Chapter 4 Energy Chapter Objectives In this chapter, you will learn about: Concept of Work Unit of Work (Joule) Calculation of Work done in simple cases Kinetic Energy Basic concepts Gravitational Potential Energy Calculation of Kinetic and Potential Energies from a set of given data Energy transformation in common daily-life situations Difference between Energy and Power Did you know that in lifting a heavy weight to a higher level it makes no difference if the weight is lifted slowly or quickly? What is the difference between a slow lift and a quick lift? In this case how can the same work are done in a shorter time without spending more energy? INTRODUCTION In Book 6, we learnt that Work, in Physics, means the displacement that a body undergoes in the direction of the Force applied. We also learnt that Energy is the ability of the body to do work. Now we will elaborate further on the two and try to understand them in greater detail. CONCEPT OF WORK Work is said to be done by a body when it undergoes a displacement (movement from one position to another) due to the application of an external force. However, if there is no displacement or movement even after applying a great force, then no work is said to be done in spite of all the effort. Examples of work that can be observed in everyday life include a horse pulling a cart, a footballer kicking a ball, etc. In each case described here there is a force exerted upon an object to cause that object to be displaced. Thus, Work done (W) = Force applied (F) >< Displacement (D) = Newton >< metres = Newton-metres This is the Sl unit of Work. Work is done always in the direction of the application of Force. UNIT OF WORK (JOULE) The Sl unit of work can also be written as Joule (J). Hence, 1 J = 1 Nm So, 1 Joule of work is said to be done when a force of IN displaces a body by 1 m. Teaching Tip: The children should be made conceptually clear about what Work and Energy are.
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CALCULATION OF WORK DONE IN SIMPLE CASES Using the formula given above, we can calculate the work done in simple cases. Let us see some examples of the calculation of work done. 1. 2. 3. Calculate the work done in pushing a lorry weighing 6 tons over a kilometre. The acceleration with which the lorry -2 moves is 0.5 ms Ans: Given, M = 6 tons = 6000 kgs; D = 1 km -2 = 1000 m; f = 0.5 ms Hence, W = F x D = 6000 kgs x 0.5 ms = 3000000 Nm = 3000000 J = 3 x 106 J >< 1000 m Calculate the work done by a weightlifter when he raises a weight of 300 kgs to a height of 0.9 m above the ground. Ans: Given, M = 300 kgs D- ; -0.9 m; f = g = 9.8 ms Hence, W = F x D -2 = 300 kgs x 9.8 ms = 2646 Nm = 2646 J = 2.646 x 103 J >< 0.9 m Aloke runs up a flight of 40 steps, each of height 5 cms. If he weighs 70 kgs, find the work done by Aloke in climbing the stairs. Ans: Given, M = 70 kgs• D , = 5 cm >< 40; f = g = 0.05 m x 40 = 2m Hence, W -2 = 9.8 ms = 70 kgs x 9.8 ms = 1372 Nm = 1372 J = 1.372 x 103 J BASIC CONCEPTS ENERGY >
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Energy can be defined as the capacity or ability to do work. The unit of energy is also the same as the unit of Work, i.e., Nm or Joule. Energy, like matter, can neither be created nor destroyed but can be transformed from one form to another. There are different types of energies, like Mechanical, Thermal, Chemical, Nuclear etc. Mechanical energy is the energy possessed by a body by virtue of its position or motion. It can be further sub-divided into Potential and Kinetic Energy. KINETIC ENERGY Kinetic Energy is the energy possessed by a body by virtue of its motion. Its formula is, Kinetic Energy (KE) = —mv2 where, m = mass of the body, and v = velocity of the body. For example, an aeroplane runs along the runway for some distance before taking off. Its Kinetic Energy during running provides it with the up-thrust that helps in take-off. A similar thing is experienced by a glider when he runs a short distance before jumping off a cliff and gliding away in air. Similarly, a small piece of stone falling from a great height, possesses a large amount of Kinetic Energy that makes it hit the ground with great force. The damage caused by speeding cars colliding with each other is more when both their kinetic energies are great because of their high velocities. When asteroids or comets collide with planets, a great amount of energy is released in the form of heat, light and sound. This is so because of the immensity of the impact which is a result of the large amounts of kinetic energy possessed by the asteroids and the planets by virtue of their huge masses and great velocities. ACTION TIME 1 Aim: To demonstrate the dependence of kinetic on the mass of an object Materials required: Stone and Paper Procedure: 1. Take a stone and drop it from a given height. 