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2 WORK, ENERGY AND POWER Topic-1 Work, Energy and its Conservation Concepts covered: Work, Energy (Potential and Kinetic) Conservation of Energy Revision Notes Energy is the capacity of a body to do work. Its S.I. unit is joule. When a non-zero force (F) is applied on an object, it displaces by (d) by making an angle (q) with the direction of force. Then work done mathematically, is defined as. W = Fd cos q Work is said to be done only when force applied on a body makes the body move. S.I. unit of work is joule. Work is equal to force multiplied by displacement in the direction of force. Work can be positive, negative or zero. If the angle between force and the displacement is acute, then work is said to be positive. If the angle between force and the displacement is 90 i.e., displacement is perpendicular to the force applied, work is said to be zero. If the angle between force and the displacement is obtuse, the work is said to be negative. When a coolie walks horizontally while carrying a load on his head, no work is done against the force of gravity. When a body rotates in a circular path, no work is done against the centripetal force, as force and displacement are normal to each other. Work done can be zero if : (i) force applied is zero i.e., no force acts on the body. (ii) displacement of body is zero. (iii) angle between force and displacement is 90 . C.G.S. unit of energy or work is erg. One joule of work is said to be done when a force of 1 Newton displaces a body through a distance of 1 metre in its own direction. 1 erg of work is said to be done when a force of 1 dyne displaces a body through a distance 1 cm in its own direction. One kilowatt hour (1 kWh) is the energy spent (or work done ) by a source of power 1 kW in 1 hour. Mechanical energy is of two types i.e., 1 2 (i) Kinetic energy = mv 2 (ii) Potential energy = mgh Kinetic energy is the energy possessed by a body by virtue of its motion. Examples include a moving train, a running boy, etc. Types of kinetic energy : (i) Translation kinetic energy (e.g., a car moving in straight path, a freely falling body posses translational kinetic energy) (ii) Rotational kinetic energy (e.g., a spinning top, a rotating fan posses rotational kinetic energy) (iii) Vibrational kinetic energy (e.g., a wire clamped at both the ends when struck in the middle vibrates, possessing vibrational kinetic energy) Potential energy is the energy possessed by a body by virtue of its position or configuration. Potential energy is of two types : (i) Elastic potential energy (ii) Gravitational potential energy According to the law of conservation of energy, energy can neither be created nor be destroyed but it can be changed from one form to another. According to the work-energy theorem, the work done by a force on a moving body is equal to increase in its kinetic energy. Derivation of expression of potential energy, U = mgh Let a body of mass m be lifted upwards to a height h above the ground. Then, work done on the body against the force of gravity = force displacement Force, F = mg Work done, W = mg h This work done will be stored in the body in form of potential energy, U = mgh 1 Derivation of expression of Kinetic energy, K = mv2 2 A body of mass m moving with initial velocity v is acted upon by a constant opposing force F which produces retardation and the body is brought to rest. Force, F = mass retardation (i) Using 2nd kinematic equation of motion, v2 = u2 + 2as . (ii) Where, initial velocity, u=v Final velocity, v=0 Acceleration, a= a So, the equation (ii) becomes 02 = v2 + 2 ( a) s s = v2 2a (iii) Kinetic energy will be equal to the amount of work the body does before coming to rest. Kinetic energy = F s v2 = ma [Using equation (i) and (iii)] 2a 1 2 K = mv 2 Law of conservation of energy : In a closed system, i.e., a system that is isolated from its surroundings, the total energy of the system is conserved. So, the energy cannot be created or destroyed but may be changed from one form to another. Mnemonics Concepts: Positive, Negative and Zero work done. Mnemonics : Appu Planned On a Day to visit New Zealand. Interpretation : A : Acute P : Positive O : Obtuse N : Negative N : Ninety Z : Zero When angle between the force and displacement is acute, the work done is positive. When angle between the force and displacement is obtuse, the work done is negative. When angle between the force and displacement is ninety degree, the work done is zero. Key Equations Work = Force displacement (in the direction of force) Work = Fscos Gravitational potential energy, P = mgh or, Work done by the force of gravity = mgh Work energy theorem : Kinetic energy = 1 joule = 107 ergs 1 mv2 2 1 watt hour = 3600 J = 3.6 kJ 1 kilowatt hour = 3.6 106 J 1 calorie = 4.186 joules 1 eV = 1.6 10-19 J p2 = 2 mK Where, p = Momentum Topic-2 and K = Kinetic energy Work-energy theorem : 1 1 mv2 mu2 2 2 where, v = final velocity and u = initial velocity W= Power and Sources of Energy Concepts covered: Power, Sources of energy, Conversion of energy from one form to another Revision Notes Power is the rate of doing work. Its S.I. unit is Watt. 1 Watt = 1 Js-1 If one Joule of work is done in 1 second, the power spent is said to be 1 Watt. 1 horse power = 746 Watts = 0.746 kW 1 kW = 1000 W, 1 MW = 106 W and 1 GW = 109 W The C.G.S unit of power is erg per second. 1 Watt = 1 J s-1 = 107 erg s-1 Solar energy is the energy radiated by the Sun. Solar panels, solar furnaces and solar cells use solar energy to do useful work. The energy released on burning coal, oil, wood or gas is the heat energy. Light is also a form of energy. We can see objects in presence of light only. The energy contained in fossil fuels such as coal, petroleum and natural gas is called chemical energy. The energy possessed by the fast moving water is called the hydro energy. It is used to generate electricity. The energy released due to loss in mass during nuclear reaction is called nuclear energy. The heat energy stored in the core of Earth is called geothermal energy. The energy possessed by the fast-moving air is called wind energy. Windmills use this energy to produce electricity. Sound energy is possessed by vibrating bodies. A natural source providing us energy continuously is called a renewable or non-conventional source of energy. Examples of renewable source of energy are solar energy, wind energy, energy from flowing water, energy from biomass, ocean thermal energy, geothermal energy, etc. The sources of energy which have accumulated in nature over a very long period and cannot be quickly replaced when exhausted are called non-renewable sources of energy or conventional sources of energy. Examples of non-renewable sources of energy are coal, petroleum and natural gas. Key Equations Power = Work done W = Timetaken t Power = Energy spent used E = Time taken t Power = Force Velocity = F v Mnemonics Concept : Energy Sources: Mnemonics : Champak arrived Nasik via Rajkot. Nitin Chopra received him. Interpretation : C : Conventional Energy Sources N : Non R : Renewable N : Non C : Conventional Energy Sources R : Renewable
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