Iesc110 PDF - Work and Energy

C hapter 10 WORK AND ENERGY In the previous few chapters we have talked draws diagrams, organises her thoughts, about ways of describing the motion of collects question papers, attends classes, o...

C hapter 10 WORK AND ENERGY In the previous few chapters we have talked draws diagrams, organises her thoughts, about ways of describing the motion of collects question papers, attends classes, objects, the cause of motion and gravitation. discusses problems with her friends, and Another concept that helps us understand and performs experiments. She expends a lot of interpret many natural phenomena is ‘work’. energy on these activities. In common Closely related to work are energy and power. parlance, she is ‘working hard’. All this ‘hard In this chapter we shall study these concepts. work’ may involve very little ‘work’ if we go by All living beings need food. Living beings the scientific definition of work. have to perform several basic activities to You are working hard to push a huge rock. survive. We call such activities ‘life processes’. Let us say the rock does not move despite all The energy for these processes comes from the effort. You get completely exhausted. food. We need energy for other activities like However, you have not done any work on the playing, singing, reading, writing, thinking, rock as there is no displacement of the rock. jumping, cycling and running. Activities that You stand still for a few minutes with a are strenuous require more energy. heavy load on your head. You get tired. You Animals too get engaged in activities. For have exerted yourself and have spent quite a example, they may jump and run. They have bit of your energy. Are you doing work on the to fight, move away from enemies, find food load? The way we understand the term ‘work’ or find a safe place to live. Also, we engage in science, work is not done. some animals to lift weights, carry loads, pull You climb up the steps of a staircase and carts or plough fields. All such activities reach the second floor of a building just to require energy. see the landscape from there. You may even Think of machines. List the machines that climb up a tall tree. If we apply the scientific you have come across. What do they need for definition, these activities involve a lot of work. their working? Why do some engines require In day-to-day life, we consider any useful fuel like petrol and diesel? Why do living physical or mental labour as work. Activities beings and machines need energy? like playing in a field, talking with friends, humming a tune, watching a movie, attending 10.1 Work a function are sometimes not considered to be work. What constitutes ‘work’ depends What is work? There is a difference in the on the way we define it. We use and define way we use the term ‘work’ in day-to-day life the term work differently in science. To and the way we use it in science. To make understand this let us do the following this point clear let us consider a few examples. activities: 10.1.1 NOT MUCH‘WORK’ IN SPITE OF Activity _____________ 10.1 WORKING HARD! We have discussed in the above Kamali is preparing for examinations. She paragraphs a number of activities spends lot of time in studies. She reads books, which we normally consider to be work 2024-25  in day-to-day life. For each of these activities, ask the following questions Activity _____________ 10.3 and answer them: Think of situations when the object (i) What is the work being done on? is not displaced in spite of a force (ii) What is happening to the object? acting on it. (iii) Who (what) is doing the work? Also think of situations when an object gets displaced in the absence of a force acting on it. 10.1.2 SCIENTIFIC CONCEPTION OF WORK List all the situations that you can To understand the way we view work and think of for each. Discuss with your friends whether define work from the point of view of science, work is done in these situations. let us consider some situations: Push a pebble lying on a surface. The pebble moves through a distance. You exerted 10.1.3 W ORK DONE BY A CONSTANT a force on the pebble and the pebble got FORCE displaced. In this situation work is done. How is work defined in science? T o A girl pulls a trolley and the trolley moves understand this, we shall first consider the through a distance. The girl has exerted a case when the force is acting in the direction force on the trolley and it is displaced. of displacement. Therefore, work is done. Let a constant force, F act on an object. Lift a book through a height. To do this Let the object be displaced through a you must apply a force. The book rises up. distance, s in the direction of the force (Fig. There is a force applied on the book and the 10.1). Let W be the work done. We define work book has