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in warming the house, cooking, heating the water and drying the washed clothes. 7. Biogas Activity 5.19 (Work in groups) To conduct research on how to produce biogas Materials: bio-digester, reference materials (including this book), internet 1. Using reference materials (including this book) or internet, research about how biogas is produced. Make notes and present your finding in class. 2. Make a trip to a farm with biogas plant and take turn to ask about working of biodigester. 3. Write a report explaining how a biodigester works? 4. Hold a group discussion and discuss about biogass as a source of energy. Biomass is the total mass of organic matter in plant or animal. It is used to generate energy e.g. through burning to give heat energy. When bacteria acts on biomass, a gas called biogas is produced which is flammable hence is used as fuel to produce heat. It is a mixture of 65% methane and 35% carbondioxide. 142 A biogas plant or digester collects and directs the gas through pipes to the kitchen for cooking in a house or to a generator where electricity is produced. Fig. 5.17 shows a biogas plant. Biogas pipe Biogas Storage Tank Biogas inlet Biogas outlet Biogas Digester Fig. 5.17: Biogas plant 8. Fuels Fuels are substances which produce heat when burnt in the presence of oxygen. They include kerosene, diesel, biogas, are sources of energy in homes, industries. In the process of combustion, the chemical energy in the fuel is converted into heat energy that is converted to other forms as desired. 9. Chemical energy Chemical energy is stored in the chemical bonds of atoms and molecules. It can only be seen when it is released in a chemical reaction. When chemical energy is released, from a substance, the substance is entirely changed into an entirely different substance. Some substances that store and release chemical energy are; (i) Electrolytes – the chemical reactions in an electrolyte in the batteries produce electricity. (ii) Petroleum – petroleum is made of molecules containing carbon and hydrogen. In vapour form, its natural gas and in liquid form, it is crude oil. Energy from petroleum is used to drive vehicles and to produce electricity. Examples include jet fuel, gasoline and others. (iii) Wood – dry wood acts as a store of chemical
energy. This chemical energy is released when wood burns and it’s converted into heat and light energy. 143 (iv) Food – the chemical energy in food is released while the food is being digested. As the bonds between the atoms of the food break, new substances are created and chemical energy is given out. Warning Subjecting a battery to misuse or conditions for which it was not made for can result into battery failure or uncontrolled dangerous conditions which include explosion, fire and the emission of toxic fumes. Keep batteries well out of reach of children. 10. Light energy The potential of light to perform work is called light energy. It is formed through chemical radiation and mechanical means. It is a form of energy produced by hot bodies and travels in a straight line. It’s the only form of energy that we can see directly (visible light). It can be converted like sunlight energy is used during photosynthesis by plants to create chemical energy. UV lights are often used by forensic scientists to see details that are not seen by unaided eyes. 5.6.2 Secondary sources of energy Secondary sources are energy sources that are generated from primary sources. For instance, electricity is a secondary source because it is generated for example from solar energy using solar panels or from flowing water using the turbines to generate hydroelectricity. Other secondary sources of energy include; petroleum products, manufactured solid fuels, gases, heat and bio fuel. 5.7 Renewable and non renewable sources of energy Activity 5.20 (Work in pairs) To distinguish between renewable and nonrenewable sources of energy Materials: matchbox, reference books Steps 1. Take one matchstick from the matchbox and light it. 2. Leave it to burn for a few seconds and then put it off. 3. Use the same matchstick and try to lit it again. Observe and explain what happens. 4. From the knowledge of sources of energy, what do you think renewable and non-renewable sources of energy are? 144 5. Discuss your observations in steps 2 and 3 with your deskmate. 6. Now, conduct a research from internet and reference book on renewable and non-renewable energy source. 7. Compare and discuss your findings with other groups in your class. Hey!!! Be safe Always be careful with fire. It can cause massive damage which can result to loss of properties and lives. There are energy sources that cannot be used again once used to generate energy. They are called non renewable sources while those that can be used again without
exhausting them are called renewable resources. (a) Renewable energy sources A renewable energy source is an energy source which can’t be depleted/exhausted. They exist infinitely i.e. never run out. They are renewed by natural processes. Examples include; (i) Sun However, some like trees they can also be depleted, like trees and animals if used too much more than the natural process can renew them. So it’s advisable to take precaution while using them, that is, they should be conserved. (iii) Geothermal (iv) Biomass (ii) Wind By doing so it will lead to access to affordable and reliable energy while increasing the share if renewable energy in our country. Hence contributing to affordable, reliable sustainable and modern energy for all. Achieving sustainable development goals (SDGs) by 2030 is a drive that countries across the world are working towards together. Gaining more of our energy from renewable sources is an important part of the strategy. (b) Non-renewable energy sources These are sources which can be depleted because they exists in fixed quantities. So they will run out one day. Examples are coal, crude oil, natural gas, and uranium. Fossil fuels like coal, crude oil, natural gas are mainly made up of carbon. They are usually found in one location because they are made through the same process and material. Millions of years ago dead sea organisms, plants, and animals settled on the ocean floor and in porous rocks. With time, sand, sediments and impermeable rock settle on the dead organic matter, as the matter continue to decay forming coal, oil and natural gas. Earth movements and rock shifts creates spaces that force these energy sources to collect at well-defined areas. With the help of technology, engineers are able to drill down into the sea bed to mine these sources and harness the energy stored in them. 145 5.8 Environmental effects of the use of energy sources Activity 5.21 (Work in groups) To investigate the environmental effects of the use of energy sources Materials: reference books, Internet Steps 1. Conduct research from the Internet and reference books on environmental 2. effects of the use of energy sources. In your research, identify the effects and suggest the measure to be taken to ensure safe use of those resources. 3. Record down your findings from your discussion and report them in a class discussion. In Activity 5.24, you should have learnt that, there is no such thing as a completely “clean�
� energy source. All energy sources have atleast an effect to the environment. Some energy sources have a greater impact than others. Energy is mostly lost into the environment in form of heat and sound. The following are some of the effects of use of the energy sources to the environment: • air and water pollution • climate change and global warming. • deforestation • land degradation (a) Air and water pollution Fossil fuels e.g petroleum, diesel are used in factories. Very harmful by-products may be released to the atmosphere or water bodies. Carbon monoxides, sulphur dioxide and carbon dioxide may be released to the atmosphere causing air pollution that may harm living things that depend on air. When human beings inhale some of the polluted air, they can develop respiratory diseases. The wastes disposed to the water bodies can cause death of living things in the water. It also make the water unsafe for human consumption. Factories and industries operators are encouraged to use bio-fuels which are less harmful to the environment. Most factories are trying to clean up the waste so as to reduce the environmental pollution. (b) Climate change and global warming Most energy sources e.g fossil fuels, coal etc, when used as sources of energy, produce wastes such as carbon dioxide, sulphur dioxide and mercury which are 146 the greenhouse gases. The accumulation of these gases in the atmosphere make the temperatures to be higher than the normal. This is referred to as global warming. Sometimes, these gases interfere with the climate causing very high temperature in the atmosphere, acidified rains, frequent droughts, floods etc. This results to climate change. The greenhouse gases e.g. excess carbon dioxide, sulphur dioxide etc destroy the ozone layer exposing living things to dangerous emissions from the sun e.g. UV rays. Release of these harmful gases into the atmosphere is a global problem and very many environmental agencies are encouraging on the proper disposal of these wastes. United Nations Conference on Environment and Development (UNICED) lead Nations to sign a joint treaties to pursue of economic development in ways that would protect the earth’s environment and non renewable resources but it is still a problem up to now. (c) Deforestation Using firewood and charcoal in most African countries lead to loss of biodiversity and erosion due to loss of forest cover. These may lead to deforestation i.e. the reduction of forest cover. Of great concern is that Africa is losing forest twice as fast as the rest of the world. Human beings are encouraged to use green energy that
is renewable and have less effect to the environment. With your help we can support projects that help to train and educate forest communities so that they can use forests in a sustinable manner and protect their livelihoods for years. (d) Land degradation Land degradation is the process in which the value of bio-physical environment is affected by human – induced activity on the land. It is caused by over-cutting of vegetation e.g. forest, and woodland, for firewood and disposing factory wastes to the soil that may contaminate the soil. Use of non-biodegradable sources of energy is encouraged. Saving our energy Let’s adopt the use of biogas in cooking, energy saving stoves and reduce the use of firewood to the possible level and amount of smoke generated reducing the impact of indoor air pollution. This will reduce environmental impacts. 147 Exercise 5.6 1. Differentiate between energy and power. 2. In groups of two, identify any three primary sources of energy and hold a discussion on their: (a) definition and origin. (b) importance to us and our country. 3. Choose any renewable energy resource. Brainstorm on two to three jobs opportunities available in that field. 4. Distinguish between the terms renewable resource and non-renewable resources. 5. Give one example of a body with potential energy due to its state. 5.9 Energy transformations Activity 5.20 (Work in groups) To investigate energy transformation Materials: an electric heater, radio, water in a basin. Steps 1. Place the electric heater in the basin with water and connect it to the socket. 2. Put on the switch. Observe and explain what happens after a couple of minutes. Suggest the types of energy involved in this case. 3. Now, disconnect the heater and connect the radio to the socket. 4. Turn the radio on and suggest the types of energy involved. 5. Repeat the activity by connecting wires, battery, switch and bulb. Observe and explain what happens when you make simple circuit and the switch is closed. 6. What is the meaning of energy transformation? Give five examples of energy transformation? 7. What is the name given to devices such as the radio, heater, battery, bulb etc. that converts energy from one form to another? 8. Discuss with your group members other forms of energy transformation and show with diagrams how energy is transformed from one form to another on the chalkboard. 148 Hey!!! Be safe Don’t touch water
while an electrical heater is on, you may get an electrical shock. From your discussion, you should have observed that the water in the basin boils. Electrical energy has been converted to heat energy which boils the water. When the radio was connect to the socket and turned on, electrical energy is converted to sound energy. In step 5, when the wires are connected, the bulb is seen to give off light when you close the switch. This is because chemical energy in the battery has been converted to electrical energy which is then changed to light energy in the bulb and some part to heat energy. Therefore, energy in many of its forms may be used in its natural process or to provide some services to society such as heating, refrigeration, or performing mechanical work to operate machines. This is possible because energy can be changed from one form to another. This process of changing of energy from one form to another is called energy transformation. A device that converts energy from one form to another is known as a transducer. Fig 5.18 is a chart that shows some examples of energy transformation in our day to day activities. 149 Chemical n actio ar re ucle Electrical c tri c E l e e ll o l a r c S Nuclear Nuclear reactor Heat o c o u ple c tric h E le a t e T h er m Sound ti o r V i b g s s Mechanical Generator Electric motor W i n d m i l l Light Let us consider a few examples of energy transformation: Fig. 5.18: A flow chart of energy transformation 1. Hammering a nail Chemical energy in our bodies Potential energy of hammer Fig. 5.19: Energy transportation Heat K.E Sound 150 2. Lighting a bulb using a battery Chemical energy in the battery Electrical energy Radiant heat Light energy 3. Hydroelectric power Fig. 5.20: Energy transformation Potential energy of water in the water reservour Kinetic energy of falling water K.E of rotation of turbines Electrical energy Heat and sound Fig. 5.20: Potential energy and its transformation Other examples of energy transfomers. Wind turbines use wind energy to transform it into electricity. Energy from food (chemical energy) can be transformed in energy to play and run. A solar cell/ panel convert radiant energy of sunlight to electrical energy that can be used to give off lightning a bulb or to power a computer The sun gives the grass thermal energy which helps it to grow by transforming the energy into chemical energy using photosynthesis. Animals eat grass and help them to grow and have power
to run. A microphone changes electric energy to sound energy and so on. One other example of energy transformations occurs when lightning strike. If it hits a tree, it’s electrical energy will be changed to heat and thermal energy. The tree will become hot and can even burn as a result of electric discharge, it can split and the leaves dry. 151 Exercise 5.7 1. Table 5.2 shows how energy is converted from form A to form B and the devices concerned. Complete the table. Form A Form B Electrical Sound Electrical Kinetic _ Sound _ _ Electrical Electrical Electrical _ Device Loudspeakers _ Photocell _ Thermocouple Heater Table 5.2: Forms of energy 2. Describe the energy changes that occurs in the following processes. (a) When you lift a brick to a certain height. (b) When you lift a brick and let it slide down a rough slope until it reaches the surface of the slope. 3. Describe the forms of energy shown in Fig 5.21. Fig. 5.21: Forms of energy 4. Name the changes in energy that take place when a torch is switched on. 5. Name the energy changes that take place when lighting a match box. 152 5.10 Law of conservation of energy To demonstrate the law of conservation of energy Activity 5.23 (Work in pairs) Materials: a ball Steps 1. Hold a football at a height of 1 m above the ground. What type of energy does the ball posses at that position? 2. Release the ball to start falling freely to the ground. What type of energies does the ball posses while falling? 3. What type of energy does the ball posses while just about to touch the ground. 4. Ignoring air resistance, compare the amount of energy possesed by the ball in step 1 and 3. What can you conclude? When the ball was stationary at a point 1 m above the ground in Activity 5.26, it possed P.E only. When released the P.E started being converted to K.E hence the ball dropped. When it was just about to touch the ground, all the P.E had been converted to K.E hence by ignoring air resistance, Height point of swing Height point of swing Maximum kinetic energy Fig. 5.22: Initial P.E = final K.E We say that energy has been conserved. This is summarised in the law of conservation of energy. The law of conservation of energy states that energy cannot
be created or destroyed but is simply converted from one form into another. Or in other words we can state it that in a closed system the total amount of energy is conserved. Energy can be inter-converted among many forms, mechanical, chemical, nuclear, electric, and others but the total amount of it remains constant. For instance, in boiling water using a kettle, electrical energy drawn from the power source flows into the heating element of the kettle. As the current flows 153 through the element, the element rapidly heats up, so the electrical energy is converted to heat energy that is passed to the cold water surrounding it. After a couple of minutes, the water boils and (if the power source remains in the water) it starts to turn into steam. Most of the electrical energy supplied into the kettle is converted to heat energy in the water though some is used to provide latent heat of evaporation (the heat needed to turn a liquid into a gas without a change in temperature). If you add up the total energy supplied by the power source and the total energy gained by the water, you should find they are almost the same. The minor difference would be due to energy loss in other forms. Why aren’t they exactly equal? It’s simply because we don’t have a closed system. Some of the energy from the power source is converted to sound and wasted (kettles can be quit noisy). The kettles also give off some heat to their surrounding so that’s also wasted energy. Another example is a flying ball, that hits a window plane in a house, shattering the glass. The energy from the ball was transferred to the glass making it shatter into pieces and fly in various directions. 5.11 The law of conservation of mechanical energy Activity 5.24 (Work in pairs) To verify the law of conservation of mechanical energy Materials: A smooth metallic hemispherical bowl, a ball bearing Steps 1. Place the hemispherical bowl on the bench in a stable position. Mark at point A on the inside surface of the bowl at point A on the inside surface of the bowl 2. Place the ball bearing at point A and release it to slide downwards freely along the inside surface of the bowl as shown in Fig. 5.22. A h B C E D Fig. 5.22: A ball bearing sliding oscillating in a bowl 3. Mark point E where the ball rises to on the opposite side in the bowl. 154 4. Compare the vertical height of points
A and E. What do you notice aboue the heights? 5. Repeat the activity with point A at a lower vertical height. 6. What type of energy does the ball bearings possess at points A, B, C, D and E. 7. Compare and comment on the total amount of energy possessed by the ball bearing at points A, B, C, D and E. 8. Make a conclusion based on your observation in step 7. You should have learnt that the law of conservation of mechanical energy states that The total mechanical energy (sum of potential energy and kinetic energy) in a closed system will remain constant/same. A closed system is one where there are no external dissipative forces (like friction, air resistance) which would bring about loss of energy. The sum of potential energy and kinetic energy anywhere during the motion must be equal to the sum of potential energy and kinetic energy anywhere else in the motion. To demonstrate the law of conservation of mechanical energy (a) A swinging pendulum Activity 5.28 (Work in pairs) To demonstrate the law of conservation of M.E using a swinging pendulum Materials: a bob, string Steps 1. Tie a string to the bob and fix it to a rigid object.( See Fig. 6.16). 2. Pull the bob to the right or left side at an angle and then release it. Observe the movement of the bob. 3. Draw a diagram for the motion of the pendulum and discuss with your class the energy changes at various points e.g. A, B, C, D and E shown in Fig. 5.24. A E B D Fig. 5.24: A swinging pendulum C 4. Explain the energy changes at points A, B, C, D 155 From the above activity, you should have noticed that the bob will attain a maximum potential energy due to its height above the ground at point A she have minimum kinetic energy because it is at rest. When it swings after letting it go, it will start loosing potential energy as it gain kinetic energy at point B because of its motion. As it passes through the lowest point point C, its potential energy is minimum kinetic energy will be maximum. Because of its kinetic energy, it swings up to the other side and now its kinetic energy starts decreases as, potential energy increases at point D until when it reaches the maximum point E where it stops moving momentarily. At that point, it has maximum potential energy but minimum kinetic energy. At all positions, the total mechanical
