Examville.com - Work, Energy And Power

Work, Energy and Power 1. Work is said to be done when a force applied on the body displaces the body through a certain distance in the direction of applied force. 2. Work done may be positive n negative or zero depending upon the direction of the force and the displacement of the body. 3. Work done by a force is W = F.S = FScosθ. Work done by a force is equal to the dot or scalar product of the force and the displacement of the body. (a). when θ = 0 0 , the force and displacement are in the same direction, then work done is positive i.e. W = FS. (b). When θ = 90 0 , the force and displacement are at right angle to each other, hence W = FScos90 0 = 0. So no work is done. (c). When θ = 180 0 , the force and displacement are in the opposite direction, so work done is negative. 4. Work is said to be one absolute unit if one absolute unit of force displaces the body through unit distance in the direction of force. Absolute units of work are (a). erg in c.g.s system. 1erg = 1 dyne x 1cm Work done is said to be I erg if I dyne force displaces the body through 1 cm in its own direction. (b). joule in SI unit system. I joule = 1 newton x 1m

Work done is said to be 1 joule if 1 newton force displaces the body through 1m in its own direction. I joule = 10 7 erg. 5. Work is said to be gravitational unit of work if a gravitation unit of force displaces the body through unit distance in the direction of force Gravitational units of work are (a). g-cm in c.g.s.system (b). Kg-m in SI unit system. 1 g cm = 981 erg 1 Kg-m = 9.81J 6. The energy of a body is its capacity for doing work. It is measured by the total amount of work that a body can do. The unit and dimensions of energy are same as that of work. Mechanical energy is the sum of Kinetic energy and Potential energy of the body. 7. The energy possessed by a body by virtue of its motion is called Kinetic energy. K.E = 1/2mv 2 The energy possessed by a body by virtue of its position or configuration is called potential energy. P.E = mgh. 8. Work done = Change in K.E. 9. Potential energy of a body on the surface of earth is zero. 10. According to Hooke’s law, the restoring force is proportional to the displacement x and its direction is always opposite to the displacement.

F=-Kx Work done to stretch a spring is stored as P.E of the stretched spring = 1/2 Kx 2 where K is the spring constant. 11. According to Law of conservation of energy, energy can neither be created nor destroyed but can be converted from one form to another. Total mechanical energy of a body remains conserved during the free fall of the body. 12. Power is defined as the rate at which work is done. It is a scalar quantity. Power of a body or agent, P = W/t = F.v = Fvcosθ 13. SI unit of power is Js - 1 or W. 1W = 1Js - 1 . Practical unit of power is horse power (H.P.) 1H.P = 746W. 14. The term collision refers to the interaction between two bodies or particles due to which the direction and magnitude of the velocity of colliding particles change. Collision is of three types (a). Perfectly elastic collision – A collision between two particles is said to be elastic if both the linear momentum and the kinetic energy of the system(two particles)remain conserved. (b). Inelastic collision – A collision is said to be inelastic if the linear momentum of the system remains conserved but kinetic energy is not conserved. In such kind of collisions, the loss of kinetic energy appears in the form of heat, sound and light energy etc.

(c).Perfectly inelastic collision – A collision is said to be perfectly inelastic if the two bodies after collision stick together and move as one body. In this collision, linear momentum of the system remains conserved. 15. In every type of collision, the linear momentum of the system remains conserved. 16. In perfectly elastic collision, the velocities of two colliding bodies after collision are v 1 = [2m 2 u 2 + u 1 (m 1 – m 2 )] / (m 1 + m 2 ) And v 2 = [2m 1 u 1 + u 2 (m 2 – m 1 )] / (m 1 + m 2 ) 17. The ratio of relative velocity of separation to the relative velocity of approach is called coefficient of restitution (e) e = (v 2 – v 1 ) / (u 1 – u 2 ) The value of e depends upon the nature of materials of the colliding bodies. For a perfectly elastic collision, e = 1. For an inelastic collision, e = 0. 18. Moderators are the substances used to slow down neutrons to make them capable of causing fission. Heavy water and graphite are moderators. 19. The mass of a body or a particle increases with increase in the velocity of the particle according to relation m = m 0 / √ 1 – (v 2 / c 2 ) 20. Mass and energy are inter convertible. The energy equivalent to mass m is given by E = mc 2 . 21. In pair production, energy is converted into mass in the form of material particles (e - and e + ).

22. Annihilation of matter illustrates the conversion of mass into energy. 23. According to Einstein special theory of relativity, the maximum velocity that any body can acquire is equal to the velocity of light. Mass of particle becomes infinite if it moves with velocity of light. (c = velocity of light = 3 x 10 8 ms - 1 ). When the mass becomes infinite, then acceleration produced in the body by the given force F becomes equal to zero.

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