moved. Hence, work is done. to be equal to the product of the force and A closer look at the above situations displacement. reveals that two conditions need to be Work done = force × displacement satisfied for work to be done: (i) a force should W = Fs (10.1) act on an object, and (ii) the object must be displaced. If any one of the above conditions does not exist, work is not done. This is the way we view work in science. A bullock is pulling a cart. The cart moves. There is a force on the cart and the cart has moved. Do you think that work is done in this situation? Activity _____________ 10.2 Think of some situations from your Fig. 10.1 daily life involving work. List them. Thus, work done by a force acting on an Discuss with your friends whether object is equal to the magnitude of the force work is being done in each situation. multiplied by the distance moved in the Try to reason out your response. direction of the force. Work has only If work is done, which is the force acting on the object? magnitude and no direction. What is the object on which the work In Eq. (10.1), if F = 1 N and s = 1 m then is done? the work done by the force will be 1 N m. What happens to the object on which Here the unit of work is newton metre (N m) work is done? or joule (J). Thus 1 J is the amount of work 114 SCIENCE 2024-25 done on an object when a force of 1 N displaces it by 1 m along the line of action of the force. Look at Eq. (10.1) carefully. What is the work done when the force on the object is zero? What would be the work done when the displacement of the object is zero? Refer to the conditions that are to be satisfied to Fig. 10.4 say that work is done. Consider a situation in which an object is moving with a uniform velocity along a Example 10.1 A force of 5 N is acting on particular direction. Now a retarding force, F, an object. The object is displaced is applied in the opposite direction. That is, through 2 m in the direction of the force the angle between the two directions is 180º. (Fig. 10.2). If the force acts on the object Let the object stop after a displacement s. In all through the displacement, then work such a situation, the work done by the force, done is 5 N × 2 m =10 N m or 10 J. F is taken as negative and denoted by the minus sign. The work done by the force is F × (–s) or (–F × s). It is clear from the above discussion that the work done by a force can be either positive or negative. To understand this, let us do the Fig. 10.2 following activity: Activity _____________ 10.4 uestion Q Lift an object up. Work is done by the 1. A force of 7 N acts on an object. force exerted by you on the object. The The displacement is, say 8 m, in object moves upwards. The force you exerted is in the direction of the direction of the force displacement. However, there is the (Fig. 10.3). Let us take it that the force of gravity acting on the object. force acts on the object through Which one of these forces is doing the displacement. What is the positive work? work done in this case? Which one is doing negative work? Give reasons. Work done is negative when the force acts opposite to the direction of displacement. Work done is positive when the force is in the Fig. 10.3 direction of displacement. Example 10.2 A porter lifts a luggage of Consider another situation in which the force and the displacement are in the same 15 kg from the ground and puts it on direction: a baby pulling a toy car parallel to his head 1.5 m above the ground. the ground, as shown in Fig. 10.4. The baby Calculate the work done by him on the has exerted a force in the direction of luggage. displacement of the car. In this situation, the Solution: work done will be equal to the product of the force and displacement. In such situations, Mass of luggage, m = 15 kg and the work done by the force is taken as positive. displacement, s = 1.5 m. WORK AND ENERGY 115 2024-25  Work done, W = F × s = mg × s raised hammer falls on a nail placed on a piece = 15 kg × 10 m s-2 × 1.5 m of wood, it drives the nail into the wood. We = 225 kg m s-2 m have also observed children winding a toy = 225 N m = 225 J (such as a toy car) and when the toy is placed Work done is 225 J. on the floor, it starts moving. When a balloon is filled with air and we press it we notice a Q change in its shape. As long as we press it uestions gently, it can come back to its original shape 1. When do we say that work is when the force is withdrawn. However, if we done? press the balloon hard, it can even explode 2. Write an expression for the work producing a blasting sound. In all these done when a force is acting on examples, the objects acquire, through an object in the direction of its different means, the capability of doing work. displacement. An object having a capability to do work is 3. Define 1 J of work. said to