energy is constant (conserved). That is kinetic energy + potential energy = constant. Therefore, mechanical energy has been conserved. (b) A body thrown upwards Activity 5.26 To demonstrate the law of conservation of M.E using a ball thrown upwards (Work individually) Materials: tennis ball Steps 1. Throw a tennis ball upwards. Observe and describe the movement of the ball up to the maximum (highest) point. 2. Now, drop the ball from a high point e.g from top of the building or a cliff (see Fig 5.25). 3. Sketch its motion on a paper at three different intervals, starting from the lowest when thrown upwards or from highest when dropped from a cliff. 4. Explain why the ball falls back to the ground after thrown upwards. 5. Indicate the forms of energy at each stage. 6. Discuss your observations and drawing with your colleagues in class. In your discussion, you should have learnt that when a body (e.g. a ball) is thrown up vertically, it has maximum speed, (maximum kinetic energy) at the starting point. The ball moves up with a reducing speed because of the force of gravity acting on it downwards until it reaches the maximum point/ height where it stops moving momentarily and it falls back. 156 At maximum height, it has a maximum potential energy and minimum kinetic energy because the body is not moving. So the kinetic energy at the bottom is all turned into potential energy at the maximum point (Fig 5.25). P.Emax K.E = 0 cliff P.E = K.E object P.E = 0 K.Emax ground Fig. 5.25: Sketch of a ball thrown upwards The ball is under free fall because it is only being acted upon by the force of gravity. Initially the ball has maximum potential energy and no kinetic energy. As it falls down, its potential energy keeps on reducing as its position above the ground reduces but its kinetic energy is increasing because it speeds up as it falls downwards. The kinetic energy at the ground level is equal to the potential energy at the top of the wall. Hence mechanical energy is conserved. Exercise 5.8 1. A pendulum bob swings as shown in the diagram. Fig 5.26 Pendulum bob Start Fig 5.25: A pendulum swinging At which position (s) is: the kinetic energy of the pendulum bob least. (a) (b) the potential energy of the pendulum bob most. 157 (c) (d
) the kinetic energy of the pendulum bob the most. the potential energy of the pendulum bob the least. 2. State the following laws: (a) (b) law of conservation of energy law of conservation of mechanical energy. 3. Describe how mechanical energy is conserved. 5.12 Ways of conserving energy Activity 5.27 (Work in groups) To do research about conservation of energy and identify ways of conserving energy Materials: internet, reference book (including this book) 1. What is the meaning of the word conservation of energy? 2. Conduct a research from Internet and reference books on ways of conserving 3. energy. In your research, identify different ways of conserving energy and find out what energy efficiency is. 4. Discuss your finding with other pairs in class and give a report of your findings to the whole class. From your research and discussion you should have established that energy conservation is the act of saving energy by reducing the length of use. In other words, to conserve energy, you need to cut back on your usage. For example, driving your car fewer miles per week, turning your thermostat down a degree or two in the winter time and unplugging your computer or home appliance when they are not in use. All these ways reduce the amount of energy you use by doing without or using less fuel or electricity. It can help reduce the monthly heating and electricity bills and save money at the gas pump. You also reduce the demand of fuels like coal, oil, and natural gas. Less burning of fuels means lower emissions of carbon dioxide, the primary contributor of to global warming and other pollutants. Other examples include: (i) Clean or replace air filters of cars as recommended. Energy is lost when air conditioners and hot air furnaces have to work harder to draw air through dirty filters. So save money by replacing old air filters with new (standard) ones which will take less electricity. 158 (ii) Select the most energy efficient models when you replace the old appliances. Look for the energy star label because the product saves energy and prevents pollution. (iii) Turn your refrigerator down. Refrigerators accounts for about 20% of the house hold electricity costs. (iv) Buy energy-efficient compact fluorescent bulbs for the lights you use most. Although they cost more, they save money in the long run because they only use a quarter the energy used by ordinary incandescent lamps and lasting 8-12 times longer. (v) Reduce the amount of waste you produce by
buying minimally packaged goods, choosing reusable products over disposable ones, and recycling. Use 30% to 50% less paper products, 33% less glass and 90% less aluminum. (vi) People who live in colder areas should super insulate your walls and ceiling. It can save your the electricity of heating or fire wood costs. (vii) Plant shady trees and paint your house a light colour if you live in a hot place or paint them a dark colour if you live in cold conditions. If we do not conserve energy, it will be exhausted and we will have nothing to use. Energy conservation is also important when in managing climate change. Currently erratic climates and climatic changes are the greatest threats that we are facing today. Hence it is important to conserve energy. 5.13 Energy efficiency Energy efficiency is the act of saving energy but keeping the same level of service. For example, if you turn off the lights when you are leaving a room, that’s energy conservation, if you replace an efficient incandescent light bulb with a more efficient compact fluorescent bulb, you are practicing energy efficiency. Energy efficiency uses advances in sciences and technology to provide services and products that require the use of less energy. Exercise 5.9 1. (a) Demonstrate how mechanical energy is conserved. (b) What is energy efficiency? 2. By identifying practical activities in our daily lives, discuss how you can conserve energy. 159 Project work 1 Energy saving charcoal burner In most developing countries, wood is the most important source of energy mainly for cooking. The amount of wood consumed depends on the climate, culture and availability. Most people use open, three stone fireplaces for cooking. The fireplaces are often dirty, dangerous and inefficient. The smoke and soot settles on utensils, walls, ceiling and people. The smoke produced in fireplaces irritates people posing danger to health. The fireplaces have been found to be about 10-15% efficient. In view of the above, energy saving stoves have been designed. Most of these stoves use charcoal. Charcoal is preferred to wood in urban areas because of its portability, convenience and cleanliness. In designing energy saving stoves, one should try to minimise energy losses to the surrounding. One of the many advantages of a charcoal stove, is that the rate of charcoal burning can be controlled. Materials Metal sheets and clay Construction Cut the metal sheet into a circular sheet (Fig. 5.27(a)). The radius AO will depend on the size
of the stove required. Mark arc AB which represents the circumference of the mouth of the charcoal burner. Draw AO and OB. Draw arc CD. The radius OD will depend on the area of the base on which the charcoal is to rest. Cut the section ACDB. Assembly Fold the plate ACDB in a shape of a cone as shown in Fig. 5.27(b). Rivet the sides AC and BD together. Repeat the procedure to construct the lower compartment. But this time make AC and DB shorter. A C B D O A, B C, D (a) Circular metal sheet (b) Upper compartment Fig. 5.27: Making the upper compartment of an energy saving charcoal burner Bring the two compartment together and join them by riveting Fig. 5.28(a). Cut off a small section of the lower compartment and construct a gate. Mould clay in such a shape that it fits into the upper compartment. Make the air holes while the clay is still wet. 160 Allow the clay to dry. Construct the stands for holding the cooking pot. A complete stove should look like the one shown in Fig. 5.28(b). Base with air inlet holes Gate Clay Metal Gate (a) Upper and lower compartment joined (b) Complete charcoal burner Fig. 5.29(a): Upper and lower compartments joined to make a complete charcoal burner Larger stove can be made by cutting the sheet as shown in Fig. 5.29. A C D B or O C D A B Fig.5.29: Larger jikos Project work 2 Solar heater Solar energy can be trapped with the help of solar heater and utilized to heat water. The most common type of solar water heater incorporates a flat-plate solar collector and a storage tank. The tank is positioned above the collector. Water from the tank is circulated through the collector and back to the tank by means of convectional currents caused by the heated water. Construction of a solar heater Suggested materials A 20 litre jerry can container, plastic pipes, cellophane paper, half open 20 litre jerry can, black paint or smoke soot and a wire mesh. Assembly Heat collector Paint the plastic pipes black. Use a wire mesh and curve the plastic pipes as shown in Fig. 5.30. The size of the wire mesh should be able to fit into an open 20 litre jerry can container. 161 1 2 Pipes Strings to tie the pipes onto the wire mesh Frame work Half
open jerry can Fig. 5.30: Heat collector Heat exchanger Use another 20 litre jerry can (Fig. 5.31) and open at the top to allow the pipes to enter and then seal it using the same material and a hot object. The hot object will make the materials to fuse together. Make provisions for water to enter and leave the heat exchanger when required. 1 Hot water Water gains energy Pipes Cold water 2 Fig. 5.31: Heat exchanger Join pipe 1 of the heater collector to pipe 1 of the heat exchanger. Do the same with pipe 2. Make sure the collector is inclined at a certain angle to allow water from the heat exchanger to flow freely. (Fig. 5.32). Cover the heat collector with a cellophane paper. 162 Hot water Heat exchanger Cold water Pump Cold water Stand Heat collector Hot water rises Transparent plastic paper θ Fig 5.33: Solar heater How to use Fill the pipes of the heat collector with water and expose them to the sun. Allow water from a reservoir to fill the heat exchanger. Topic summary • Work is the product of force and distance moved in the direction of the • force. A joule is the work done when a force of one newton acts on a body and makes it to move a distance of one metre in the direction of the force. • When work is done on an object, energy is transferred. Work is said to be done if a force acts on a body and makes it move (get displaced) in the direction of the force • Energy is the ability to do work. • Moving objects have kinetic energy that depends on the mass of the body • and the velocity. Potential energy is the energy possessed by a body due to its position. It depends on the objects height above the ground. • The total amount of kinetic energy and potential energy in a system is the mechanical energy of the system. Mechanical energy = KE + PE. • Falling, swinging, and projectile motion all involve transformations between kinetic and potential energy. 163 • • According to the law of conservation of energy, energy cannot be created or destroyed but can only be converted from one form to another. Energy is converted changes from one form to another by transducers such as light bulbs, hair driers. For example, a hair drier converts electrical energy into thermal energy, kinetic energy and sound energy. • Fuel is a substance which when burnt produces heat. Topic Test 5 1. Define the term power and give its
SI unit. 2. A motor raised a block of mass 72 kg through a vertical height of 2.5 m in 28 s. Calculate the: (a) work done on the block. (b) useful power supplied by the motor. 3. A person of mass 40 kg runs up a flight of 50 stairs each of height 20 cm in 5 s. Calculate: (a) the work done. (b) the average power of the person. (c) explain why the energy the person uses to climb up is greater than the calculated work done. 4. A runner of mass 65 kg runs up a steep slope rising through a vertical height of 40 m in 65 s. Find the power that his muscles must develop in order to do so. 5. A fork-lift truck raises a 400 kg box through a height of 2.3 m. The case is then moved horizontally by the truck at 3.0 m/s onto the loading platform of a lorry. (a) What minimum upward force should the truck exert on the box? (b) How much P.E. is gained by the box? (c) Calculate the K.E of the box while being moved horizontally. (d) What happens to the K.E once the truck stops? 6. A stone falls vertically through a distance of 20 m. If the mass of the stone is 3.0 kg, (a) Sketch a graph of work done by the gravity against distance. (b) Find the power of the gravitational pull. 164 7. Mugisha climps 16 m rope in 20 s. If his mass is 60 kg, find the average power he developed. 8. A car is doing work at a rate of 8.0 × 104 W. Calculate the thrust of the wheels on the ground if the car moves with a constant velocity of 30 m/s. 9. Uwimbabazi took 55.0 s to climb a staircase to a height of 14.0 m. If her mass is 40 kg, find: (a) How much force did she exert in getting to the that level? (b) Her power? 10. In Fig. 5.33 three positions of a monkey swinging from a branch of a tree are shown. A B C Fig. 5.33: A monkey swinging (a) What kind of energy does the monkey have at each position? (b) What happens to the energy when the monkey is midway between A and C? (c) In
which positions does the monkey have the least energy? What name is given to this type of energy? (d) What type of energy would the moneky have if it stopped swinging but still hanging? 165 11. A device which converts one form of energy to another is called a transducer. Name one transducer in each of the cases energy transformation given below. (a) Heat to kinetic energy (b) Electrical to light (c) Sound to electrical (e) Chemical to electrical (d) Potential energy to kinetic energy 12. Discuss the energy transformations in Fig. 5.34. Fig. 5.34: A boy jumping 13. (a) State the law of conservation of energy. (b) Differentiate between renewable and non-renewable sources of energy. Give two examples of each. (c) Explain the energy transformation in a hydroelectric power station. 166 UNIT 4 Machines Topics in the unit Topic 6: Machines Learning outcomes Knowledge and Understanding • Define machines and explain the dynamics of objects Skills • Design and carry out tests on pulleys and simple pulleys of different velocity ratios may be assembled Predict what might happen. • Observing carefully. • Use appropriate measures. • Collect and present results appropriate in writing or drawing. • Derive and Calculate mechanical advantage, velocity ratio and efficiency of a given machine. • Draw a labeled diagram to explain a lever. Attitudes • Appreciate use of machine to ease work. Key inquiry questions • Why do vehicles use low gears in steep places? • Why are pulleys important in load lifting? • Why does a cyclist get tired when cycling up-hill? • How can we design machines to enable humans to move masses greater than the human mass? 167 168 TOPIC 6 Machines Unit outline • Definition of simple machines. • Examples of simple machine (lever, pulley, wedge and axle, inclined plane, screw). • Working principal of simple machines. • Machine work out and friction in the machine. • Mechanical advantage and velocity ratio of a machine. • Determination of output of simple machine (efficiency). • Experiment to determine efficiency of simple machines. Introduction In everyday life, people perform various tasks in order to improve their standards of life, environment, quality of health, and understanding of natural phenomena in order to exploit and be in terms with them. Some of the tasks people do include; drawing of water from a well using a windless, construction of houses using timber, nail and harmer, loading and unloading
of good into the ships for export, joining of timber and metal using screws, splitting of firewood using a wedge, digging a garden in preparation for planting, lifting heavy objects into tracks. The devices that help us to perform work easily are called machines. Machines can either be simple or compound. In topic 3, we learnt about some of the applications of moment of a force. Most simple machines apply the same principle in making work easier. In this topic we are going to learn, understand and apply the principles behind simple machines. 6.1 Definition of simple machines Activity 6.1 (Work in groups) To find out the definition and importance of a machine Materials: closed soda bottle, a bottle opener Steps 1. Open a soda bottle with your hand. Is it easy to open the bottle using your hand? 2. Now try opening the same bottle using an opener. Is it easier to open the bottle using an opener? Which of the two tasks is easier and why? 3. Based on your observation in steps 1 and 2, define a simple machine. 169 In topic 3, we learnt about moments and how it is applied in machines. In the above experiment the bottle opener applies moments to open a soda. It is a simple machine. A machine is a mechanical device or a system of devices that is used to make work easier. For example in loading an oil drum onto a truck, it is easier to roll it up an inclined plane (Fig. 6.1(a)) than lifting it up onto the truck (Fig. 6.1(b)). (a) Rolling up a drum into a truck (b) Lifting up a drum into a truck Fig. 6.1: Machines make our work easier A machine may be defined as any mechanical device that facilitates a force applied at one point to overcome another force at a different point in the system. Examples of simple machines include lever, pulley, wedge, wheel and axle, inclined plane, and screws. A simple machine is a machine that is made up of only one type of machine. Examples of simple machines are the screw, lever, inclined plane, pulley, wheel and axel and gears. A compound machine is made up of more than one simple machines working together to perform a particular task with ease. An example of a compound machine is the car engine. The car engine consist of pulley, belts, gears, wheel and axel, pistons and other simple machines working together to bring about the movement of the car. In mechanical machines, the force
that is applied is called the effort (E) and the force the machine must overcome is called the load (L). Note that both the load and effort are forces which act on the machine. 6.2 Mechanical advantage, velocity ratio and efficiency of machines Activity 6.2 (Work in groups) To investigate and determine mechanical advantage, velocity ratio and efficiency of machines Materials: Internet, reference books, inclined plane Instructions 1. 2. In pairs conduct research from the Internet or reference books on the terms used to describe the ability of doing work easily by use of machines. In your research, find out what is mechanical advantage? What is velocity ratio? What is efficiency of machine? 3. Modify the set-up using locally available materials such as stones and timbers to make an inclined plane. Draw the set-up. 170 4. Write a brief procedure on how to determine M.A, V.R, and efficiency of the inclined plane. 5. Write a report about your investigation and explain how the experiment can be improved. 6. Present your findings in a class discussion. Mechanical advantage (M.A) of machines Machines overcome large loads by applying a small effort i.e. the machines magnify the force applied. Mechanical advantage is the ratio of load to the effort. It describes how the applied force compares with the load to be moved. A machine with a mechanical advantage (M.A) of 1 does not change the force applied on it. A machine with a M.A of 2 can double your force, so you have to apply only half the force needed. Mechanical advantage = force applied by the machine to do the work (Load) force applied to the machine by the operator (Effort) ∴ Mechanical advantage (M.A) = load (N) effort (N) Since mechanical advantage is a ratio, it has no units. Velocity ratio (V.R) of a machine Velocity ratio of a machine is the ratio of the velocity of the effort to the velocity of the load. Velocity ratio (V.R) = velocity of the effort velocity of the load = displacement of effort time displacement of load time Since the effort and the load move at the same time, ∴ Velocity ratio (V.R) = displacement of effort displacement of load or (V.R) = effort distance load distance Velocity ratio has no units Efficiency of machines For a perfect machine, the work done on the machine by the effort is equal to the work done by the machine on the load. However,
