ||

Potential energy | V(x) | J | ||

Mechanical energy | E | J | E= K+V | |

Spring Constant | K | |||

Power | P | W | P=F.v |