possess energy. The object which does 4. A pair of bullocks exerts a force the work loses energy and the object on which of 140 N on a plough. The field the work is done gains energy. being ploughed is 15 m long. How does an object with energy do work? How much work is done in An object that possesses energy can exert a ploughing the length of the field? force on another object. When this happens, energy is transferred from the former to the 10.2 Energy latter. The second object may move as it receives energy and therefore do some work. Life is impossible without energy. The demand Thus, the first object had a capacity to do for energy is ever increasing. Where do we work. This implies that any object that get energy from? The Sun is the biggest possesses energy can do work. natural source of energy to us. Many of our The energy possessed by an object is thus energy sources are derived from the Sun. We measured in terms of its capacity of doing can also get energy from the nuclei of atoms, work. The unit of energy is, therefore, the same the interior of the earth, and the tides. Can as that of work, that is, joule (J). 1 J is the you think of other sources of energy? energy required to do 1 joule of work. Sometimes a larger unit of energy called kilo Activity _____________ 10.5 joule (kJ) is used. 1 kJ equals 1000 J. A few sources of energy are listed above. There are many other sources 10.2.1 FORMS OF ENERGY of energy. List them. Discuss in small groups how certain Luckily the world we live in provides energy in sources of energy are due to the Sun. many different forms. The various forms Are there sources of energy which are include mechanical energy (potential energy not due to the Sun? + kinetic energy), heat energy, chemical The word energy is very often used in our energy, electrical energy and light energy. daily life, but in science we give it a definite and precise meaning. Let us consider the following examples: when a fast moving Think it over ! cricket ball hits a stationary wicket, the wicket How do you know that some entity is a is thrown away. Similarly, an object when form of energy? Discuss with your friends raised to a certain height gets the capability and teachers. to do work. You must have seen that when a 116 SCIENCE 2024-25  James Prescott Joule was an outstanding British physicist. He is best known for his research in electricity and thermodynamics. Amongst other things, he Fig. 10.5 formulated a law James Prescott Joule for the heating The trolley moves forward and hits the (1818 – 1889) ef fect of electric wooden block. current. He also Fix a stop on the table in such a verified experimentally the law of manner that the trolley stops after conservation of energy and discovered hitting the block. The block gets the value of the mechanical equivalent displaced. Note down the displacement of the of heat. The unit of energy and work block. This means work is done on the called joule, is named after him. block by the trolley as the block has gained energy. 10.2.2 KINETIC ENERGY From where does this energy come? Repeat this activity by increasing the mass on the pan. In which case is the Activity _____________ 10.6 displacement more? In which case is the work done more? Take a heavy ball. Drop it on a thick In this activity, the moving trolley does bed of sand. A wet bed of sand would work and hence it possesses energy. be better. Drop the ball on the sand bed from height of about 25 cm. The A moving object can do work. An object ball creates a depression. moving faster can do more work than an Repeat this activity from heights of identical object moving relatively slow. A 50 cm, 1m and 1.5 m. moving bullet, blowing wind, a rotating wheel, Ensure that all the depressions are distinctly visible. a speeding stone can do work. How does a Mark the depressions to indicate the bullet pierce the target? How does the wind height from which the ball was move the blades of a windmill? Objects in dropped. motion possess energy. We call this energy Compare their depths. kinetic energy. Which one of them is deepest? A falling coconut, a speeding car, a rolling Which one is shallowest? Why? stone, a flying aircraft, flowing water, blowing What has caused the ball to make a deeper dent? wind, a running athlete etc. possess kinetic Discuss and analyse. energy. In short, kinetic energy is the energy possessed by an object due to its motion. The Activity _____________ 10.7 kinetic energy of an object increases with its speed. Set up the apparatus as shown in How much energy is possessed by a Fig. 10.5. moving body by virtue of its motion? By Place a wooden block of known mass in front of the trolley at a convenient definition, we say that the kinetic energy of a fixed distance. body moving with a certain velocity is equal to Place a known mass on the pan so the work done on it to make it acquire that the trolley starts moving. that velocity. WORK AND ENERGY 117 2024-25  Let us now express the kinetic energy of Solution: an object in the form of an equation. Consider Mass of the object, m = 15 kg, velocity an object of mass, m moving with a uniform of the object, v = 4 m s–1. velocity, u. Let it now be displaced through a distance s when a constant force, F acts on it From Eq. (10.5), in the direction of its displacement. From 1 Ek = m v2 Eq. (10.1), the work done, W is F s. The work 2 done on the object will cause a change in its velocity. Let its velocity change from u to v. 1 = × 15 kg × 4 m s–1 × 4 m s–1 Let a be the acceleration produced. 