there is no such a machine because some energy is wasted in overcoming friction and in moving the moveable 171 parts of the machine. Hence, more energy is put into the machine than what is output by it. Thus, Work input = Useful work done + Wasted work done To describe the actual performance of a machine we use the term efficiency. Efficiency tells us what percentage of the work put into a machine is returned as useful work. The efficiency of a machine is defined as the ratio of its energy output to its energy input. Efficiency = useful energy output energy input × 100% or efficiency = useful work output work input × 100% = load × distance moved by load effort × distance moved by effort × 100% = load effort × distance load is moved distance moved by effort × 100% = M.A × 1 V.R × 100% ∴ Efficiency = M.A V.R × 100% Example 6.1 A machine whose velocity ratio is 8 is used to lift a load of 300 N. The effort required is 60 N. (a) What is the mechanical advantage of the machine? (b) Calculate the efficiency of the machine Solution (a) Mechanical advantage = load effort = 300 N 60 N = 5 (b) Efficiency = M.A V.R = 5 8 × 100% = 62.5% 172 Example 6.2 An effort of 250 N raises a load of 900 N through 5 m in a machine. If the effort moves through 25 m, find (a) the useful work done in raising the load (b) the work done by the effort (c) the efficiency of the machine Solution (a) Useful work done in raising the load = load × distance moved by load = (900 × 5) = 4 500 J (b) Work done by the effort = effort × distance moved by effort = 250 × 25 = 6 250 J (c) Efficiency = = work output work input × 100% 4 500 J 6 250 J × 100% = 72% Example 6.3 Calculate the efficiency of a machine if 8 000 J of work is done on the machine to lift a mass of 120 kg through a vertical height of 5 m. Solution Work done in lifting the load = 1 200 × 5 = 6 000 J Work input = 8 000 J Efficiency = work output work input × 100% = 6 000 J 8 000 J = 75% × 100% 173 6.3 Types of simple machines Activity 6.3 To identify types of simple machines (Work in pairs)
Steps 1. Now, access the internet and reference books and conduct research on classification of simple machines. 2. Classify simple machines 3. Discuss your findings with other groups in your class. Simple machines are classified into two groups i.e. force multiplier and distance or speed multipliers. Force multipliers are those that allow a small effort to move a large load e.g. levers. Distance or speed multipliers are those that allow a small movement of the effort to produce a large movement of the load e.g. fishing rod, bicycle gear etc. Let us consider some simple machines and show how they operate. 6.3.1 Levers Activity 6.4 (Work in groups) To demonstrate the working of levers Materials: a nail, claw hammer, piece of cloth, a pair of scissors, groundnut, pliers. Part 1 Steps 1. Drive a long iron nail into a piece of timber. 2. Try to remove the nail from the timber using your fingers. Is it easy to remove the nail using your finger? 3. Use a claw hammer instead of your fingers. Explain? 4. When using fingers and a claw hammer, which task did you apply more effort? Explain why. Part 2 Steps 1. Cut piece of cloth into two pieces using your hands. 2. Use a pair of scissors instead of your hands. Between using your hands and using a pair of scissors, which task did you apply more effort? 174 Part 3 Steps 1. Crash a groundnut using your fingers. Are you able to crash it? 2. Now crush it using a nut cracker. Why is it easier and faster to crash a groundnut using a nut cracker than your hand. Using the simple machine, the work becomes easier. These types of machines used in the above activity are called levers. Levers are simple machines that apply the principle of moments. A lever consists of a rigid bar capable of rotating about a fixed point called the pivot. The effort arm is the perpendicular distance from pivot to the line of action of effort (See Fig. 6.2). There are 3 classes of levers. The difference between these types depends on the position of the pivot (fulcrum) with respect to the load and the effort. 1. First class. The pivot is between the load and the effort. Examples (Fig. 6.2). Load Pivot Pivot Effort Effort Load (a) Crowbar (b) Scissors Load Effort Pivot Pivot Load Effort (c) Claw
hammer (d) Pliers Fig. 6.2: Pivot between the load and the effort 2. Second Class: The load is between the effort and the pivot. Examples (Fig. 6.3). Load Effort Pivot Load Pivot Effort (a) Wheelbarrow (b) Bottle opener Fig. 6.3: Load between efforts and pivots 175 3. Third class: The effort is between the load and the pivot. Examples (Fig. 6.4). Effort Pivot Load (a) Fishing rod Effort Pivot Load Effort (b) Tweezers Fig. 6.4: Efforts between load and pivots Mechanical advantage of levers Consider a lever with the pivot between the load and the effort (Fig. 6.5). load arm Pivot x L effort arm y E Fig. 6.5: Mechanical advantage for levers. Taking moment about the pivot load × load arm = effort × effort arm load effort = effort arm load arm, But load effort = mechanical advantage Mechanical Advantage, M.A = effort arm load arm = y x This also applies to the other types of levers. Since effort arm is usually greater than load arms, levers have mechanical advantage greater than 1. Velocity ratio (V.R) levers Consider three types of levers in which the load and the effort have moved a distance d L and d E respectively (Fig. 6.6). x x C B dL A L y y D dE E F C x y A dL B L C y D dE F Fig. 6.6: Determination of velocity ratio of levers x D dE F E A dL B 176 Triangles ABC and DFC are similar triangles. V.R = dE dL = y x In Fig. 6.6(a) and (b), y is greater than x. The velocity ratio is therefore greater than 1. However in (c), y is less than x, and therefore the velocity ratio is less than 1. Cases (a) and (b) are examples of force multipliers. All force multipliers have M.A and V.R greater than 1. Case (c) is an example of distance multiplier in which both the velocity ratio and mechanical advantage are less than 1. Example 6.4 A lever has a velocity ratio of 4. When an effort of 150 N is applied, a force of 450 N is lifted. Find: (a) mechanical advantage (b) efficiency of the lever. Solution
(a) Mechanical advantage = (b) Efficiency = M.A V.R = 3 4 = 75% Example 6.5 load effort = 450 N 150 N = 3.0 × 100% A worker uses a crow bar 2.0 m long to lift a rock weighing 650 N (Fig. 6.7). 650 N x ( 2 – x ) m 250 N Fig. 6.7: Crow bar (a) Calculate the position of the pivot in order to apply an effort of 250 N. (b) Find the: (i) velocity ratio (ii) mechanical advantage and (iii) efficiency of the lever. (c) What assumptions have you made? Solution (a) Applying the principle of moments (b) (i) velocity ratio = effort distance load distance = 1.44 0.56 = 2.57 650x = 250(2 – x) 650x = 500 – 250x 900x = 500 x = 0.56 m from the end with 650 N. 177 (ii) mechanical advantage = 650 250 = 2.6 (iii) efficiency = M.A V.R × 100% = 2.6 2.6 × 100% = 100% (c) We have assumed that there is no friction and that the crowbar has weight. Exercise 6.1 1. A machine requires 6 000 J of energy to lift a mass of 55 kg through a vertical distance of 8 m. Calculate its efficiency. 2. A machine of efficiency 65% lifts a mass of 90 kg through a vertical distance of 3 m. Find the work required to operate the machine. 3. A machine used to lift a load to the top of a building under construction has a velocity ratio of 6. Calculate its efficiency if an effort of 1 200 N is required to raise a load of 6 000 N. Find the energy wasted when a load of 600 N is lifted through a distance of 3 m. 4. Define the following terms as applied to levers: (a) mechanical advantage (b) velocity ratio 5. Find the velocity ratio of the levers shown in Fig. 6.8. 5 c m 1 Load 85 cm Fig. 6.8: Levers 6.3.2 Inclined plane Activity 6.5 (Work in groups) To determine the work done when pulling an object on a flat surface and on an inclined plane Materials: piece of wood, a spring balance, tape measure, a trolley, a cardboard, reference books, Internet. Steps
1. Attach a spring balance on the trolley. Place a piece of wood in the trolley. 2. Pull the piece of wooden from the ground vertically upwards using the spring balance. Record the force reading on the spring balance. 178 h (a) A piece of wood moved vertically upwards through (h) s (b) Moving the load along the slope through s Fig 6.9: Determination of work done 3. Using a tape measure, measure the height (h) of a table. Calculate the amount of work done when the load is lifted from the floor to the top of table (Fig. 6.9(a)). Incline a wooden plank against the edge of the table. 4. 5. Measure the force needed to pull the load (piece of wood in a trolley) up along inclined plane at a constant speed up to the top of the table (Fig. 6.9(c)). 6. Measure the distance (s) moved by the trolley along the inclined plane. 7. Determine the work done on the trolley when it is pulled up the inclined plane. 8. Discuss in your group, which of the three ways it was easier to lift the trolley. 9. Analyse what force balanced the force applied as the block was being pulled across the table. 10. Give examples where we use an iclined plane to lift loads. An inclined plane also known as a ramp is a flat supporting surface tilted at one angle, with one end higher than the other used for raising or lowering loads. Fig. 6.10 below is an example of an inclined plane. 179 ) E E ff o r t ( d θ A Fig. 6.10: Inclined plane C h B It is easier to lift a load from A to C by rolling or moving it along the plank than lifting it upwards from B to C. Velocity ratio of an inclined plane Velocity ratio (V.R) = distance moved by effort (d) distance moved by load (h) Mechanical advantage (M.A) of an inclined plane If the inclined plane is perfectly smooth (no friction), then the work done on load is equal to the work done by effort Work on load = Work done by effort load × h = effort × d load effort = d h Hence mechanical advantage = d h d h The ratio for an inclined plane is always greater than 1, hence its mechanical advantage is greater than 1. In practice, mechanical advantage is usually less than the calculated values due
to frictional force. The effect of length of an inclined plane on its mechanical advantage Activity 6.6 To investigate how the length of an inclined plane affects its mechanical advantage Materials: A trolley, inclined plane, masses Steps 1. Measure the mass of a trolley. Place it on an inclined plane of length l, (Fig. 6.11). Add slotted masses until the trolley just begins to move up the plane. 180 2. Record the values of the load, effort and the length l of the inclined plane. 3. Repeat the activity with inclined planes of different lengths. Make sure the height, h, and the load are kept constant. Pulley Wire Trolley (load) h l Friction compensated slope of length l Slotted mass Effort = mg Fig. 6.11: How the length of inclined plane affects the mechanical advantage. 4. Record your results in Table 6.1. Table 6.1: Effort, length and MA values Effort E (N) Length, l Mechanical advantage = L E 5. What happens to the applied effort when the length of the inclined plane is increased? Work done on the load = load × distance moved by the load = L × h Work done on the effort = effort × distance moved by the effort = E × l ∴ E = But the work done on the load is equal to the work done by the effort i.e. El = L h Lh l mgh l But mgh is a constant: ∴ E α 1 l Therefore a small effort travels a long distance to overcome a large load. since L = mg =. 181 6.3.3 Screws and bolts Activity 6.7 (Work in pairs) To investigate the working of screws and bolts Materials: a screw, bolt, soft wood, a screw driver Steps 1. Take a taping screw and count the number of threads it has. 2. Use a screw driver to drive the screw into a soft wood. Once it reaches the end, remove it from the wood. 3. Feel the threads with your fingers. 4. Measure the depth of the hole made by the screw. 5. Measure the total length of all the threads. 6. Compare the length of the threads with the depth of the hole. 6. Count the number of threads. 8. Determine the distance between two consecutive threads (Suggest the name given to this distance). 9. How many revolutions does the screw head makes when the threads disappears completely into the wood? 10.
Repeat the above steps using a bolt and a nut (Fig 6.12). 11. Discuss your findings with other groups in a class discussion. Fig 6.12(a) shows a screw, bolt and nut. Nut Bolt Top view Pitch Screw Bolt Fig. 6.12 (a): Screws, bolts and nut The distance between the two successive threads is called pitch. When the screw is turned through one revolution by a force applied at the screw head, the lower end moves up or down through a distance equal to its pitch. The working of screws and bolts is based on the principle of an inclined plane. 182 Velocity ratio of a bolt As the bolt is turned through one revolution, the screw moves one pitch up or down. The effort turns through a circle of radius R as the load is raised or lowered through a distance equivalent to one pitch (Fig. 6.13). Velocity ratio = distance moved by effort distance moved by load = circumference of a circle, C pitch (p) = 2πR p V.R = 2πR p Effort R pitch (p) Fig. 6.13: Velocity ratio for a bolt The effect of friction on mechanical advantage, velocity ratio and efficiency From activity 6.7 you noticed that the threads felt warm after being driven into the wood. This means some of the work done was wasted as heat due to friction. The mechanical advantage of a machine depends on the frictional forces present, since part of the effort has to be used to overcome friction. However, the velocity ratio does not depend on friction but rather on the geometry of the moving parts of the machine. Consequently a reduction of mechanical advantage by friction reduces the efficiency of a machine. 6.3.4 The wheel and axle Activity 6.8 (Work in groups) To demonstrate action of wheel and axle Materials: cylindrical rod, y-shaped branches, a stone, a string. Steps 1. Construct a wheel and axle using locally available materials as shown in Fig. 6.14 below. Cylindrical rod Tree branch A B eye C Fig 6.14: A wheel and axle 183 2. Turn the cylindrical rod at A to raise the stone. Is it easy to raise the stone by turning the road at this point? 3. Repeat turning the cylindrical rod but this time by turning at C. What do you realise when raising the stone at this point of turn as compared to the previous point? Explain. 4. Compare the energy needed to turn the cylindrical rod in
the two cases. 5. Which feature of the set-up represent the wheel and axle? 6. Observe the setup from B and draw the wheel, axle, load and effort. 7. Using various loads, find the force which in each case will just raise the load. Record your results in tabular form as shown in Table 6.2 below. Load Effort M.A Table 6.2: Values of load, efforts and N.A 8. Draw a graph of M.A against load. Fig 6.15 shows simplified examples of wheel and axle. r • R effort load (b) wheel axle (a) load effort effort load (c) Fig 6.15: Simple wheel and axle 184 The wheel has a large diameter while the axle has a small diameter. The wheel and axle are firmly joined together and turn together on same axis. The effort is applied to the handle in the wheel. When the effort is applied, the axle turns, winding the load rope on the axle and consequently raising the load. Velocity ratio = distance moved by effort distance moved by load = 2π × radius of wheel(R) 2π × radius of axle (r) M.A may be obtained by taking moment Load × radius of axle = effort × radius of wheel M.A = Load Effort = radius of wheel radius of axle = R r Exercise 6.2 1. Give an example of a lever with a mechanical advantage less than 1. What is the real advantage of using such a machine? 2. Describe an experiment to determine the velocity ratio of a lever whose pivot is between the load and the effort. 3. An effort of 50 N is applied to drive a screw whose handle moves through a circle of radius 14 cm. The pitch of the screw thread is 2 mm. Calculate the: (a) velocity ratio of the screw. (b) load raised if the efficiency is 30%. 6.3.5 Pulleys Activity 6.9 (Work in groups) To demonstrate the action of a pulley Materials: Reference books, flag, a flag post Steps 1. Raise a flag up the flag post. 2. Explain how the flag post raises the flag. 3. We use a pulley to raise water from a well. Does it work the same way as the flag post? 4. Compare and discuss your findings with other groups in your class. 5. Let one of the group members present your findings to the whole class. 185 A pulley is usually a grooved wheel
or rim. Pulleys are used to change the direction of a force and make work easy. There are three types of pulleys i.e. single fixed pulley, single movable pulley and block and tackle. (a) Single fixed pulley Fig. 6.16 shows a single fixed pulley being used to lift a load. This type of pulley has a fixed support which does not move with either the load or the effort. The tension in the rope is the same throughout. Therefore the load is equal to the effort if there is no loss of energy. The mechanical advantage is therefore 1. The only advantage we get using such a machine is convenience and ease in raising the load. Bucket Load (water) Effort Fig. 6.16: Single fixed pulley Since some energy is wasted due to friction and in lifting the weight of the rope, the mechanical advantage is slightly less than 1. The load moves the same distance as the effort and therefore the velocity ratio of a single fixed pulley is 1. Examples of real life applications of a single fixed pulley are as shown in Fig. 6.17. (b) Raising bricks (a) Raising a flag (c) Raising water from a well Fig. 6.17: Examples of single fixed pulley 186 My health Ensure you have covered the well/borehole in our homes after use. Its water may be polluted or even cause death due to accidents. The single movable pulley Fig.6.18 shows a single movable pulley. A movable pulley is a pulley-wheel which hangs in a loop of a rope. A simple movable pulley may be used alone or combined with a single fixed pulley. The total force supporting the load is given by the tension, T, plus effort, E, but since the pulley is moving up, the tension is equal to the effort. Therefore, the upwards force is equal to twice the effort (2E). Hence the load is equal to twice the effort (2E). Mechanical advantage = load effort = 2E E = 2 However, since we also have to lift the pulley, the mechanical advantage will be slightly less than 2. Experiments show that the effort moves twice the distance moved by the load. Therefore, velocity ratio = Distance moved by effort Distance moved by load = 2 Tension T Effort E Load L Fig. 6. 18: A single movable pulley A block and tackle A block and tackle consists of
two pulley sets. One set is fixed and the other is allowed to move. The pulleys are usually assembled side by side in a block or frame on the same axle as shown in Fig. 6.19 (a). The pulleys and the ropes are called the tackle. To be able to see clearly how the ropes are wound, the pulleys are usually drawn below each other as shown in Fig. 6.19 (b). E Block and tackle side by side E Upper fixed pulley block Lower moving pulley block (a) Pulley put side by side (b) Pulley drawn below each other Fig. 6.19: Block and tackle systems. 187 Velocity ratio of a block and tackle Activity 6.10 (Work in groups) To determine velocity ratio of a block and tackle Materials: A block and tackle pulley system, a load, a metre rule Steps 1. Set up a block and tackle system with two pulleys in the lower block and two pulleys in the upper block as shown in Fig. 6.19 (b). 2. Count the number of sections of string supporting the lower block. Raise the load by any given length, l, by pulling the effort downwards. Measure the distance, e, moved by the effort. Record the result in a table. (Table 6.3). 3. Repeat the activity by increasing the distance moved by the effort. How does change of length affect the effort? 4. Plot a graph of e, against, l (Fig. 6.20). Determine the gradient of the graph. Table 6.3: Distance by effort and distane by land Distance moved by effort (e) in cm Distance moved by load l cm 10 20 30 40 5. Compare the value of the gradient obtained with the number of sections of supporting strings. What do you notice? Explain. From Activity 6.10, you should have observed that the distance moved by the effort is distance moved by the load. 1 4 The graph of effort against the load is as shown in Fig 6.20 below. e ∆e ∆l l (cm) Fig. 6.20: Graph of the effort against the load. 188 The gradient ∆e which is the velocity ratio is found to be 4. When the value of ∆l the gradient is compared with the number of sections of string supporting the lower block, we note that they are the same i.e also 4. Tip: The velocity ratio of a pulley system is equal to the number
of strings sections supporting the load. Precaution: The weight of the block in the lower section of the system has to be considered as this increases the load to be lifted. Mechanical advantage of a block and tackle Activity 6.11 (Work in groups) To determine the mechanical advantage of a block and tackle Materials: A block and tackle pulley, a load Steps 1. Assemble the apparatus as in Fig. 6.19 shown in Activity 6.10 and connect a spring balance on the effort string. For a given load, pull the string on the effort string until the load just begins to rise steadily. 2. Repeat the activity with other values of load. 3. Record the values of the effort in a table (Table 6.4). Table 6.4: Values of load (L), effort (E) and L E L E L E 4. For each set of load and effort, calculate the mechanical advantage. Plot a graph of mechanical advantage against the load (Fig. 6.21). Describe the shape of the graph. 189 Fig 6.21 shows a graph of mechanical advantage against the load. M.A Fig. 6.21: Graph of mechanical advantage against the load Load (N) As the load increases, the mechanical advantage also increases. When the load is less than the weight of the lower pulley block, most of the effort is used to overcome the frictional forces at the axle and the weight of the lower pulley block. That is, the effort does useless work. However, when the load is larger than the weight of the lower block, the effort is used to lift the load. This shows that the machine is more efficient when lifting a load that is greater than the weight of the lower block. Using the value of the velocity ratio obtained in Activity 6.11, calculate the efficiency of the pulley system. Plot a graph of efficiency against load (Fig. 6.22). Efficiency (%) Fig. 6.22: The graph of efficiency against load Load (N) The efficiency of the system improves with larger loads. Example 6.6 For each of the pulley systems shown in Fig. 6.23, calculate: (i) velocity ratio (ii) mechanical advantage (iii) efficiency 190 Solution (a) (i) velocity ratio = 2 (number of sections of string supporting the lower pulley) (ii) mechanical advantage 200 N 150 N = = 4 3 = 1.33 60 N 150 N (iii) efficiency = 4 3 × 1 2 ×