2. Notice the speed with which it reaches the ground. 3. Repeat the same with a paper. Observation: Notice the difference in the speed. POTENTIAL ENERGY Potential Energy is the energy possessed by a body by virtue of its position, shape or state; Kinetic Energy is possessed by virtue of its motion. Potential Energy is also of two-types: Gravitational Potential Energy and Elastic Potential Energy. GRAVITATIONAL POTENTIAL ENERGY The Gravitational Potential Energy is the energy possessed by a body when it is at some height from the surface of the earth and can be formulated as: Gravitational Potential Energy (PE) = Mass of the body >< Acceleration due to Gravity >< Height form the ground =m>
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= mgh The Elastic Potential Energy can be defined as the Potential Energy possessed as a result of the deformation of an elastic object. The best example of such Potential Energy is in the form of a stretched spring. The force required to stretch the spring will be directly proportional to the amount of the stretch. This is known as Hooke's Law. The formula for Elastic Potential Energy is: Elastic Potential Energy = —kx2 where, k = a Constant Number, and x = the distance of stretch CALCULATION OF KINETIC AND POTENTIAL ENERGIES FROM A SET OF GIVEN DATA 1. Calculate the Potential Energy of a body of mass 10 kg at a height of 3 m above sea level and at a height of 7 m above sea-level. G = 10 m/s2 Ans: Given, m = 10 kg; hi = 3 m; h2 = 7m; g = 10 m/s2 Thus, PE3 = mghl = 10 x 10 x 3 = 300 Joules And, PE7 = mgh2 = 10 x 10 x 7 = 700 Joules 2. Calculate the Kinetic Energy of a ball weighing 300 g travelling at a velocity of 160 km/h. Ans: Given, M = 300 g = 0.3 kg; v = 160 km/h = 160 >< — m/s = E m/s 18 9 so, KE = -mv2 2 = 2.96 Joules 3. A scooter weighing 150 kg travels a distance of 2 km at a velocity of 50 km/h and then comes to rest. Find the total energy (Kinetic + Potential) of the scooter if its height is 1.5 m. Take g = 10 m/s2 125 Ans: Given, M = 150 kg; d = 2 km; v = 50 km/h = 50 x — m/s = — m/s; h = 1.5 m; g = 10 m/s2 18 9 so, KE + PE = -mv2 + mgh 2 = 16717.6 Joules ENERGY TRANSFORMATION IN COMMON DAILY LIFE SITUATIONS As said earlier, Energy can neither be created, nor destroyed. It can only be transformed from one form to another. This is also known as the Law of Conservation of Energy. Some daily life situations where energy is transformed from one form to another are: (i) The chemical energy of batteries is transformed into electrical energy, which can again be transformed into heat, light and mechanical energy. (ii) The thermal energy from a coal-based power plant is converted into electrical energy to be transmitted to far off distances. There it is again converted to heat and light energy. (iii) The solar energy is transformed into photoelectric energy in photo-voltaic cells. DIFFERENCES BETWEEN ENERGY AND POWER The rate of doing work is known as power. It can also be defined as the rate of consumption of energy. Work done by a body Thus, Power = Time taken
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= Joules/sec = Watt Thus, the differences between work and power can be summarised below as: 1. 2. 3. Work done by a force is equal to the product of the force and the distance moved in the direction of the force, while power is the rate of doing work of a source; Work done does not depend on time but power consumed does depend on time; The Sl unit of Work is Joule (J) while the Sl unit of Power is Watt (W). INFO HUB Friction is a form of Force that exists between two bodies in touch with each other. The surfaces of both bodies are rough and they tend to hold on to each other. It is due to Friction that bodies stay in rest or come to rest from motion. A great deal of energy is lost in overcoming the forces of friction. The Force of Friction can be calculated as: F Friction — PI F Normal where, = Coefficient of Friction of a surface Scientific Quest 1. 2. 3. Explain how planets possess both kinetic and Potential Energy. Find out the different sub-types of Kinetic Energy. How can electrical energy be a type of Kinetic Energy? KEY TERMS Work: The displacement that a body undergoes in the direction of the Force applied Energy: It is the ability of a body to do work Mechanical Energy: Can be defined as the energy possessed by a body by virtue of its position or motion Kinetic Energy: Is the energy possessed by a body by virtue of its motion Potential Energy: Is the energy possessed by a body by virtue of its position Power: This is the rate of work done with respect to time or the rate of consumption of energy with respect to time