2 We studied three equations of motion. The = 120 J relation connecting the initial velocity (u) The kinetic energy of the object is 120 J. and final velocity (v) of an object moving with a uniform acceleration a, and the displacement, s is Example 10.4 What is the work to be done v2 – u2 = 2a s to increase the velocity of a car from 30 km h–1 to 60 km h–1 if the mass of This gives the car is 1500 kg? v2 – u 2 s= (10.2) 2a Solution: From section 9.4, we know F = m a. Thus, Mass of the car, m =1500 kg, using (Eq. 10.2) in Eq. (10.1), we can write the initial velocity of car, u = 30 km h–1 work done by the force, F as 30 × 1000 m  v2 - u 2  = W =ma × 60 × 60 s  2a  = 25/3 m s–1. or Similarly, the final velocity of the car, 1 2 ( W = m v2 – u 2 ) (10.3) v = 60 km h–1 = 50/3 m s–1. If the object is starting from its stationary position, that is, u = 0, then Therefore, the initial kinetic energy of the car, 1 W = m v2 (10.4) 1 2 Eki = m u2 2 It is clear that the work done is equal to the change in the kinetic energy of an object. 1 = × 1500 kg × (25/3 m s–1)2 1 2 If u = 0, the work done will be m v2. 2 = 156250/3 J. Thus, the kinetic energy possessed by an The final kinetic energy of the car, object of mass, m and moving with a uniform velocity, v is 1 Ekf = × 1500 kg × (50/3 m s–1)2 1 2 Ek = m v2 (10.5) 2 = 625000/3 J. Thus, the work done = Change in Example 10.3 An object of mass 15 kg is kinetic energy moving with a uniform velocity of 4 = Ekf – Eki m s –1. What is the kinetic energy possessed by the object? = 156250 J. 118 SCIENCE 2024-25 Q uestions Activity ___________ 10.11 1. What is the kinetic energy of an Lift an object through a certain object? height. The object can now do work. 2. Write an expression for the kinetic It begins to fall when released. energy of an object. This implies that it has acquired some 3. The kinetic energy of an object of energy. If raised to a greater height it mass, m moving with a velocity can do more work and hence possesses of 5 m s–1 is 25 J. What will be its more energy. From where did it get the energy? Think kinetic energy when its velocity and discuss. is doubled? What will be its kinetic energy when its velocity In the above situations, the energy gets is increased three times? stored due to the work done on the object. The energy transferred to an object is stored 10.2.3 POTENTIAL ENERGY as potential energy if it is not used to cause a change in the velocity or speed of the object. Activity _____________ 10.8 You transfer energy when you stretch a rubber band. The energy transferred to the Take a rubber band. Hold it at one end and pull from the band is its potential energy. You do work while other. The band stretches. winding the key of a toy car. The energy Release the band at one of the ends. transferred to the spring inside is stored as What happens? potential energy. The potential energy The band will tend to regain its original possessed by the object is the energy present length. Obviously the band had in it by virtue of its position or configuration. acquired energy in its stretched position. Activity ___________ 10.12 How did it acquire energy when stretched? Take a bamboo stick and make a bow as shown in Fig. 10.6. Activity _____________ 10.9 Place an arrow made of a light stick on Take a slinky as shown below. it with one end supported by the Ask a friend to hold one of its ends. stretched string. You hold the other end and move away Now stretch the string and release the from your friend. Now you release the arrow. slinky. Notice the arrow flying off the bow. Notice the change in the shape of the bow. The potential energy stored in the bow due to the change of shape is thus used What happened? in the for m of kinetic energy in How did the slinky acquire energy when throwing off the arrow. stretched? Would the slinky acquire energy when it is compressed? Activity ___________ 10.10 Take a toy car. Wind it using its key. Place the car on the ground. Did it move? From where did it acquire energy? Does the energy acquired depend on the number of windings? Fig.10.6: An arrow and the stretched string