100% 200 N (a) 210 N Fig. 6.23: Pulley system (b) = 66.7% (b) (i) velocity ratio = 5 (ii) mechanical advantage (iii) efficiency = load effort = 210 N 60 N = 3.5 = 3.5 5 × 100% = 70% Example 6.7 Draw a diagram of a single string block and tackle system with a velocity ratio of 6. Calculate its efficiency if an effort of 1 500 N is required to raise a load of 5 000 N. Solution See Fig. 6.24 Effort 1 500 N velocity ratio = 6 mechanical advantage = 5 000 N 1 500 N = 10 3 efficiency = M.A V.R × 100 = 10 3 × 1 6 × 100 Load 5 000 N = 55.6% Fig. 6.24: Block Tackle pulley system 191 Example 6.8 A block and tackle pulley system has a velocity ratio of 4. If its efficiency is 65%. Find the (a) mechanical advantage. (b) load that can be lifted with an effort of 500 N. (c) work done if the load is lifted through a vertical distance of 4.0 m. (d) average rate of working if the work is done in 2 minutes. Solution (a) efficiency = 65 = M.A V.R M.A 4 × 100% (b) MA = × 100% 2.6 = load effort load 500 mechanical advantage = 2.6 Load = 1 300 N (c) work = force × distance in the (d) Rate of doing work = Power direction of force = 1 300 × 4 = 5 200 J Power = work done time = 5 200 120 = 43.3 W Exercise 6.3 1. (a) Draw a system of pulleys with two pulleys in the lower and upper block. (b) Describe how you would find experimentally its mechanical advantage. 2. Fig. 6.25 shows a pulley system. Find; (a) (b) (c) (d) the velocity ratio of the pulley system. the mechanical advantage, if the system is 80% efficient. the effort. the work done by the effort in lifting the load through a distance of 0.6 m. (e) how much energy is wasted? 192 Effort 180 N Load Fig. 6.25: Pulleys system 3. A pulley system has a velocity ratio of 3. Calculate the effort required to lift a
load of 600 N, if the system is 65% efficient. 4. A pulley system has a velocity ratio of 4. In this system, an effort of 68 N would just raise a load of 216 N. Find the efficiency of this system. Topic summary • A machine is a device that makes work easier. • Mechanical advantage (M.A) is the ratio of load to effort. • Mechanical advantage = load effort. The mechanical advantage of a machine depends on loss of energy of the moving parts of a machine. Mechanical advantage has no units. • Velocity ratio (V.R) is the ratio of distance the effort moves to that moved by the load. Velocity ratio = Distance moved by the load. Distance moved by the effort Velocity ratio is a ratio of similar quantities hence it has no units. • Theoretical value of velocity ratio may be obtained from the dimensions of the machine e.g. in pulleys–number of the sections of string supporting the load. Table 6.5: Expressions for velocity ratio of various machinery Machine Inclined plane Screw VR 1 sin θ 2πr pitch, P, Wheel and axle Radius of wheel, R Radius of axle, r = R r • Efficiency = work output work input × 100% = mechanical advantage velocity ratio × 100% 193 Topic Test 6 1. Define the following terms: (a) Power of a machine (c) Mechanical advantage (M.A) (b) Efficiency (d) Velocity ratio (V.R) 2. A farmer draws water from a well using the machine shown in Fig. 6.26 below. The weight of the bucket and water is 150 N. The force, F exerted by the farmer is 160 N. The bucket and its content is raised through a height of 15 m. (a) What is the name given to such a machine? (b) Why is the force, F, larger than the weight of the bucket and water? (c) What distance does the farmer pull the rope? (d) How much work is done on the bucket and water? Effort 150N (e) What kind of energy is gained by the Fig. 6.26: A simple pulley system bucket? (f) How much work is done by the farmer? (g) Where does the energy used by the farmer come from? (h) Show with a flow diagram the energy conversion in lifting the water from the well. 3. A factory worker lifts up a bag of cement of mass 50 kg
, carries it horizontally then up a ramp of length 6.0 m onto a pick-up and finally drops the bag of cement on the pick-up (Fig. 6.27). Fig. 6.27: Worker lifting cement on the pick-up (a) Explain the energy changes in the various stages of the movement of the worker. (b) During which stages is the worker doing work on the bag of cement. 194 (c) If the worker has a mass of 60 kg and the ramp is 1.5 m high, find the (i) velocity ratio. (ii) efficiency of the inclined plane if the mechanical advantage is 3. 4. Fig. 6.28 shows the cross-section of a wheel and axle of radius 6.5 cm and 1.5 cm respectively used to lift a load. Calculate the efficiency of the machine. Effort 50 N Load 150 N Fig. 6.28: Wheel and axle 5. A student wanted to put 10 boxes of salt at the top of the platform using an inclined plane (Fig. 6.29). plat form If the resistance due to friction is 10 N, calculate (a) the work done in moving the box 10 boxes. (b) the efficiency of this arrangement. A W = 40.0 N 6. 5 m B 3.0 m C ground (c) the effort required to raise one box to the platform. Fig. 6.29: A crane 6. A crane just lifts 9 940 N when an effort of 116 N is applied. The efficiency of the crane is 65%. Find its: (a) mechanical advantage (b) velocity ratio 7. Fig. 6.30 shows a pulley system. An effort of 113 N is required to lift a load of 180 N. (a) What distance does the effort move when the load moves 1 m? (b) Find the work done by the effort. (c) Find the work done on the load. (d) Calculate the efficiency of the system. 195 113 N 180 N Fig 6.30 A pulley system 8. The Fig. 6.31 shows a single fixed pulley. Calculate its: (a) V.R (b) Efficiency 9. In the system shown in Fig. 6.32, the winding machine exerts a force of 2.0 × 104 N in order to lift a load of 3.2 × 104 N. (a) What is the velocity ratio? (b) Calculate the M
.A. (c) Find the efficiency. 15 000 N 20 000 N Fig 6.31: Single fixed pulley 2.0 x 104 N Winding machine 3.2 × 104 N Fig. 6.32: A winding crane 10. Fig. 6.33 shows a pulley system. (a) What is the velocity ratio of the system? (b) Calculate the efficiency of the system. (c) Show the direction of the force on the string. 11. A block and tackle pulley system has five pulleys. It is used to raise a load through a height of 20 m with an effort of 100 N. It is 80% efficient. Effort 150 N Load 400 N Fig. 6.33: A block and (a) Is the end of the string attached to the upper or lower block of pulleys if the upper block has three pulleys? Show it in a diagram. (b) State the velocity ratio of the system. (c) Calculate the load raised. (d) Find the work done by the effort. (e) Find the energy wasted. tackle pulley 12. A man pulls a hand cart with a force of 1 000 N through a distance of 100 m in 100 s. Determine the power developed. 196 UNIT 5 The Properties of Waves Topics in the unit Topic 7: Introduction of waves Topic 8: Sound waves Learning outcomes Knowledge and Understanding • Understand and explain the motion, types and properties of waves Skills • Design tests to investigate waves using strings and ripple tanks. • Observe carefully • Predict cause and effect • Use appropriate measures • Collect and present results including representing waves in displacement- position and displacement-time graphs Interpret results accurately • • Report findings appropriately Attitudes • Appreciate the wave motion and that there are certain features common to all waves. • Appreciate use of ultrasound in medical diagnosis and radar. Key inquiry questions • What constitute a wave? • What parameters characterize a wave? • What evidence is there that wave exists? • How can we apply our knowledge of waves? 197 TOPIC 7 Introduction to Waves Unit outline • Oscillations • Characteristics of oscillations • Factors affecting oscillations • Types of waves • Characteristics of wave motion Introduction When a stone is dropped in a pool of still water, ripples spread out in a circular form. This constitutes what is called water waves. There are many different types of waves that we make use of such as light and sound waves, microwaves, infrared and radio waves used
to transmit radio and television signals. In this unit, we shall study the production of waves and some common terms and properties used in describing wave motion. By understanding more about waves, more uses are made of them. The study of waves begin with the concept of oscillations. 7.1 Oscillations Movements form a major part in our lives. Movements can be regular or irregular. Some movements follow a fixed path and keep repeating. These kinds of movements are important in our lives as shown in the following examples: • A pendulum clock repeats movement to keep time. • Wheels of bicycles and vehicles keep repeating their movements round in a circular path and this makes them to move faster and easily to other places. • Heartbeats are also rhythmic movements that help us remain alive. • Swings in children’s playgrounds. All these and many others are repetitive to-and-fro movements called oscillations. Therefore, oscillations are repeated, regular movements that happen at a constant rate. 198 7.1.1 Characteristics of an oscillation • The displacement, d, of a vibrating body is the distance of that body from the mean/fixed position. • The amplitude, a, of a vibration is the maximum displacement from the fixed/ mean position in either direction. • Periodic time, T, is the time taken to complete one oscillation or cycle. • The frequency, f, is the number of complete oscillations (or cycles) made in one second.SI unit for frequency is the hertz, Hz. One hertz is defined as one oscillation per second or one cycle per second. Consider the following cases of oscillations: (a) A simple pendulum One oscillation is the movement Amplitude is the distance BA or BC. B Simpole Pendulum Fig. 7.1: A simple pendulum B Simpole Pendulum (b) A vibrating spring A Vibrationg String B A C t1 a t2 C Vibrating springs Vibrationg String B A One oscillation is the movement A C A t1 a A t2 a T B C t3 B a A A The amplitude is the distance BA or BC. C t4 Time B Displacementtime graph Fig. 7.2: A vibrating spring T!"#$%&'"()"*"+ Simpole Pendulum (c) A clamped metre rule a t3 t4 Time Displacementtime graph B A C C B
A One oscillation is the movement A. C B B A Vibrationg String The amplitude is the distance BA or BC. B!"#$%&'"()""+ Fig. 7.3: A clamped rule A T a a 199 t3 Time t4 t1 a t2 Displacementtime graph!"#$%&'"()""+.1.2 Factors affecting oscillations Activity 7.1 (Work in groups) Materials: Bob, stand, string To investigate how length affects the rate of oscillation Steps 1. Set up apparatus as shown in Fig. 7.4 showing a simple pendulum consisting of a bob attached at the end of a light cord. The other end of the string is clamped rigidly in position. 2. Displace the bob slightly to one side then displace slightly and release the bob Fig. 7.4: Simple pendulum 3. release it and observe what happens. Increase the length of the cord the change in vibration time. Why do you think there is change in vibration time? 4. Repeat this several times. We observe that the longer the cord of the pendulum, the slower it oscillates. Activity 7.2 (Work in groups) Materials: Stand, mass, spring and clamp To investigate how mass affects the rate of oscillation Steps 1. Attach a mass to one end of a spiral spring whose other end is rigidly clamped in position Fig. 7.5. Pull the mass slightly downwards then release it and observe what happens. 2. Repeat this activity three times each time using a bigger mass. Fig. 7.5: Hanged spiral spring 3. How does the change in mass affect the rate of oscillations? Explain. The bigger the mass, the slower the vibration of the spring. Activity 7.3 To investigate how frequency affects the rate of oscillation (Work in groups) Materials: G-clamp, mass, Steps 1. Fix a mass at the end of a metre rule and clamp the other end as shown in Fig. 7.6. 200 2. Displace the free end of the rule then release and observe what happens. Repeat this activity by attaching another mass two more times. -3. Repeat this activity using half of the metre rule. 4. How does frequency affect the rate of Oscillation? Explain. G clamp Fig. 7.6: Oscillations of a loaded metre rule. From the Activities (a) the bigger the mass, the
slower the ruler swings. (b) the longer the ruler, the slower it swings. All the above activities indicate that the frequency of a vibrating system is affected by: (a) Length – the longer or larger the body the lower the frequency e.g a shortened guitar wire produces higher pitch. (b) Mass – the bigger the mass /thickness the lower the frequency (longer periodic time). This is usually the case in guitar wires, where thinner ones give higher pitch. Note that a pendulum is not affected by mass of the bob attached. (c) It can be shown that increase in tension increases the frequency /pitch of a vibrating body for example a string /wire. 7.2 The concept of a wave There are many cases in real life where energy produced at one place is consumed at a different place. In such cases, the energy need to be transferred from the place of production to the place of consumption. This can take place in a number of different ways including: •. Physically moving the matter carrying the energy and delivering it to the place where the energy is to be consumed. • Vibration of the particles of a medium leading to transfer energy from one particle to next. In this topic, will learn more about this mode of energy transfer. If a stone is thrown into a still swimming pool or pond, circular water ripples are seen moving from the point where the stone hit the water outwards to the banks. This implies that the energy from the stone is transferred from the hitting point to other regions through the ripples. Such ripples are examples of waves. 201 What is a wave? A wave can be defined as “a periodic disturbance (movement) that transfers energy from one point to another with no net movement of the medium particles.” Examples of waves include sound waves, water waves, light waves, radio waves, X-rays, gamma rays, seismic waves and microwaves. 7.2.1 Formation of waves and pulses Formation of wave motion As learnt earlier, waves transfer energy but not matter. This energy is transferred through pulses and waves. A pulse is a sudden short-lived disturbance in matter. Wave or wave train is a continuous disturbance of the medium which arises due to regular pulses being produced. The following experiments demonstrate wave motions. Formation of pulses A pulse is a single wave disturbance that moves through a medium from one point to the next point. Let us now demonstrate the formation of pulse in Activity 7.4. Activity 7.4
(Work in groups) To demonstrate the formation of pulses using a rope Materials: Rope, pins, nails, helical springs and table Steps 1. Fix one end of a rope to a wall. Hold the free end of the rope so that the rope is fully stretched. 2. Quickly move your hand upwards and then return to the original position as shown in Fig. 7.7(a). Observe what happens to the rope. 3. Now move your hand suddenly downwards and return to the original position as in Fig. 7.7(b). Observe what happens to the rope. (a) (b) Fig. 7.7: Production of a pulse using a rope 4. Tie one end of the rope to the fixed pole as shown in Figure 7.8. 202 wave motionwave motionwave pulsestringwave pulse fixed end Fig. 7.8: A rope fixed at one end 5. Hold the free end of the rope and shake it in an up and down motion. Observe how the rope behaves and explain the motion. 6. Place the helical spring to lie on a table and hold it firmly to the table on one end. 7. Gently pull the free end then push it repeatedly while keenly observing what happens. Explain your observation. What do you think can behave the same way as the spring when compressed? In Activity 7.4, we notice that pulses that move from one end of the rope to the other are produced. If the disturbance is continuous waves or wave trains are formed. When pulses are produced regularly and give rise to a continuous wave motion. Waves or a wave train is a continuous disturbance of the medium which arises due to the regular pulses being produced. In Activity 7.4, when the hand (source) is moved continuously up and down or forward and backward, the particles of the rope or spring (medium) also move up and down or forward and backward. When the source is moved at regular intervals, the disturbance is also produced at regular intervals (Fig. 7.9). rope wave motion (a) wave motion (b) slinky spring fixed end fixed end Fig. 7.9: Production of continuous pulses in a string and a slinky 203 Continuous disturbance of a medium at a point produce continuous waves or wave trains. The waves or wave trains produced are of two types: transverse waves and longitudinal waves. Types of waves There are two types of waves namely; Mechanical waves and Electromagnetic waves. Electromagnetic waves These are waves
that do not require a medium to travel from one point to another. They can travel through empty space (vacuum). Examples of electromagnetic waves are X-rays, gamma rays, visible light etc. They are produced by electric and magnetic fields. Mechanical waves These are waves which require a medium to travel from one point to another. They are produced by vibrating objects. They are transmitted by the vibration of the medium particles. Such waves can be seen or felt. Example of mechanical waves include waves on a rope or spring, water waves, sound waves in air, waves on a spring, seismic wave etc. A mechanical wave can be a progressive or stationary wave. A progressive (travelling) wave is a disturbance which carries energy from one place to another without transferring matter. There are two type of progressive mechanical waves:Transverse and Longitudinal waves. (a) Transverse waves Transverse waves are mechanical waves in which the particles of the medium move in a direction perpendicular to the direction of travel of the wave. Therefore, in a transverse wave, the direction of disturbance is at right angles to the direction of travel of the wave. From Activity 7.4, we notice that when the rope is shook up and down, it is seen to make rises and falls which move through the fixed end (Fig. 7.10). 204 Fig. 7.10: A rope in motion The rope particles are displaced up and down as they move towards the fixed end. These up and down disturbance are perpendicular to the direction of motion of the wave. The rises are known as crests while the falls are known as troughs (Fig. 7.11). Crest trough rope wave motion Fig. 7.11: Transersal waves fixed end (b) Longitudinal waves Longitudinal waves are mechanical waves in which particles of the medium move in direction parallel to the direction of the wave motion. The particles of the transmitting medium vibrates to and fro along the same line as that in which the wave is travelling. From Activity 7.4, we notice that when the spring is compressed gently, the coils are observed to move towards the fixed end. In some regions, the coils are close together while in other regions the coils are far apart as shown in Fig. 7.12. The region where the coil are close together are known as a compressions while the regions where they are far apart are known as rarefactions. (See Fig 7.12 (a) and (b)) (a) Rarefactions compressions 205
wave motionfixed endslinky spring (b) Key: C - Compressions R - Rarefaction Fig. 7.12: Longitudinal wave Thus, a longitudinal wave consists of compressions and rarefactions. Compressions is a region on a longitudinal wave with a high concentration of vibrating particles. On the other hand rarefaction is a region of the longitudinal wave with low concentration of vibrating particles. Example of longitudinal wave is sound waves. Figure 7.13 shows a longitudinal plane waves. Loud speaker Compression Rarefaction Compression Rarefaction Compression Wave λ λ Fig. 7.13: shows a longitudinal plane waves Differences between Transverse and Longitudinal waves Table 7.1: Difference between transverse and longitudinal waves Transverse waves Particles of the medium are displaced perpendicular to the direction of motion of the wave. Form crests and troughs. Example include: Electromagnetic waves, water waves, waves made by a rope when its moved up and down. Longitudinal waves Particles of the medium are displaced parallel to the direction of motion of the wave. Form compressions and rarefactions. Example include: sound waves, waves made by a spring when pushed. Exercise 7.1 1. What is an oscillation? 2. Distinguish between a pulse and wave train. 3. What factors affect the frequency of an oscillating: (b) mass – spring system (a) pendulum 206 RCCRCλλFixed pointwavelengthwavelength 4. Define the term ‘wave’. 5. Differentiate between transverse and longitudinal waves giving an example for each. 6. Name the type of wave found in the following activities: (a) Children playing rope jumping. (b) A spring being displaced forward and backward. (c) Waves due to dropping a stone into water on a basin. (d) A car moving on a bump. 7. Distinguish between compression and rarefaction 8. Briefly explain how a pulse in formed. 9. Name two factors that affect oscillations of an object. 7.3 Characteristics of wave motion Wavelength of transverse waves Consider a long rope with one of its ends rigidly tied to a peg while the other end is free. Produce a pulse by moving the hand upwards and notice the distance travelled by the disturbance. If the hand is moved up and down once through a complete cycle, the time taken by the hand is the periodic time (T). Fig.