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QUICK NOTES Work is said to be done by a body when it undergoes a displacement (movement from one position to another) due to the application of an external force. However, if there is no displacement or movement even after applying a great force, then no work is said to be done in spite of all the effort. Energy, like matter, can neither be created nor destroyed but can be transformed from one form to another. Mechanical energy is the energy possessed by a body by virtue of its position or motion. It can be further sub-divided into Potential and Kinetic Energy. The Gravitational Potential Energy is the energy possessed by a body when it is at some height from the surface of the earth. The Elastic Potential Energy can be defined as the Potential Energy possessed as a result of the deformation of an elastic object. The rate of doing work is known as power. It can also be defined as the rate of consumption of energy. **** RUN-THROUGH **** I. Very Short Answer Questions A. Tick the correct answer. 1. The displacement that a body undergoes in the direction of the applied force is known as: a. Energy b. Power 2. The ability of a body to do work is called: a. Energy b. Power c. Force c. Force d. Work d. Work 3. When there is no displacement even after application of a great force a. Power is still is consumed c. no Work is considered to be done 4. Work is always done in the a. opposite direction b. direction 5. The Si Unit of Work is: a. Nm c. Joule like 6. form to another. b. Work is considered to be done d. no Power is consumed of application of Force. c. perpendicular direction d. none of these b. the same as the Moment of a Force d. all of these can neither be created nor destroyed but can be transformed from one b. Force, work c. Energy, work a. Energy, matter d. Force, matter 7. a. Electrical energy is possessed by virtue of its position or motion. b. Kinetic c. Potential d. Mechanical 8. Potential energy are of two types: a. Gravitational, Elastic b. Nuclear, Electrical c. Thermal, Geo-thermal 9. The rate of doing work is d. none of these a. Energy b. Power c. Force d. (a) and (c)
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10. Watt is the Sl unit of a. Power b. Force c. Energy d. (b) and (c) B. Choose the correct option and fill in the blanks. 1. Work, means the (velocity/displacement) 2. Energy is the ability of the body to that a body undergoes in the direction of the Force applied. . (do work/spin) 4. of work is said to be done when a force of IN displaces a body by 1 m. (Watt/Joule) , like matter, can neither be created nor destroyed but can be transformed from one form to another. (Energy/Power) 5. Mechanical energy can be further sub-divided into and Kinetic Energy. (Potential/Geo-thermal) 6. Kinetic Energy is the energy possessed by a body by virtue of its 7. Potential Energy is the energy possessed by a body by virtue of its . (motion/position) , shape or state. (motion/position) Potential Energy. 8. Potential Energy is also of two-types: (Gravitational, Elastic/Mechanical, Thermal) Potential Energy and C. State True or False. Correct the false statements. 1. Energy can always be destroyed and created. 2. Work and Energy have the same Units. 3. Energy and Moment of a Force have the same Units. 4. Thermal Energy and Chemical Energy are types of Mechanical Energy. 5. Gravitational and Elastic Energy are types of Mechanical Energy. 6. Kinetic energy is formulated by -kx2. 7. The formula for Potential Energy is mgh. Work done by a body 8. The formula for Power is Time taken D. Sort the following in correct columns. Mechanical energy, Gravitational Potential Energy, Radioactive Decay, Elastic Potential Energy, Thermal Energy, Household Current, Solar Energy, Electromagnetic Potential Energy, Roller Coaster, Waterwheel, Electromagnetic Radiation, Machines, Wind Energy, Wave Energy, Sound Energy, Hydroelectric Power, Nuclear Potential Energy, Nuclear Power, Nuclear Weapons Potential Energy Different types of Energies E. Give one example of each of the following: 1. Potential Energy 2. Kinetic Energy 3. Elastic Energy 4. Gravitational Energy 5. Transformation of Energy Kinetic Energy