How can you test this? on the bow. WORK AND ENERGY 119 2024-25 10.2.4 POTENTIAL ENERGY OF AN OBJECT The potential energy of an object at More to know AT A HEIGHT a height depends on the ground level or the zero level you choose. An An object increases its energy when raised object in a given position can have a through a height. This is because work is certain potential energy with respect done on it against gravity while it is being to one level and a different value of raised. The energy present in such an object potential energy with respect to is the gravitational potential energy. another level. The gravitational potential energy of an object at a point above the ground is defined as the work done in raising it from the ground It is useful to note that the work done by to that point against gravity. gravity depends on the difference in vertical It is easy to arrive at an expression for heights of the initial and final positions of the object and not on the path along which the gravitational potential energy of an object the object is moved. Fig. 10.8 shows a case at a height. where a block is raised from position A to B by taking two different paths. Let the height AB = h. In both the situations the work done on the object is mgh. Fig. 10.7 Fig. 10.8 Consider an object of mass, m. Let it be raised through a height, h from the ground. Example 10.5 Find the energy possessed A force is required to do this. The minimum by an object of mass 10 kg when it is at force required to raise the object is equal to a height of 6 m above the ground. Given, the weight of the object, mg. The object gains g = 9.8 m s–2. energy equal to the work done on it. Let the work done on the object against gravity be Solution: W. That is, work done, W = force × displacement Mass of the object, m = 10 kg, = mg × h displacement (height), h = 6 m, and = mgh acceleration due to gravity, g = 9.8 m s–2. Since work done on the object is equal to From Eq. (10.6), mgh, an energy equal to mgh units is gained Potential energy = mgh = 10 kg × 9.8 m s–2 × 6 m by the object. This is the potential energy (EP) = 588 J. of the object. The potential energy is 588 J. Ep = mgh (10.6) 120 SCIENCE 2024-25  Example 10.6 An object of mass 12 kg is 10.2.6 LAW OF CONSERVATION OF ENERGY at a certain height above the ground. In activities 10.13 and 10.14, we learnt that If the potential energy of the object is the form of energy can be changed from one 480 J, find the height at which the form to another. What happens to the total object is with respect to the ground. energy of a system during or after the process? Given, g = 10 m s–2. Whenever energy gets transformed, the total energy remains unchanged. This is the law of Solution: conservation of energy. According to this law, Mass of the object, m = 12 kg, energy can only be converted from one form potential energy, Ep = 480 J. to another; it can neither be created or Ep = mgh destroyed. The total energy before and after 480 J = 12 kg × 10 m s–2 × h the transformation remains the same. The law 480 J of conservation of energy is valid in h = 120 kg m s –2 = 4 m. all situations and for all kinds of transformations. The object is at the height of 4 m. Consider a simple example. Let an object of mass, m be made to fall freely from a height, 10.2.5 A RE VARIOUS ENERGY FORMS h. At the start, the potential energy is mgh and kinetic energy is zero. Why is the kinetic INTERCONVERTIBLE? energy zero? It is zero because its velocity is Can we convert energy from one form to zero. The total energy of the object is thus mgh. another? We find in nature a number of As it falls, its potential energy will change into instances of conversion of energy from one kinetic energy. If v is the velocity of the object form to another. at a given instant, the kinetic energy would be ½mv2. As the fall of the object continues, the Activity ___________ 10.13 potential energy would decrease while the kinetic energy would increase. When the object Sit in small groups. Discuss the various ways of energy is about to reach the ground, h = 0 and v will conversion in nature. be the highest. Therefore, the kinetic energy Discuss following questions in your would be the largest and potential energy the group: least. However, the sum of the potential energy (a) How do green plants produce food? and kinetic energy of the object would be the (b) Where do they get their energy from? same at all points. That is, (c) Why does the air move from place to place? potential energy + kinetic energy = constant (d) How are fuels, such as coal and or petroleum formed? 