7.14 shows a graph of displacement of particles against time. We see that the particles of the rope just vibrate up and down about their mean or rest position, but do not move with the wave. The disturbance is transferred from particle to particle. The distance travelled by the disturbance (wave energy) during each periodic time T is called the wavelength, λ, of the wave 10 11 12 13 7 T 2T 3T λ λ λ Fig. 7.14: Wavelength of a transverse wave. 15 particles time distance From the graph (Fig. 7.14), particles 2, 6, 10, 7, etc. are at similar positions and, move in the same direction. Such positions are called the crests of a wave. Similarly, particles 4, 8, 12 etc, are at similar positions and are moving in the same direction. Such positions are called the troughs of a wave. 207 Particles that are at similar positions and are moving in the same direction are said to be in phase. A crest is the position of maximum positive displacement, and a trough is the position of maximum negative displacement as shown in Fig. 7.15. The distance between two successive particles in phase such as two successive crests or troughs is equal to the wavelength of the wave. λ crest crest crest crest time + trough trough trough λ Fig. 7.15: Crest and troughs in a transverse wave Wavelength of a longitudinal wave Fig. 7.16 shows the energy propagation in a slinky spring Fig. 7.16: Compressions and rarefactions in a longitudinal wave. Just like the production of crests and troughs in a transverse wave, we have the regions of compressions (C) and rarefactions (R) in a longitudinal wave. A compression is a region where the particles of the medium are closely packed. In this region, the pressure of the particles of the medium is high, hence the density is high. A rarefaction is the region where the particles of the medium are spread out. In this region the pressure of the particles of the medium is low, hence the density is low. The wavelength of a longitudinal wave can be described as the distance between two successive compressions or rarefactions. Fig. 7.17 is a displacement -time graph for a wave. We will use it to describe other characteristics of waves. 208 Fig. 7.17: Displacement – Time graph Periodic time, T The time taken
for one vibration /oscillation. It is also the time taken to cover a distance of one wave length. Thus, the value of T in Fig. 7.17 is the periodic time. By definition, periodic time is the duration for one complete oscillation. Amplitude, (A) As a body or particles vibrate, they change position from the mean rest position. The position of a point from the resting position at any given time is called its displacement. The maximum value of displacement is called amplitude (A) as shown on the Fig. 7.17. Frequency, (f) Frequency (f) is the number of cycles made per unit time. We can write this mathematically as, number of vibrations (n) Frequency (f) = –––––––––––––––––––– time taken (t) n In symbols, f = – t If n = 1 (i.e 1 oscillation), then t = T (periodic time) 1 1 Hence f, = – and T = – T f For example, if a newborn baby’s heart beats at a frequency of 120 times a minute, its frequency is f = ––– = 2 Hz and T = – = – = 0.5 s 120 I I 60 f 2 209 A C B B A C Vibrationg String B Simpole Pendulum Speed of wave This is the distance covered by a wave per unit time. It is measured in metres per second, (m/s). The speed of wave is given by: T A Wave speed = a distance travelled by a wavetrain time taken a Phase of a wave – is the fraction of wave cycle which has elapsed relative to the origin. Time t4 t3 t2 t1 The wave equation T Consider a source that produces n waves of wavelength (λ) in period time (T) seconds (Fig. 7.18) Displacementtime graph nλ = d!"#$%&'"()"*"+ Fig. 7.18: Displacement – distance graph The distance travelled by a wave train in one period time is the wavelength of a wave. Wave speed, v = distance travelled time taken Thus, the velocity of the wave is given by: nλ T.........................................(i) velocity (v) = but n T = f Substituting for T in (i), we get v = Thus, v = fλ = λf λ 1 f The speed of a wave is given by:
Frequency × wavelength The equation v = fλ is called the wave equation. This formula holds for all waves. 210 Example 7.1 A slinky is made to vibrate in a transverse mode with a frequency of 4 Hz. If the distance between successive crests of the wave train is 0.7 m calculate the speed of the waves along the slinky. Solution λ = 0.7m, ƒ = 4Hz Wave speed = frequency × wavelength = 4Hz × 0.7m = 2.8 m/s Example 7.2 Calculate the frequency of a wave if its speed is 30 cm/s and the wavelength is 6 cm. Solution Wave speed = frequency × wavelength v = ƒ × λ ƒ = – = –– = 5 Hz v 30 λ 6 Example 7.3 A source of frequency 256 Hz is set into vibrations. Calculate the wavelength of the waves produced, if the speed of sound is 332 m/s in air. Solution v = ƒ × λ v 332 ƒ 256 λ = – = ––– = 1.30 m. Example 7.4 The speed of a certain wave in air is 3 × 108 m/s. The wavelength of that wave is 5 × 10–7m. Calculate the frequency of that wave. Solution v = f λ ƒ = – = –––––– = 0.6 × 1015 Hz = 6.0 × 1014 Hz v 3 × 108 λ 5 × 10–7 211 Example 7.5 Fig. 7.19 shows a wave produced in a string. B A D C 4.0 cm Fig. 7.19 (i) Calculate the wavelength of the wave. (ii) If ten complete waves are produced in a duration of 0.25 seconds, calculate the speed of the waves. Solution (i) Wavelength (λ) = length of a number of waves number of waves = 4 cm 2 = 2 cm (ii) f = 10 0.25 = 40 Hz v = f λ = 0.02 × 40 = 0.8 m/s Example 7.6 Fig. 7.20 shows the displacement–time graph of a wave travelling at 200 cm/s.2 0.2 0.2 0.4 0.6 0.8 time (s) Fig. 7.20: Displacement – time graph Determine the: (a) amplitude (b) Period (
c) frequency (d) wavelength 212 Solutions (a) 0.3 cm (c) f = 1 T = 2.5 Hz (b) T = 0.4 s f = 2.00 (d) λ = 2.5 v = 0.8 m Example 7.7 A spring vibrates at the rate of 20 cycles every 5 seconds (a) Calculate the frequency of the waves produced. (b) If the wavelength of the waves is 0.01 m, find the speed of the waves. Solutions (a) 20 cycles = 5 seconds 4 cycles = 1 second ∴ f = 4 Hz (b) v = f λ = 4 × 0.01 = 0.04 m/s Exercise 7.2 1. Draw a wave and mark on it the wavelength and amplitude. 2. Explain the phrase ‘a wave has a frequency of 5 Hz’. 3. A flag is fixed in an ocean. If two waves pass the flag every second, what is (a) its frequency? (b) the period of the water waves? 4. Derive the wave equation. 5. A sound wave has a frequency of 170 Hz and a wavelength of 2 m. Calculate the velocity of this wave. 6. The range of frequencies used in telecommunication varies from 1.0 × 106 to 2.0 × 107 Hz. Determine the shortest wavelength in this range. (The Speed of the wave is 3 × 103 m/s). 7. The speed of sound in air is 320 m/s. Calculate the frequency of sound when the wavelength of sound is 60 cm. 8. Define the term ‘wave’. 9. Distinguish between: (a) Mechanical wave and electromagnetic wave (b) Transverse wave and longitudinal wave. 213 (c) Compression and rarefaction. 10. The figure below shows a displacement-time graph for a certain wave ) m ( 0.25 0 Time (s0.25 2.5 × 10–4 7.5 × 10–4 Fig. 7.21: Displacement - time graph (a) Identify the type of wave. (b) State the period of the wave (c) Determine the frequency of the wave. (d) If the wave has a wavelength of 3.5 cm, what is its velocity? 11. A wave source generates 300 waves signals in a second. Each of the wave signals has a wavelength of 4.5 cm
. (a) Determine the: (i) Frequency of the wave. (ii) Period of the wave. (iii) velocity of the wave. (b) Determine the time taken by the generated waves to hit a barrier that is 250 m away from the wave. 12. Using specific properties of light, explain why it is a transverse wave. 13. Define the following terms and state its S.I units: (a) Amplitude (b) Period (c) Wavelength (d) Frequency 14. Clouds FM broadcasts on a frequency of 88.5 kHz producing signals of wavelength 3389.83 m. Determine: (a) The period of its signals 214 (b) The velocity of radiowaves (c) The velocity of radio free East Africa if its signals have a wavelength of 3405.22 m. 15. (a) Give the meaning of the symbols in the equation v = f λ. (b) Calculate the wavelength of a wave if the speed is 45 m/s and the frequency is 5 Hz. 16. Radio wave travel with a speed of 3 × 108 m/s in air. If a radio station broadcasts at a wavelength 125 m, calculate the frequency of the transmitted waves. Topic summary • A wave is a periodic disturbance that transfers energy in space from one point to another in a medium. • When a rope fixed at one end is shaken up and down two waves trains are produced: transversal and longitudinal. • In longitudinal waves, motion of the medium particles are displaced in the same direction as that of the travel of wave. In the transversal waves motion of the medium particles are displaced perpendicular to the direction of the travel of the wave. • Wavelength is the distance between successive crests or troughs of a wave. • Amplitude is the displacement of a particle from its mean or rest position. • Period is the time taken for a wave to make one cycle. • Frequency is the number of waves passing at a given point per second. • Compression is a region in a longitudinal wave with high concentration of vibrating particles. • Rarefaction is a region in a longitudinal wave with low concentration of vibration particles. • A pulse is a single disturbance that moves through a medium from one point to the next point. • A ripple tank is an apparatus used to demonstrate the various properties of waves like reflection, refraction, diffraction and interference. • A wavefront is an imaginary line which joins a set of particles which
are in phase in a wave motion. 215 • A ray is a line draw to show the direction of travel of wave energy and is perpendicular to the wavefront. • Water and sound waves like light waves, obey the laws of reflection. Topic Test 7 1. Two waves that are in phase, they form a type of interference called _____. A. Constructive C. Coherent B. Destructive D. Out of phases 2. When a plane waves are reflected, the reflected waves take the shape of the reflecting surface. Draw the reflected waves emerging from a: (a) Convex reflector (b) Concave reflector 3. Copy and complete this paragraph about waves. When a wave enters a shallow region, it __________ down and bends towards the _________. This change of direction is called ___________. 4. What happens to the following properties of waves after the waves move into shallow water. (a) Frequency (b) Speed (c) Wavefront direction (d) Wavelength 5. The figure 7.22 shows a displacement-time graph for a certain wave ) m ( 0.25 0.25 0 Time (s) 2.5 × 10–4 7.5 × 10–4 Fig. 7.22: Displacement - time graph Identify the type of wave. (a) (b) State the period of the wave. (c) Determine the frequency of the wave. (d) If the wave has a wavelength of 3.5 cm, what is its velocity? 6. A wave source generate 300 waves signals in a second. Each of the wave signals has a wavelength of 4.5 cm. (a) Determine the: (i) Frequency of the wave. 216 (ii) Period of the wave. (iii) velocity of the wave. (b) Determine the time taken by the generated waves to hit a barrier that is 250 m away from the wave. 7. Using specific properties of light, explain why it is a transverse wave. 8. Define the following terms and state its S.I units: (a) Amplitude (c) Wavelength (b) Period (d) Frequency 9. A radio station broadcasts on a frequency of 88.5 kHz producing signals of wavelength 3389.83 m. Determine: (a) The period of its signals (b) The velocity of radiowaves (c) The velocity of radio Africa if its signals have a wavelength of 3405
.22 m braodcasting on the frequency 88.5 kHz. 10. (a) Give the meaning of the symbols in the equation v = f λ. (b) Calculate the wavelength of a wave if the speed is 45 m/s and the frequency is 5 Hz. 11. Radio wave travel with a speed of 3 × 108 m/s in air. If a radio station broadcasts at a wavelength 125 m, calculate the frequency of the transmitted waves. 217 TOPIC 8 Sound Waves Unit outlines • Production of sound waves • Sources of sound waves • Nature of sound waves • Characteristics of sound waves • Propagation of sound • Sound pollution Introduction In Topic 7, we learnt that sound is an example of longitudinal waves. Since a wave is a form of energy, sound is thus a form of energy propagated in a longitudinal manner. In this topic, we shall study the production, propagation, characteristics and applications of sound waves. 8.1 Production of sound The following activity will help us understand how sound is produced. Activity 8.1 To demonstrate sound production (Work in groups) Materials: Metallic string, rubber band, metere rule, drum, piece of wood, glass beaker, pens Steps 1. Pluck a stretched metallic string or rubber band. 2. Fix on end of a half-metre rule near the edge of one side of a table and press the free end downwards slightly and release it. 3. Blow a whistle or a flute. 4. Hit a metallic rod against another. 5. Hit the ‘skin’ of a drum gently with a piece of wood. 6. Gently tap a glass beaker with a pen. 7. Why do the objects above produce such noise? 8. How is the noise produced? In each of the activites within Activity 8.1, sound is produced as the objects vibrate. Sound is a form of wave caused by vibrating bodies. 218 Sound Waves Fig. 8.1 shows some of the sound producing instruments. Drum guitar whistle speaker Fig. 8.1: Examples of sound producing instruments Activities 8.2 (Work in groups) Materials To investigate that a vibrating source produces some energy • A tuning fork • A pith ball • • water in a container glass plate • • tooth brush bristle lamp soot Steps 1. Take a tuning fork and strike hard on a rubber pad with one of the prongs on and observe what happens. 2. Make one of the vibrating prongs of the tuning fork
to touch a small pith ball suspended by a thread (Fig. 8.2) and see what happens. Prongs 3. What makes the tuning fork vibrate? Fig. 8.2: Vibrating tuning fork displaces a pith ball. 4. Dip the vibrating prongs in water in a container and observe what happens. 5. What happens to water immediately the fork is dipped in it? 6. Why does it stop vibrating after sometime? 7. Cover a glass plate with a uniform coating of lamp soot. Attach a short stiff hair of a tooth brush (bristle) to one of the prongs of a tuning fork. Set the tuning fork into vibration and let the bristle lightly touch the soot on the glass plate. Pull the glass plate gently along a straight line and observe what happens (Fig. 8.3). 219 pull bristle smoked glass plate Fig. 8.3: Vibrating tuning fork on a glass plate. The prongs start vibrating. The pith ball is seen to be jerked to one side. Water is violently agitated. A wavy trace is seen on the glass plate. The vibrating prongs of the tuning fork produce energy. Therefore, sound is a form of energy produced by vibrating objects. 8.2 Sources of sound waves All sources of sound have some structures which vibrate. A guitar has strings, a drum has a stretched skin and the human voice has a vocal cord that vibrate and produce sound. Sound travels through the air to our ears through vibrations enabling us to hear it. The air (medium of propagation) is necessary as shown by Experiment 1.11. In the experiment, the sound disappeared though the striker can still be seen hitting the gong. Evidently sound cannot travel in a vacuum as light can do. All materials, including solids and liquids and gases transmit sound. Sound waves produced for example by a loudspeaker consists of a train of compressions and rarefactions (See Fig. 8.4). Hence, sound waves are longitudinal waves. Loud speaker Compression Rarefaction Compression Rarefaction Compression Wave λ λ Fig. 8.4: Sound waves as longitudinal waves. 220 8.3 Nature of sound waves Consider a tuning fork in a state of vibration as shown in Fig. 8.5. As prong X moves to the right, it compresses the layer of air in contact with it (Fig. 8.5(b)). The compressed
layer passes the energy to the next layer of air molecules and returns to the original position. Thus a region of compressions moves to the right (Fig. 8.5(c)). As prong X moves to the left, a region of reduced pressure or a rarefaction is produced in the vicinity of (Fig. 8.5(d)). The compressed air in the next layer, moves towards the left to ‘equalise’ the reduced pressure and hence produces another rarefaction to its right and so on. Thus a region of rarefaction moves to the right. x x x x x x (a) (b) (c) (d) (e) ( Fig. 8.5: Production of rarefactions and compressions in a sound wave. 221 Note: As long as the vibrations are periodical, the number of times representing a compression must be equal to the number representing rarefaction and evenly spaced respectively. Therefore, as the prong X vibrates to and fro, a series of compressions and rarefactions are produced. Each layer of air vibrates back and forth about its mean position along the direction in which propagation of energy takes place. Thus, sound waves are longitudinal waves. The wavelength of sound waves is the distance between two succussive compressions and rarefactions. 8.4 The concept of audible range An audible range is a range of frequencies of sound which can be detected by the human ear. Human being’s hear only sounds with frequencies from about 20 Hz to 20 000 Hz (20 kHz). These frequencies are the limits of audibility. The upper limit decreases with age. Sounds with frequencies below 20 Hz are called infrasonic sounds while sounds with frequencies above 20 kHz are called ultrasonic sounds (ultrasound). An average human ear can distinguish between two simultaneous sounds if their frequencies differ by at least 7 Hz. 8.4.1 The human ear Humans and animals detect sound waves using their ears. The human ear converts sound energy to mechanical energy and then to a nerve impulse that is transmitted to the brain. Figure 8.6 shows the parts of a human ear. Hammer Outer ear Anvil Stirrup Eardrum Nerve to brain P Cochlea Pinna Ear canal Eustachian tube Outer ear Middle ear Inner ear Fig. 8.6: The Human Ear 222 The human ear has three main sections: the outer ear, middle ear and the inner ear. Sound waves enter the outer ear and travel through the ear canal