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F. Define the following: 1. Power 2. Energy 3. Work 4. Elastic Potential Energy 5. Gravitational Potential Energy 6. Joule 7. Watt 8. Kinetic Energy 9. Mechanical Energy 10. Potential Energy G. Complete the concept map. Solids top figure) States of Matter Liquids (bottom right figure) Gases (bottom left figure) Packing of particles Movement of particles nstead of 'States of Matter' lease insert 'Energ • remove 'Packin li uids insert Kinetic Ener Il. Short Answer Questions A. Distinguish between: 1. Force and Energy 2. Force and Work 3. Force and Power 4. Moment of a Force and Energy 5. Energy and Work 6. Work and Power 7. Energy and Power 8. Moment of a Force and Power • instead of 'Solids' lease insert Potential Energ of Particles and Movement o Particles • instea
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B. Answer the following questions. 1. What is the Work? 2. What is Energy? 3. Mention one similarity between Energy and matter. 4. What is Mechanical Energy? 5. What is Joule? 6. What is Watt? 7. Define Kinetic Energy. 8. Define Elastic Potential Energy? D. Complete the following sentences. 1. Types of Energy are 2. Potential Energy is 3. Kinetic Energy is 4. Elastic Potential Energy is 5. Gravitational Potential Energy is 6. Power can be defined as Numericals Ill. 1. Determine the Power from the following data: F = 890N, d = 12 m and t = 22 ss. 2. The mass of a planet is 5 x 1021 kg and its orbital velocity is 21900 m/s. Determine its Kinetic Energy. 3. A motorcycle has a kinetic energy of 412 J. What kinetic energy would the bicycle have if it had ... a. ... twice the mass and was moving at the same speed? b. ... the same mass and was moving with twice the speed? c. ... one-half the mass and was moving with twice the speed? d. ... the same mass and was moving with one-half the speed? e. ... three times the mass and was moving with one-half the speed? 4. A 72-kg parachutist has a speed of 92 m/s at an altitude of 1102 m above the ground. a. Determine the kinetic energy possessed by the parachutist. b. Determine the potential energy possessed by the parachutist. c. Determine the total mechanical energy possessed by the parachutist. 5. A girl of mass 65.2 kg is traveling at a speed of 18.2 m/s at the top of a 21.5 m high roller coaster loop. a. Determine the girl's kinetic energy at the top of the loop. b. Determine the girl's potential energy at the top of the loop. c. Assuming negligible losses of energy due to friction and air resistance, determine the girl's total mechanical energy at the bottom of the loop (h=0 m). d. Determine the girl's speed at the bottom of the loop. 6. Calculate the Power in the following case: Mass = 73 kg; g = 9.8ms-2• d = 37 m and t = 8.9 s VI. Challenge
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1. What is Frictional Energy? What role does it play in the total mechanical energy of a body? VI. Enrichment 1. Library Research Find out more about Work, Energy and Power. 2. Know Your Scientist James Prescott Joule was an English physicist and mathematician who discovered the relationship between heat and mechanical energy. He was instrumental in the formulation of the Law of Conservation of Energy and the development of the First Law of Thermodynamics. The Unit of Work was named in his honour. James Watt was a Scottish inventor and mechanical engineer who invented the Steam Engine and lent his name to the unit of Power. Enjoy Science Quiz Time: 1. 2. 3. 4. 5. If an object has kinetic energy, then it also must have A. Speed B. Impulse C. Acceleration D. Force Which device converts solar energy into electrical energy? A. Solar cooker B. Photovoltaic cell C. Solar heater D. Solar reflector An object is raised above the ground gaining a certain amount of potential energy. high it gains A. Four times as much potential energy. B. Twice as much potential energy. C. Half as much potential energy D. Neither of these. Work done = Force x A. distance B. acceleration C. velocity D. speed If the same object is raised twice as The type of energy possessed by a simple pendulum, when it is at the mean position is A. kinetic energy B. potential energy C. potential energy + kinetic energy D. sound energy Picture Survey 1. 2. 3. Draw the Diagrammatic representation of solar cooker and explain the principles behind its working. What energy is being used in the solar cooker? What is it being transformed into? What other devices can you think of that we can incorporate in our daily lives that use the same principles as the solar cooker?
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