1 (e) What kinds of energy conversions mgh + mv 2= constant. (10.7) 2 sustain the water cycle? The sum of kinetic energy and potential energy Activity ___________ 10.14 of an object is its total mechanical energy. We find that during the free fall of the object, Many of the human activities and the the decrease in potential energy, at any point gadgets we use involve conversion of in its path, appears as an equal amount of energy from one form to another. increase in kinetic energy. (Here the effect of Make a list of such activities and air resistance on the motion of the object has gadgets. Identify in each activity/gadget the been ignored.) There is thus a continual kind of energy conversion that takes transformation of gravitational potential place. energy into kinetic energy. WORK AND ENERGY 121 2024-25  Activity ___________ 10.15 A stronger person may do certain work in relatively less time. A more powerful vehicle An object of mass 20 kg is dropped would complete a journey in a shorter time from a height of 4 m. Fill in the blanks than a less powerful one. We talk of the power in the following table by computing of machines like motorbikes and motorcars. the potential energy and kinetic The speed with which these vehicles change energy in each case. energy or do work is a basis for their Height at Potential Kinetic Ep + Ek classification. Power measures the speed of which object energy energy work done, that is, how fast or slow work is is located (Ep= mgh) (Ek = mv2/2) done. Power is defined as the rate of doing work or the rate of transfer of energy. If an m J J J agent does a work W in time t, then power is 4 given by: 3 Power = work/time 2 W 1 or P= (10.8) t Just above the ground The unit of power is watt [in honour of James Watt (1736 – 1819)] having the symbol For simplifying the calculations, take W. 1 watt is the power of an agent, which the value of g as 10 m s–2. does work at the rate of 1 joule per second. We can also say that power is 1 W when the Think it over ! rate of consumption of energy is 1 J s–1. What would have happened if nature had 1 watt = 1 joule/second or 1 W = 1 J s–1. not allowed the transformation of energy? We express larger rates of energy transfer in There is a view that life could not have kilowatts (kW). been possible without transformation of 1 kilowatt = 1000 watts energy. Do you agree with this? 1 kW = 1000 W 1 kW = 1000 J s–1. The power of an agent may vary with time. 10.3 Rate of Doing Work This means that the agent may be doing work Do all of us work at the same rate? Do at different rates at different intervals of time. machines consume or transfer energy at the Therefore the concept of average power is same rate? Agents that transfer energy do useful. We obtain average power by dividing work at different rates. Let us understand this the total energy consumed by the total time from the following activity: taken. Activity ___________ 10.16 Example 10.7 Two girls, each of weight 400 Consider two children, say A and B. N climb up a rope through a height of 8 Let us say they weigh the same. Both m. We name one of the girls A and the start climbing up a rope separately. other B. Girl A takes 20 s while B takes Both reach a height of 8 m. Let us say A takes 15 s while B takes 20 s to 50 s to accomplish this task. What is the accomplish the task. power expended by each girl? What is the work done by each? Solution: The work done is the same. However, A has taken less time than B to do (i) Power expended by girl A: the work. Weight of the girl, mg = 400 N Who has done more work in a given time, say in 1 s? Displacement (height), h = 8 m 122 SCIENCE 2024-25  Time taken, t = 20 s power, P = Work done/time taken From Eq. (10.8), mgh Power, P = Work done/time taken = t mgh = 500 N × 6.75 m t = 9s 400 N × 8 m = 375 W. = 20 s Power is 375 W. = 160 W. Q (ii) Power expended by girl B: Weight of the girl, mg = 400 N uestions Displacement (height), h = 8 m 1. What is power? Time taken, t = 50 s 2. Define 1 watt of power. 3. A lamp consumes 1000 J of mgh Power, P = electrical energy in 10 s. What is t its power? 400 N × 8 m 4. Define average power. = 50 s = 64 W. Activity ___________ 10.17 Power expended by girl A is 160 W. Take a close look at the electric meter Power expended by girl B is 64 W. installed in your house. Observe its features closely. Take the readings of the meter each day at 6.30 am and 6.30 pm. Example 10.8 A boy of mass 50 kg runs Do this activity for about a week. up a staircase of 45 steps in 9 s. If the How many ‘units’ are consumed height of each step is 15 cm, find his during day time? power. Take g = 10 m s–2. How many ‘units’ are used during night? Tabulate your observations. Solution: Draw inferences from the data. Compare your observations with Weight of the boy, the details given in the monthly mg = 50 kg × 10 m s–2 = 500 N electricity bill (One can also estimate Height of the staircase, the electricity to be consumed by h = 45 × 15/100 m = 6.75 m specific appliances by tabulating their Time taken to climb, t = 9 s