to the middle ear. The ear canal channels the waves to the eardrum. The eardrum is a thin, sensitive membrane stretched tightly over the entrance of the middle ear. The waves cause the eardrum to vibrate. It passes these vibrations to the hammer which is one of the three bones in the middle ear. The hammer vibrates causing the anvil, the other small bone touching the hammer to vibrate. The anvil passes the vibrations to the stirrup, another small bone touching the anvil. From the anvil, the vibrations pass into the inner ear. The vibrating stirrup touches a liquid filled sack and the vibrations travel into the cochlea, which is shaped like a shell. Inside the cochlea, there are hundreds of special cells attached to the nerve fibres which transmit the information to the brain. The brain processes the information from the ear enabling us to distinguish the different types of sounds. 8.4.2 Human audible frequency ranges The compressions and rarefactions produced in air by sound waves reach the eardrum of a person and force the eardrum into similar vibrations. The physical movements of the eardrum are transmitted to the brain and produce a mental sensation of hearing. The human ear can detect sound waves of frequencies about 20 to 20 000 Hz (cycles per second). We cannot hear the sound waves, if the frequency is less than 20 Hz or is above 20 000 Hz. The upper limit, however varies with persons and age, it is higher in the case of children than in the old people. It is still higher in certain animals like bats. Just as other types of waves, sound waves obey the wave equation, v = λf. Therefore, the audible frequency ranges is given by; fmaximum = λ fminimum = λ v ______ minimum v ______ maximum Example 8.1 A certain animal can hear sound of wavelength in the range of 2 m to 10 m. Calculate its audible range of frequency. Take the speed of sound in air as 330 m/s. 223 Solution v fminimum = ______ λ maximum fmaximum = v ______ λ minimum = 330 m/s 10 m 330 m/s = 2 m = 33 Hz = 165 Hz Its audible frequency range is 33 Hz to 165 Hz 8.5 Ultrasonic sound Ultrasonic sound is a sound wave that have a frequency above the normal human audible frequency range. Very high frequency waves can penetrate deep sea-water without loss of energy by diffraction. Examples
of sources of ultrasonic sound is ship siren and some factory sirens. Therefore, ultrasonic sound has a fundamental frequency that is above the human hearing range i.e. sound with fundamental frequency above 20 000 Hz. The reverse of ultrasonic wave is the infrasonic. Infrasonic is a wave in which the fundamental frequency is lower than the human ear hearing range (audible range). 8.5.1 Uses of ultrasonic sound waves The following are some of the uses: 1. In medical and surgical diagnosis Ultrasonic waves are used in place of X-rays during X-radiography scanning parts of the body using an ultrasonic beam. Ultrasonic is also used to sterilize surgical instruments, jewellery and cleaning medicare instruments. Ultrasonic waves are also used to monitor patient’s heart beats, kidney, growth of foetus (prenatal scanning) and destroy kidney stones. 2. In industries Ultrasonic waves is used in cleaning of the machine parts in industries. Objects or parts with dirt are placed in a fluid through which ultrasonic waves are passed. The waves are used in analysing the uniformity and purity of liquids and solid particles. 3. In fishing Ultrasonic waves are is used to locate shoals of fish in deep sea by the process called echolocation i.e. use of echo to locate an object. More interesting is that this method can detect different types of fish. This is because different fish reflect sound to different extents. 224 4. In security Ultrasonic waves are used in security systems to detect even the slightest movement. Many buildings have ultrasonic motion sensors that detect motion. 5. Estimation of distance by bats: Bats judge the distance away from an object by emitting ultrasound and interpreting the time taken by the reflected wave (echo) to return. The sound they emit is partially or totally reflected from the surface on an obstacle depending on the density of the medium at that point. This helps them to tell where to pass through or perch. 6. Mapping: Sound bounces off an object, the shorter the time lapse between the initial sound and the echo, the smaller the distance. It is particularly useful in mapping the depth of the ocean and also finding lost objects at sea. 7. Ultrasonic echoes are used to determine the shape and size of an object that is not visible such as sunken ship or a baby in the womb. Example 8.2 A ship sends out a sound wave and receives an echo after 1 second. If the
speed of sound in water is 1 500 m/s, how deep is the water? Data: Time taken = 1 s; speed, v = 1 500 m/s for to and fro Solution Time taken for sound to reach the seabed = t 2 = 1 2 = 0.5 s From; v = d t or use v = 2d total time d = v × t = 1 500 m/s × 0.5 s = 750 m Exercise 8.1 1. Define the term sound. 2. Describe an experiment to show how sound is produced. 3. Explain the following terms in respect to sound wave: (a) Compression (b) Rarefaction 225 4. Distinguish between utrasonic and infrasonic waves. 5. An animal has audible frequency range of 40 Hz to 20 000 Hz. Calculate the corresponding wavelengths of the frequencies. 6. Explain why a human being cannot hear sound above 20 000 Hz. 7. Explain how ultrasonic sound is used in: (a) Industry (b) Security 8. Define: (a) Sound (c) Echo (b) Pitch (d) Reverberation 9. Distinguish between: (a) Infrasonic sound and ultrasonic sound (b) Sound and echo 10. With the aid of a well labelled diagram, describe how the human ear works. 11. A gun is fired and an echo heard at the same place 1.5 seconds later. How far is the barrier which reflected the sound from the gun? (velocity of sound = 330 m/s). 12. State four uses of echo. 13. A policeman standing between two parallel walls fires a gun. He hears an echo after 2.0 seconds and another one after 3.5 seconds. Determine the separation of walls. (Take velocity of sound 340 m/s). 14. Winfred is standing 600 m from a cliff. She bangs two pieces of wood together and hears an echo 3.5 seconds later. Determine the velocity of sound. 15. A spectator watching athletics in a stadium sees the light from the starting gun and hears its sound after 3 seconds. How far is the spectator from the starting point? (Speed of sound in air is 330 m/s) 16. Maryanne is standing between two walls. She is 400 m from the nearest wall. The walls are “y” m apart. Each time she presses a hooter, she hears two echoes one after
2.5 seconds and the second one after 4.5 seconds. Determine: (a) The velocity of sound. (b) The separation distance “y”. 226 8.6 Characteristics of sound waves The three main characteristics of musical sounds are: (a) Pitch It is the characteristic of a musical sound which enables us to distinguish a sharp note from a hoarse one. For example, the voices of women or children, usually of high pitch than of men. Similarly, the note produced by the buzzing of a bee or the humming of a mosquito is of much higher pitch than the roaring of a lion, though the latter is much louder. Pitch is purely qualitative and cannot be measured quantitatively. The greater the frequency of a vibrating body, the higher is the pitch of sound produced and vice versa. It should be noted that pitch is not frequency; it is a characteristic depend on the frequency. Frequency is a physical quantity and can be measured. Pitch cannot be measured. The pitch of sound depends on the following two factors: 1. Frequency of the sound produced Pitch is directly proportional to the frequency. 2. Relative motion between the source and the observer When a source of sound is approaching, a listener or the listener approaches the pitch of sound appears to become higher. On the other hand, if the source is moving away from the listener or the listener moves away from the source, the pitch appears to become lower. (This effect is known as the Doppler’s effect). (b) Intensity and loudness sound Intensity of sound at any point is the quantity of energy received per second on a surface area of 1 m2 placed perpendicular to the direction of propagation at those points. Thus, the intensity of sound is purely a physical quantity, quite independent of the ear and can be measured quantitatively. It is measured in joules/second/m2. (Js–1m–2) The loudness of sound is the degree of sensation of sound produced in the ear. It depends on the intensity of sound waves producing the sound and the response of the ear. In general, the sound waves of higher intensity are louder. Intensity of sound depends on the following factors: 1. Amplitude of vibrating body The intensity or loudness I, of sound is directly proportional to the square of the amplitude of the vibrating body. If the amplitude of the vibrating body is doubled, the loudness of sound produced becomes two times greater. 227 2. Distance from the
vibrating body The intensity or loudness of sound I, is inversely proportional to the square of the distance from the vibrating body. ∴ Intensity α 1 (distance)2 Surface Area of the vibrating surface If the distance from the source of sound is doubled, its intensity of sound becomes 1 and so on. 4 3. Intensity is directly proportional to surface area of the vibrating body. This is because the greater the area of the vibrating surface, the larger the energy transmitted to the medium and the greater is the loudness of the sound produced. 4. Density of the medium The intensity of sound is directly proportional to the density of the vibrating medium For example, an electric bell ringing in a jar filled with oxygen produces a much louder sound than the jar filled with hydrogen. Similarly, the intensity sound of a tuning fork is much higher when the stem of the fork is placed on the table than in air. 5. Motion of the medium If wind blows in the direction in which the sound is travelling, the intensity of sound at a point in the direction of the wind increases and vice versa. Thus, if we shout on a windy day, the sound heard is much louder at a certain distance in the direction of the wind than at the same distance in the opposite direction. (c) Quality (Timbre) of sound Quality is that characteristic of musical note which enables us to distinguish a note produced by one instrument from another one of the same pitch and intensity produced by a different instrument. If, for example, a note of a given pitch is successfully produced by a violin, a guitar or a piano, the ear can distinguish between the three notes. For example, Fig. 8.7 represents two separate waves, one of which has the frequency twice that of the other. When the resultant of these two waves fall upon the ear, the ear is able to recognise the individual waves which have given rise to the resultant wave as they have different qualities (timbre). Fig. 8.7: Waves of two different frequencies 228 Musical sounds and noises In general, sound may be roughly classified as either (a) musical sounds (b) noises. If we pluck the string of a guitar or a stretched sonometer wire or set a tuning fork into vibrations, the sound produced has a pleasant effect on our ears. If however, we listen to the slamming of a door, the sound produced by thunder clouds or the rattling sound of some parts of a car, the sounds produced have an unpleasant effect on
the ears. A sound of which appears pleasant to the ear is called a musical sound whereas that which produces an unpleasant or jarring effect on the ear is called a noise. The curves shown in Fig. 8.8 (a) and (b) bring out the difference between noises and musical sounds. (a) (b) Noise Musical sound Fig. 8.8: Noise and musical sound Musical sound is regular and periodic with pulses following each other very rapidly producing the sensation of a continuous sound. Noises, on the other hand, are generally sudden and have no regular period; and are usually complex in nature. 8.7 Propagation of sound Sound waves cannot be transmitted through a vacuum. The transmission of sound waves requires at least a medium which can be a solid, liquid or a gas. Activity 8.3 (Work in groups) Materials To show that sound requires material medium to travel through • Air tight bell jar • Steps • Electric bell Power supply (battery) and connecting wire • Vacuum pump 1. Suspend the electric bell inside an air-tight bell jar as shown in the Fig. 8.9. 229 switch + – S stopper gong air tight bell jar electric bell striker vacuum rubber tube to vacuum pump valve Fig. 8.9: Electric bell 2. Switch on the bell, while there is some air in the bell jar. 3. Start the pump to take the air molecules out of the jar as you listen to the change in the intensity of sound. 4. Return the air to the bell-jar again by opening the stopper slightly as you listen the change in sound. 5. How does the bell produce sound? When there is air in the jar the bell is heard ringing. When the pump is switched on to remove the air, the sound dies down gradually and is eventually not heard at all. When air is allowed to return to the jar, the sound is heard once again. This experiment shows that a medium like air is necessary for propagation of sound. Sound cannot travel through a vacuum. 8.8 Speed of sound in solids, liquids and gases The speed of sound is different in solids, liquids and gases. The arrangement of particles in matter determines how fast sound can travel in matter. The following experiment will help us illustrate that sound require material media to travel. 230 Activity 8.4 (Work in groups) Materials To design and investigate the speed of sound in solids and fluids • A metal spoon Steps • A tuning fork 1. Tie a metal spoon or a
light tuning fork to one end of a string and hold the other end near the ear, by not touching it. 2. Let someone touch the spoon with a finger or the set prongs of the fork into vibration by gently hitting the prongs with a rubber. Listen to the sound produced. 3. Remember to repeat the experiment with the free end of the string in contact with the ear. Compare the loudness of sound heard in both cases. Which sound is louder? 4. Write a report about the speed of sound in solids, liquids and gases. Present your findings in a classroom discussion. The loudness of sound heard is more when the string is in contact with the ear. The string transmits sound through it and does it better than air. This experiment shows that sound can travel through solids. Similarly if sound is produced inside water e.g in a swimming pool, it can be heard a short distance away. From the experiments, it has been established that the speed of sound in water is about 1 500 m/s and in steel about 5 500 m/s. Comparison of the speed of sound in solids, liquids and gases The speed of sound varies in solids, liquids and gases. Activity 8.5 will help us to show the speed of sound in solids, liquids and gases. Comparing speed of sound in solids and gases Activity 8.5 (Work in groups) Materials Wooden plank Steps 1. Let one learner place the ear on one end of 20 m wooden plank, while another taps the plank once with a stone on the opposite end. What do you hear? 2. Which sound is heard faster and why do you think this is? 231 In Activity 8.5, two sounds, will be heard by the listerner: one coming through the wooden plank followed by another through the air. This shows that sound travels faster in solids than in air. Several experiments proved that • The speed of sound is higher in liquids than in gases and slower than in solids. • The speed of sound is faster in solids than in liquids because the particles or atoms in solids are closely packed. This makes it easier for particles to transmit sound from one point to another. • The speed of sound in liquids is faster than in gases because the particles in liquids are relatively closer than those in gases. • Therefore the speed of sound is slowest in gases. Lightning and thunder About the middle of the 18th Century, an American Scientist Benjamin Franklin demonstrated that charged thunder clouds in
the atmosphere produce thunderstorms. These thunderstorms produce a lot of sound which we hear as thunder on the earth. Due to the spark discharge occuring between two charged clouds or between a cloud and the earth, electric spark discharge, called the lightning occurs. Though the sound due to thunder is produced first, we see the flash of lightning first and after a few seconds we hear the sound of thunder. This is due to the fact that light travels much faster than sound in air. Experiments have proved that the speed of light in air (or vacuum) is 3.0 ×108 m/s. Take care! Avoid walking in drain water or standing under tall trees when it is raining. Example 8.3 The time interval between “seeing” the flash of lightning and “hearing” the sound of thunder clouds is 5 seconds. (a) Calculate the distance between the thunder clouds and the observer on the earth. (b) Explain why the calculated distance is only approximate. (Speed of sound in air = 330 m/s) 232 Solution (a) speed of sound = v = x t distance time x = v × t = 330 × 5 = 1 650 m/s ∴ The distance between the thunder clouds and the observer is 1 650 m. (b) The clouds may be moving. 8.8.1 Factors affecting the speed of sound in gases (a) Density The higher the density of a gas, the higher the speed of sound. For example, the density of oxygen is 16 times higher than the density of hydrogen hence sound travels faster in hydrogen than in oxygen (speed of sound in hydrogen = 4 × speed of sound in oxygen). (b) Humidity Moist air containing water vapour is less dense than dry air. The density of water vapour is about 0.6 times that of dry air under the same temperature conditions. If the humidity of air increases, density of air decreases hence the speed of sound in air increases. Early in the morning the percentage of humidity of air is more and sound travels faster in the morning air. (c) Pressure The speed of sound is not affected by any change in pressure provided temperature is constant. For example, on a day when the temperature and humidity of air is the same in Lilongwe and a city at the sea level, the speed of sound is the same in the two cities, although the air pressure in Lilongwe is lower than that at the city situated at the sea level. (d) Temperature A
change in the temperature of a gas changes its density and hence affects the speed of sound through it. If temperature increases, the density of air decreases and hence the speed of sound increases. If temperature decreases the reverse is the effect. 233 (e) Wind Wind “drifts” air through which the sound waves travel. If air blows in the direction of sound, then the speed of sound increases. The speed of wind is added to the speed of sound in air, to get the resultant speed of sound. If wind blows in the opposite direction to that of sound, then the sound travels more slowly. Table 8.1 summarises how the speed of sound in matter is related and their corresponding reasons. Table 8.1 Matter Solid Liquid Gas Exercise 8.2 Speed of sound Reason Fastest Medium Slowest Particles are closely packed Particles loosely packed Particles are very far apart 1. Explain why the speed of sound in solids is faster than the speed of sound in air. 2. Name two factors that affect the speed of sound in air. 3. State the characteristics of sound waves. 4. Explain why at night sound from a source is clear than during hot daytime. 5. Describe two factors that affect the pitch of sound. 6. Define the following terms: (a) Resonance (b) Quality 7. Distinguish between music and noise. 8. Explain the factors that affect the frequency of sound. 9. During thunder and lightening, there are two types of waves produced. (a) Name the two waves. (b) Which one reaches the ground first? Explain. 10. Sound is a longitudinal wave. How is it propagated? Describe an experiment to demonstrate the fact that sound is actually produced by vibrating body. 8.9 Reflection of sound waves Just like light, sound waves undergo reflection on striking plane hard surface as well as curved surfaces. 234 Activity 8.6 (Work in groups) Materials To investigate the laws of reflection of sound waves • Two tubes A and B • Hard drawing board • • Flat piece of metal Stopwatch Steps 1. Set up two tubes A and B, about 1.2 m long and 4 or 5 cm in diameter as shown in Fig. 8.10. Place a flat piece of a large metal or a hard drawing board facing the tubes about 10 cm from their ends. 2. Place a stop watch at the mouth of the tube A and place your ear at the end of the tube B. A soft board S is