known wattages and hours of From Eq. (10.8), operation). WORK AND ENERGY 123 2024-25  What you have learnt Work done on an object is defined as the magnitude of the force multiplied by the distance moved by the object in the direction of the applied force. The unit of work is joule: 1 joule = 1 newton × 1 metre. Work done on an object by a force would be zero if the displacement of the object is zero. An object having capability to do work is said to possess energy. Energy has the same unit as that of work. An object in motion possesses what is known as the kinetic energy of the object. An object of mass, m moving with 1 2 velocity v has a kinetic energy of 2 mv. The energy possessed by a body due to its change in position or shape is called the potential energy. The gravitational potential energy of an object of mass, m raised through a height, h from the earth’s surface is given by m g h. According to the law of conservation of energy, energy can only be transformed from one form to another; it can neither be created nor destroyed. The total energy before and after the transformation always remains constant. Energy exists in nature in several forms such as kinetic energy, potential energy, heat energy, chemical energy etc. The sum of the kinetic and potential energies of an object is called its mechanical energy. Power is defined as the rate of doing work. The SI unit of power is watt. 1 W = 1 J/s. Exercises 1. Look at the activities listed below. Reason out whether or not work is done in the light of your understanding of the term ‘work’. Suma is swimming in a pond. A donkey is carrying a load on its back. A wind-mill is lifting water from a well. A green plant is carrying out photosynthesis. An engine is pulling a train. 124 SCIENCE 2024-25  Food grains are getting dried in the sun. A sailboat is moving due to wind energy. 2. An object thrown at a certain angle to the ground moves in a curved path and falls back to the ground. The initial and the final points of the path of the object lie on the same horizontal line. What is the work done by the force of gravity on the object? 3. A battery lights a bulb. Describe the energy changes involved in the process. 4. Certain force acting on a 20 kg mass changes its velocity from 5 m s–1 to 2 m s–1. Calculate the work done by the force. 5. A mass of 10 kg is at a point A on a table. It is moved to a point B. If the line joining A and B is horizontal, what is the work done on the object by the gravitational force? Explain your answer. 6. The potential energy of a freely falling object decreases progressively. Does this violate the law of conservation of energy? Why? 7. What are the various energy transformations that occur when you are riding a bicycle? 8. Does the transfer of energy take place when you push a huge rock with all your might and fail to move it? Where is the energy you spend going? 9. A certain household has consumed 250 units of energy during a month. How much energy is this in joules? 10. An object of mass 40 kg is raised to a height of 5 m above the ground. What is its potential energy? If the object is allowed to fall, find its kinetic energy when it is half-way down. 11. What is the work done by the force of gravity on a satellite moving round the earth? Justify your answer. 12. Can there be displacement of an object in the absence of any force acting on it? Think. Discuss this question with your friends and teacher. 13. A person holds a bundle of hay over his head for 30 minutes and gets tired. Has he done some work or not? Justify your answer. 14. An electric heater is rated 1500 W. How much energy does it use in 10 hours? 15. Illustrate the law of conservation of energy by discussing the energy changes which occur when we draw a pendulum bob to one side and allow it to oscillate. Why does the bob WORK AND ENERGY 125 2024-25  eventually come to rest? What happens to its energy eventually? Is it a violation of the law of conservation of energy? 16. An object of mass, m is moving with a constant velocity, v. How much work should be done on the object in order to bring the object to rest? 17. Calculate the work required to be done to stop a car of 1500 kg moving at a velocity of 60 km/h? 18. In each of the following a force, F is acting on an object of mass, m. The direction of displacement is from west to east shown by the longer arrow. Observe the diagrams carefully and state whether the work done by the force is negative, positive or zero. 19. Soni says that the acceleration in an object could be zero even when several forces are acting on it. Do you agree with her? Why? 20. Find the energy in joules consumed in 10 hours by four devices of power 500 W each. 21. A freely falling object eventually stops on reaching the ground. What happenes to its kinetic energy? 126 SCIENCE 2024-25