placed in between the two tubes to prevent the sound waves from the stopwatch to reach the ear directly. Metal plate reflector A S B Stop watch Ear Fig. 8.10: Reflection of sound waves 3. Adjust the position of tube B until the sound heard is the loudest. 4. Measure angles of incidence i and reflection r. What do you notice? Explain. 5. Are the angles the same? 6. Is the sound heard same as the one from the source? 7. What property do the sound obey from the above observations? These angles are found to be approximately equal. Both the tubes containing the incidence waves and the reflected waves lie in the same plane as the normal to the reflecting surface. We can then conclude that sound waves obey the laws of reflection as is the case with light wave. You should note that since audible sounds have large wavelengths, you need a reasonably large reflector. When sound waves meet a boundary between one medium and another, a part of it is reflected, a part is refracted and the remaining part is absorbed. The relative amounts of these parts are determined by the size and the nature of the boundary under consideration. The proportion of energy reflected is greater in the case of hard substances such as stone and metal. An echo, a reflection of sound, is 235 frequently heard in mountainous regions. There is very little reflection from cloth, wool and foam rubber. Sound which is incident on such soft materials is mainly transmitted through them or absorbed. In places where the effect of echo has to be illuminated, e.g. musical recording room and concert halls, soft materials are used to line the walls of the hall. Also the ear is a sound reflector, reflecting sound waves down the ear cancel to the ear drum. Uses of reflection of sound Sound waves 2. 1. Sound waves can be used to measure the speed of sound in air by reflecting sound at hard surfaces. In public halls and churches, parabolic sound reflection is often placed behind the speaker. It reflects the sound waves back to the audience and thus increasing the loudness of the sound. 3. Sound waves undergo a total internal reflection just like light. Speaking metal tubes that are used to pass message on ships (Fig. 8.11) use total internal reflection of sound waves. Air Fig. 8.11: ‘Speaking’ metal tubes Determining speed of sound by echo method Activity 8.7 (Work in groups) To determine speed of an echo sound 1. Stand about 100 m away from a cliff or
a large hard surface such as the wall of a building and clap your hands. What do you hear? 2. How can you determine the speed of the sound you hear? In Activity 8.7, you will hear two sounds; the one you produce and the reflected sound. The reflected sound produced is called an echo. An echo is a reflection of sound from a large hard surface. 236 Activity 8.8 (Work in groups) Steps To investigate how echo sound is produced 1. Stand about 100 m from an isolated, large hard surface or a stone wall. 2. Shout loudly and start a stopwatch at the same time. Stop the watch on hearing the echo. Find the time interval between the production of the loud noise and hearing the echo. Are you able to time the echo accurately? 3. Repeat this a number of times and find the average time taken. 4. How can you increase the accuracy of this experiment? Note For activities above to be more accurate: 1. A large obstacle, e.g. a cliff or a wall is needed. This is because the wavelength of sound waves is large. 2. A minimum distance between the source and the reflecting surface is required. This minimum distance, called persistence of hearing is about 17 m. In Activity 8.8, you should have noticed that an echo is heard after some time interval. During this time, the sound travels to and from the hard surface covering twice the distance. The speed of sound in air is given by the formula: Speed = Total distance travelled by sound Total time taken Here are typical results from Activity 8.8: Distance from the wall is d, metres. Average time interval between the production of sound and hearing its echo is t seconds. Total distance travelled by sound is 2d metres. Speed of sound = Total distance travelled Total time taken v = 2 × d (m) t(s) ∴ The speed of sound in air is given by v = 2d t 237 Example 8.4 A girl standing 100 m from a tall wall and bangs two pieces of wood once. If it takes 0.606 s for the girl to hear the echo, calculate the speed of sound in air. Solution Speed of sound, v = Total distance Total time taken = 200 0.606 = 2d t = 2 × 100 0.606 = 330 m/s ∴ the speed of sound in air is 330 m/s Example 8.5 A man stands in front of a cliff and makes a loud sound. He hears
the echo after 1.2 s. If the speed of sound in air is 330 m/s, calculate the distance between the man and the cliff. Solution Let the distance between the man and the cliff be x. (Fig. 8.12) x man cliff Fig. 8.12. Speed of sound = 330 m/s = Total distance Total time 2x 1.2 2x = 330 × 1.2 = 396 m ∴ x = 198 m The distance between the man and the cliff is 198 m. 238 Example 8.6 A man standing between two parallel cliffs fires a gun. He hears the first echo after 1.5 s and second echo after 2.5 s. (a) What is the distance between the cliffs? (b) When does he hear the third echo? (Take speed of sound in air to be 336 m/s). Solution (a) The sketch is as shown in Fig. 8.13. cliff A cliff B x2 x2 x1 x1 man Fig. 8.13: A man between parallel cliffs From Cliff A: Speed, v, = Total distance travelled Total time taken v = 2x1 1.5 ⇒ 2x1 = 1.5 × v ∴ 2x1 = 1.5 × 336 x1 = 252 m From cliff B: v = 2x2 2.5 ∴ 2 x2 = 2.5 × 336 = 840 ⇒ 2 x2 = 2.5 × v x2 = 420 m ∴ The distance between the cliffs is 252 m + 420 m = 672 m (b) The first echo (after 1.5 s) reaches cliff B and returns after 2.5 s. So the man hears the 3rd echo after 1.5 + 2.5 = 4 s. Exercise 8.3 1. How is sound propagated? 2. Define the term echo. 3. A person stands infront of a wall and makes a loud sound. She hears the echo after 1.55s. If the speed of sound is 333 m/s. Calculate the distance between the person and the cliff. 239 4. A person standing 80 m from the foot of a cliff claps and hears an echo after 0.9 s. What is the speed of sound in air? 5. A pupil, standing between two cliffs and 500 m from the nearest cliff clapped his hand, and heard the first echo after 3 s and the second echo 2 s later.
Calculate: (a) The speed of sound in air, (b) The distance between the cliffs. 6. An echo of the sound produced by a whistle is heard after 0.50 s. If the speed of sound in air is 332 m/s, find the distance between the whistle and the reflecting surface. 8.10 Sound pollution Sound is a very important form of energy. Human beings and animals use sound as a way of communication. But if sound is unorganised, it becomes noise. Any unwanted sound becomes a nuisance and leads to pollution in form of noise. Therefore, sound pollution is a type of pollution caused by undesirable or unwanted sound. Sound pollution can cause damages to eardrum or hinder communication. Sources of sound pollution are: very high music from discos, concerts, celebrations, factory sirens, traffic noise, aircrafts, alarms and others. Everybody is encouraged to minimize sound pollution at all cost. The government through some agencies must prohibit sound pollution by enacting some laws to govern this. The following are some of the ways used to minimize sound pollution. 1. Factories are encouraged to use sound sirens that are environmental friendly. Most of them use the normal fire alarms. 2. During construction of musical concert halls, the constructor should use materials that absorb most of incident waves of sound to avoid reverberation (reflected multiple sound). 3. Proper laws must be enacted by the government to reduce sound pollution. 4. Proper education of the citizens on sound pollution should be done to sensitize them on the important of reducing sound pollution. Listen to moderate music! Loud music can affect your eardrum if you listen for long. 240 Exercise 8.4 1. Explain what is sound pollution? 2. Sound wave just like light wave undergo reflection. Explain two uses of reflection of sound. 3. Explain two ways in reducing sound pollution. Topic summary • All vibrating bodies produce sound. • • Sound cannot travel through a vacuum. It needs a material medium like solid, liquid or gas. Sound waves are longitudinal in nature consisting of compressions and rarefactions. • Human audible frequency range is between 20 Hz and 20 000 Hz. • • • Speed of sound in air = 332 m/s at 0ºC. Speed of light in vacuum = 3 × 108 m/s. Sound waves undergo reflection. Reflection is the bouncing back of sound wave when it strikes plan hard surface or curved surface. • Echo is the reflection of sound from a large, rigid barrier like cliff,
tall wall etc. • Speed of sound in air can be determined by echo method. • Density of air, humidity, temperature and wind affect the speed of sound. • Pressure, amplitude of wave and loudness of sound do not affect the speed of sound. • Ultrasonic wave is a sound wave that have a fundamental frequency above the human audible range frequencies. • A sound which appears pleasant to the ear is called a musical sound and the one which produces a jarring effect on the ear is called noise. 241 Unit Test 8 1. Sound cannot pass through a A. solid C. air liquid B. D. vacuum 2. A normal human being can hear sound of frequency less than 20 Hz. A. B. between 20 Hz and 20 000 Hz. C. between 20 Hz and 200 Hz. D. above 20 000 Hz. 3. Which of the following is correct? Sound waves A. are transverse in nature. B. are longitudinal in nature. C. can never undergo diffraction. D. can never interfere with each other. 4. The speed of sound is NOT affected by A. pressure C. temperature B. humidity. D. wind. 5. Which statement is true about the music produced by the loudspeaker of a radio? When the music is made louder, A. the amplitude of sound decreases. B. the amplitude of sound increases. C. the speed of sound increases. D. the speed of sound decreases. 6. Suggest a simple experiment to establish each of the following: (a) Sound is produced by a vibrating body. (b) Sound cannot travel through vacuum. 7. State three factors which affect the speed of sound in air. Choose one of the factors and explain how it affects the speed of sound in air. 8. In which gas is the speed of sound greater, hydrogen or oxygen? 9. (a) Describe an experiment to show how echoes are produced. (b) The echo method can be used to determine the speed of sound in air. (i) What measurements would you take in order to do this? (ii) Show how you would calculate the speed of sound in air from your measurements. 242 (iii) State a precaution to be taken to improve your result. 10. A person standing 80 m from the foot of a cliff claps and hears an echo after 0.9 s. What is the speed of sound in air? 11. A student, standing between two cliffs and 500 m from the nearest cliff clapped his hand, and
heard the first echo after 3 s and the second echo 2 s later. Calculate: (a) The speed of sound in air. (b) The distance between the cliffs. 12. A worker uses a hammer to knock a pole into the ground (Fig. 8.14). hammer cliff boy worker girl Fig. 8.14: A worker knocking hammer against the pole (a) A girl at the foot of the cliff hears the sound of the hammer after 2.0 s. Calculate the distance of the worker from the girl (speed of sound in air is 340 m/s) (b) A boy on the other side of the cliff observes that each time the hammer hits the pole, he hears two separate sounds, one after the other. Explain this observation. Given that the first sound is heard by the boy after 1.0 s, determine the: (i) Distance of the boy from the worker. (ii) Time interval between the two sounds. 13. A soldier standing between 2 cliffs fires a gun. She hears the first echo after 2 s and the next after 5 s. (a) What is the distance between the two cliffs? (b) When does she hear the third echo? (speed of sound in air = 336 m/s). (c) Why is the 3rd echo faint than the 2nd one? 14. A student makes observations of a distant thunderstorm and finds the time interval between seeing the lightning flash and hearing the thunder as 4.0 s. Given the speed of sound in air = 340 m/s and speed of light in air = 3.0 × 108 m/s, 243 (a) Explain why there is a time delay? (b) Calculate the distance between the thunder cloud and the student. (c) Explain why the speed of light is not taken into account in this calculation. (d) Calculate the frequency of the flash of light emitted if the mean wavelength of light emitted is 6.0 × 10–7 m. 15. In an athletics competition, the time keeper in a 100 m race starts the stopwatch on hearing the sound from the starter’s pistol and records the time as 10.00 s. Calculate: (a) The actual time taken by the athlete to cover the 100 m race. (b) The average speed of the athletee. (speed of sound in air = 340 m/s). 244 UNIT 6 Heat Transfer Topics in the unit Topic 9: Heat Transfer Learning outcomes Knowledge
and Understanding • Understand the nature of heat • and describe its effects on matter Skills • Design tests to show the factors affecting heat transfer, distinguish between conduction and radiation of heat, and between good and bad conductors of heat. • Observing carefully. • Predict expectations. • Use appropriate measures. • Collect and present results appropriate in writing. Interpret results accurately. • • Report findings appropriately • Explain applications of heat transfer. Attitudes • Appreciate the application of modes of heat transfer. Key inquiry questions • Why is heat important? • How can heat be produced? • Why is that the expansion of material a nuisance? • Why that a rough surface is a better emitter of radiation than a polished surface? • Why that a dull black surface is a better absorber of heat than a polish one? 245 TOPIC 9 Heat Transfer Unit Outline • Heat and temperature • Heat transfer by conduction • Heat transfer by convection • Heat transfer by radiation • Applications of heat transfer • Linear expansion Introduction In our environment, most interactions between systems involve transfer of heat from one system to another. For example, when we bask in the sun, we feel warmer, when we touch a hot sauce pan, we feel the heat. In this unit, we will discuss the different modes of heat transfer through which heat is transferred from one region to another. We will begin by reviewing the difference between heat and temperature. 9.1 Heat and temperature The following activity will enable us to understand the difference between heat and temperature. Activity 9.1 (Work in groups) To investigate the difference between heat and temperature Steps 1. In secondary 1, we learnt about heat and temperature. What is the difference between heat and temperature? 2. With the help of your teacher, recall and conduct an experiment to differentiate between heat and temperature. 3. Record the observation. Draw conclusions and explain your findings in a group and class discussion. 246 Heat is a form of energy that flows from a hot to a cold body while temperature is the degree of hotness or coldness of a substance. 9.2 Methods of heat transfer Activity 9.2 To describe the methods of heat transfer (Work in pairs or in groups) Fig 9.1 below shows a person heating some liquid in saucepan over fire. Fig. 9.1: Heating some liquid in a saucepan 1. Identify the modes of heat transfer marked A, B and C. 2. Discuss how each of the modes of heat transfer takes place, citing the states of matter through which the
processes take place. 3. Describe one application of each type of the above modes of heat transfer in real life. 4. Present your findings to the rest of the class in a class discussion. There are three modes of heat transfer: conduction, convection and radiation. Conduction of heat is through solids, convection in fluids and radiation in gases. 9.2.1 Heat transfer by conduction 9.2.1.1 Demonstration of conduction of heat The following experiment will illustrate conduction of heat in solids. Activity 9.3 (Work in groups) Materials: • A metal spoon • Bunsen burner To design and investigate heat transfer in solids • A beaker full of boiling water • Wax 247 Instructions 1. This activity involves an investigation. You are required to set-up the apparatus as shown in Fig. 9.2 below. Come up with a procedure and execute it to investigate the heat transfer in solids. 2. With the help of your teacher carry out the investigation. Write a report and discuss your findings in a class presentation. 3. How can the investigations be improved? 4. Besides the materials provided which other locally available materials that can be used to carry out the investigation? waxed end metal spoon Fig. 9.2: A spoon inside boiling water 5. Why do you think the free end of the spoon gets hot after sometime? Explain. Solids transfer heat from one point to another. For instance, the free end of the spoon outside the beaker in Fig. 9.2 becomes hot. Heat energy is transferred from the inside to the outside through the metal spoon i.e. from a region of higher temperature to a region of lower temperature. This process of transfer of heat energy in solids is called conduction. Conduction is the transfer of heat from one substance to another that is in direct contact with it. In conduction there is no visible movement of the heated particles. 9.2.1.2 Mechanism of conduction of heat We have already learnt that when temperature increases, the molecules have larger vibrations. This knowledge can help us understand the mechanism of conduction of heat. When the molecules at one end of a solid receive heat energy from the heat supply, they begin to vibrate vigorously. These molecules collide against the neighbouring molecules and agitate them. The agitated molecules, in turn, agitate the molecules in the next layer and so on till the molecules at the other end of the solid are agitated. Thus, the heat is
passed from one point to another till the other end becomes hot. Hence, in conduction, energy transfer takes place by vibration of the molecules. There is no actual movement of the heated particles. 248 To demonstrate that heat energy flows due to a temperature difference Activity 9.4 (Work in groups) Materials: • An iron bar about a metre long • Drawing pins with holes drilled at equal intervals • Wax • Water bath Steps • Stand/clamp • A bunsen burner 1. Fill the holes of the iron bar partially with wax and insert the drawing pins into them. 2. At one end of the bar put a wooden screen and insert it in a water bath. Heat the end points slowly and gradually (Fig. 9.3). Fig. 9.3: The higher the temperature difference the higher the energy transferred 4. After some time, note the temperature readings of the pins. Are the drawing pins falling at the same time? Why do you think that is so? The pin nearest to the bunsen burner registers the highest rise in temperature, and the one farthest away registers the least temperature rise. When one end of the rod was inserted into boiling water, a large temperature difference is set up between the two ends and heat energy flowed from the region of higher temperature to that of lower temperature. Hence heat energy flows due to temperature difference and the pins fall slowly. If the activity is repeated by replacing the hot water bath with a bunsen burner flame (temperature of the bluish part of the flame is about 900˚C), the rise in temperature registered by each pin is higher. Hence the higher the temperature difference, the higher the energy transfer and the pins fall this time faster. Heat energy flows in solids is due to temperature difference. The higher the temperature difference, the higher the energy flow. 249 Piniron barscreen 9.2.1.3 Comparing rates of conduction in metals Activity 9.5 To show that heat transfer in solids depends on the material (Work in groups) Materials • A copper rod • 3 match sticks • A bunsen burner Steps Iron rod • • Wax • Aluminium rod • Tripod stand 1. Take three rods, copper, aluminium and iron of the same length and thickness. Fix a matchstick (or a light metal pin) to one end of each rod using a little melted wax. 2. Place the rods on a tripod stand and heat the free ends with a burner as shown in Fig. 9.4. Observe what happens. copper aluminium match
stick bunsen burner iron Fig. 9.4: Comparing heat transfer through different conductors 3. Which rod falls first? Which one falls last? 4. Why do you think hey did not fall all of them at the same time? The matchstick falls off from the copper rod first then aluminium and finally from the iron rod. When the temperatures of the other ends of the rods reach the melting point of wax, the matchstick falls off. The matchsticks do not fall off at the same time, because the energy transferred is not equal for all the rods. The matchstick from the copper rod is the first one to fall off showing that of the three metals, copper is the best conductor of heat followed by aluminium and then iron. Good conductors and poor conductors of heat A material or substance which has the ability to transfer heat through itself is called a good conductor. Most metals are good conductors of heat e.g copper etc. 250 Substances like water, air, glass, wood, plastic, paper, etc which have a poor ability to transfer heat are called poor conductors of heat. Poor conductors of heat are sometimes refered to as insulators. 9.2.2 Heat transfer by convection 9.2.2.1 Convection in liquids To observe convection current in water Activity 9.6 (Work in groups) Materials • A long straw • A crystal of potassium permanganate • A beaker containing water • A bunsen burner Steps 1. With the help of a long straw, drop a small crystal of potassium permanganate to the right side of the bottom of a flask or a beaker containing water. What do you observe? 2. Heat the flask gently at the right side of the flask (Fig. 9.5). Observe what happens. glass flask potassium permanganate crystals Fig. 9.5: Convection currents in water 3. What do you observe in the beaker when you continously heat the water? Explain your observations. 4. Why do you think the potassium permanganate crystals behave in such manner? 251 Coloured streaks are observed to rise from the bottom to the top. The crystal dissolves and the hot water of less density starts rising displacing the cold dense water down. The streams of physically moving warm liquid are called convection currents. Heat energy is transferred by the convection currents in the liquid. The transfer of heat by this current is called convection. 9.2.2.2 Convection in
gases To investigate convection current in air Activity 9.7 (Work in groups) Materials • A box with a glass window, and two chimneys • A candle • Smouldering pieces of wick Steps 1. Take a box with a glass window and two chimneys fixed at the top. 2. Place a lighted candle under one chimney and hold a smouldering piece of wick above the other chimney as shown in Fig. 9.6. What do you observe? 3. Why do you think the smouldering pieces of wick behave in such manner after heating them? smoke A B smouldering wick box glass window candle Fig. 9.6: Convection currents in air. Smoke from the smoldering wick is seen to move down through chimney B then to the candle flame and finally comes out through chimney A. Air above the candle flame becomes warm and its density decreases. Warm air rises up through chimney A and the cold dense air above chimney B is drawn 252 down this chimney and passes through the box and up the chimney A. The smoke particles from the wick enable us to see path of convection current (Fig. 9.7). Heat is transferred in air through convection currents. This convection current passes energy as shown in Activity 9.8. Activity 9.8 (Work in groups) To illustrate that convection currents possess energy Materials: • A thin circular disk • A card board • A candle flame Steps 1. Take a thin circular disk of tin or cardboard and cut out six blades all round (Fig. 9.7(a)). Pivot the disk on a bent needle (Fig. 9.7(b)). 2. Hold the disk above the candle flame for some time. Observe and explain what happens. disk pivoted disc of tin with blades cut (a) bent needle (b) Fig. 9.7: A rotating disk. 3. What makes the disk to rotate in such manner? 4. What else can be used to rotate the disk? 5. What are some of the uses of convection currents? The disk starts to rotate. The rotation is due to the convection current set up. If a powerful electric bulb is available, you can make a rotating lamp shade. thin cardboard blade thin carboard cylinder cold air lamp stand hot air thick wire wrapped around a bulb with a pointed pivot to power supply Fig. 9.8 : A rotating lamp shade 253 Convection currents possess energy
. It is for this reason that steam is used to rotate the turbine in geothermal electric plants. 9.2.3 Heat transfer by radiation 9.2.3.1 The concept of radiation If you stand in front of a fireplace, you feel your body becoming warm. Heat energy cannot reach you by conduction as air is a poor conductor of heat. How about convection? The hot air molecules in and around the fireplace can only rise and do not reach you by convection. How does the energy from the fireplace then reach you? Heat energy must be transferred by a different mode other than conduction and convection. To demonstrate heat transfer by radiation Activity 9.9 (Work in groups) Materials: • Thin tin lids painted black • Thumb tacks (match sticks) • Wax Part A Steps • A bunsen burner 1. Take a thin tin lid painted black on one side. Stick a thumb tack with melted wax on the other side. 2. Keep the bunsen burner flame close to the painted side (Fig. 9.9). What happens? Explain. 3. Why do you think the thumb tack falls off after sometime. Explain? wax lid painted black Thumb tack wooden stand Fig. 9.9: Radiation 254 Part B Steps 1. Take two thin tin lids, one with shiny inner side and the other with the inner side painted dull black. 2. Stick metal thumb tacks (or match sticks) on the outside of each lid using a little molten wax. 3. Keep a bunsen burner flame midway between the lids as shown in Fig. 9.10. Watch closely to and compare what happens to the two thumb tacks. Explain your observation. tin lids wax thumb tack dull black surface shiny surface supports for lids Fig. 9.10: Good and bad absorbers As discussed in the case of the fireplace, the energy from the flame reaches the tin lid and the wax by a different mode other than conduction and convection. This third mode of heat transfer is called radiation. Radiation is the emission or transmission of energy in the form of a wave or particles through a material or space. Heat transfer from the sun travels through empty space (vacuum) and reaches the Earth. This energy is transferred by radiation. The surfaces of all luminous bodies emit radiation. A human face also emits some mild radiations. While conduction and convection need a medium to be present for them to take place, radiation can take place without a medium. The amount
of heat energy radiated depends upon the temperature of the body. In Activity 9.9, if the bunsen burner is replaced by a candle flame, it will take a longer time for the wax to melt. The temperature of the candle flame is lower than that of a bunsen burner. Heat transfer can take place without contact or in a vacuum. This method of heat transfer is called radiation. 9.2.3.2 Good and bad absorbers of heat energy by radiation If a black and shiny surface receive the same amount of heat energy by radiation, the black surface absorbs more heat than the shiny surface. 255 A dull black surface is a better absorber of heat radiation than a shiny surface. To illustrate good and bad emitters of heat Activity 9.10 (Work in groups) Materials • Three thermometers • Three identical empty cans • Three cardboards Steps 1. Take three identical empty cans of the same volume with their tops removed. Apply clean and dry paints one white and the other black on two cans (both inside and out surfaces) and leave the third can shiny. 2. Prepare three suitable cardboard covers with holes at the centre. Fill the cans to the brim with hot water at 60˚C. 3. Cover the cans with cardboards and place a thermometer in each can through the hole at the centre of the cardboard (Fig. 9.11). cardboard thermometer thermometer thermometer can can can white black shiny Fig. 9.11: Good and bad emitters 4. Record the temperature of water in the cans after a certain time interval. 5. Which can cools the water fastest? 6. Which can takes the longest time to cool the water? Explain the difference in the rate of temperate drop in the three cans. A shiny surface is a good emitter than a dull black surface 256 9.2.4 Applications of heat transfer Activity 9.11 (Work in groups) Materials • Internet Steps To find out the applications of heat transfer • Reference books 1. You have learnt about heat transfer. Referring to this book or any other source, describe three ways in which heat transfer is important in our daily lives. 2. Do a research from the internet and reference books on the applications of heat transfer. 3. In your research, highlight clearly how the modes of heat transfer are applied in vacuum flasks, construction of ventilations, domestic hot water system and solar heating. 4. What other applications of heat transfer did you come across in your research? 5. Explain to your
group members how natural phenomena like sea and land breeze take place. 6. Make a presentation on your findings to the whole class through your group secretary. 1. Vacuum flask The vacuum flask popularly known as thermos flask, was originally designed by Sir James Dewar. It is designed such that heat transfer by conduction, convection and radiation between the contents of the flask and its surroundings is reduced to a minimum. A vacuum flask, Fig. 9.12 is a double-walled glass container with a vacuum in the space between the walls. The vacuum minimises the transfer of heat by conduction and convection. The inside of the glass walls, is silvered so as to reduce heat losses by radiation. The felt pads on the sides and at the bottom support the vessel vertically. The cork lid is a poor conductor of heat. 257 plastic cover cork lid vacuum felt pads vacuum seal double-walled glass container silvered surface outside case Fig. 9.12: Vacuum flask When the hot liquid is stored, the inside shiny surface does not radiate much heat. The little that is radiated across the vacuum is reflected back again to the hot liquid, by the silvering on the outer surface. There is however some heat lost by conduction through the walls and the cork. 2. Windows and ventilators in buildings As shown in Fig. 9.13, warm exhaled air of less density goes out through the ventilator and fresh air of high density enters through the windows at a lower level. This refreshes the air in a room. warm air fresh air warm air Fig. 9.13: Ventilation in building 3. Natural convection currents over the earth’s surface (a) Sea breeze During the day, the temperature of the land rises faster than the temperature of sea water and the air over the land becomes warmer than the air over the sea water. The warm air of less density rises from the land allowing the cold dense air over the sea to blow to the land. This creates a sea breeze in the daytime (Fig. 9.14). 258 warm air from the land Sun cold air from the sea Fig. 9.14 Sea breeze cold sea water (b) Land breeze During the night, the land cools faster than the sea water. Warm air from the sea rises and the dense air from the land moves to the sea. This sets up a land breeze in the sea (Fig. 9.15). cold fresh air from the land warm air above
the sea water rises Fig. 9.15: Land breeze 4. Electrical devices An electric kettles has its heating coil at the bottom. A refrigerator has the freezing unit at the top. 5. Domestic hot water system A domestic hot water supply system works on the principle of convection current. A schematic diagram of a hot water supply is shown in Fig. 9.16. 259 expansion pipe C ball cock main supply of cold water cold water storage tank hot water tap pipe A hot water storage tank boiler pipe B, cold water heat Fig. 9.16: Hot water system Water is heated using fire wood, oil or electricity in the boiler. Hot water from the boiler goes up to the hot water storage tank through pipe A. Cold water flows down from the cold water storage tank into the boiler through pipe B (called return pipe). When the hot water is being drawn from the top of the hot water storage tank, it is replaced by water from the main cold water tank built at the top of the house. The expansion pipe C allows steam and dissolved air to escape. This ensures that the tank does not explode due to the pressure created by the steam produced. 6. Solar heating Flat plate collectors, called solar panels, are used to heat water. They can heat water up to 70˚C. A solar panel consists of thin copper pipes, painted black, which carry the water to be heated. These tubes are fitted in a copper collector plate which in turn is fitted on to a good thermal insulator in a metal frame. A glass plate covers the panel (Fig. 9.17). These panels can be fitted on the roof of houses. Heat radiation from the sun falls on the tubes and on the collector plate through the glass plate. The heat radiations trapped inside the panel by the glass plate heat the water. The hot water is then pumped to a heat exchange coil in a hot water tank which is connected to the domestic hot water system. 260 heat from the sun pipe 1 1 solar panel glass plate pipe 2 metal case 2 insulator thin copper tube pipe 2 pump to domestic hot water system hot water water gains energy in the exchanger cold water heat exchange coil pipe 1 cold water insulated cold water tank Fig. 9.17: Solar heating 7. Solar concentrations In some heating devices, instead of a flat plate collector, curved mirrors (concave or parabolic) are used to concentrate the heat radiations from the sun to a small area at their focus. If the boiler is placed at the point of focus,
very high temperatures can be reached. Exercise 9.1 1. Distinguish between heat and temperature. 2. What are the different modes of heat transfer? Explain clearly their difference using suitable examples. 3. State three factors which affect heat transfer in metals. Explain how one of the factors you have chosen affects heat transfer. 4. Describe an experiment to show that water is a poor conductor of heat. 5. Use particle behaviour of matter to explain conduction. 6. Describe a simple experiment to demonstrate that the heat radiated from a hot body depends upon the temperature of the body. 7. With a suitable diagram, explain the working of a vacuum flask. 9.3 Thermal expansion In general, nearly all substances increase in size when heated. The process in which heat energy is used to increase the size of matter is called thermal expansion. The increase in size on heating of a substance is called expansion. On cooling, substances decrease in size. The decrease in size on cooling of a substance is called contraction. Why is this so? 261 9.3.1 Thermal expansion and contraction in solids When a solid (e.g. a metal) is subjected to heat, it: (a) Increases in length (Linear Expansion). (b) Increases in volume (Volume Expansion). (c) Increases in area (Surface Expansion). 9.3.1.1 Linear expansion (a) Demonstrations of linear expansion Activity 9.12 (Work in groups) To demonstrate expansion and contraction using the bar and gauge apparatus Materials • A bar and gauge apparatus Steps • Bunsen burner 1. Move the metal bar in and out of the gauge at room temperature (Fig. 9.18). Observe what happens. wooden handle gauge metal bar Fig. 9.18: Bar and gauge apparatus 2. Keep the metal bar away from the gauge and heat the bar for sometime. 3. Try to fit the bar into the gauge. Does it fit or not? Explain your observation. 4. Allow the bar to cool and try to fit it into the gauge. Does the bar now fit into the gauge? Explain. A bar and gauge apparatus consists of a metal bar with a suitable wooden handle and a gauge. When both the metal bar and the gauge are at room temperature, the bar just fits into the gauge. On heating, the metal bar expands. There is an increase in length. It hence expands linearly and therefore, the bar cannot fit into the gauge. 262 On cooling the bar easily fits into the gauge
due to contraction. Solids expand i.e increase in length on heating and contract i.e reduced in length on cooling. Activity 9.13 (Work in groups) To demonstrate the bending effect of expansion and contraction Materials: • A bimetallic strip Steps • Bunsen burner 1. Observe a bimetallic strip at a room temperature (Fig. 9.19). wooden handle brass iron Fig. 9.19: A bimetallic strip 2. Take the bimetallic strip with the brass strip at the top and heat it with a bunsen burner flame for sometime. Observe what happens. Explain the observation. Sketch the shape of the bimetallic strip after heating. 3. Remove the flame and allow the bar to cool to a room temperature. What happens to the bimetallic strip? Sketch its shape after cooling. 4. Discuss with your friend what will happen if the bar is cooled below room temperature. Sketch the strip at that temperature. When the bimetallic strip is heated, it bends downwards with the brass strip on the outer surface of the curvature, as shown in Figure 9.20(a). Why does this happen? When the flame is remove and the bar left to cool to room temperature, the bar returns back to its initial state (straight) as shown in Figure 9.19 above. If the bar is cooled below room temperature, it bends upwards with the iron strip underneath as shown in Figure 9.20 (b). What has happened? brass Bunsen burner iron brass iron (a) Heating the bimetallic strip (b) Cooling the bimetallic strip below room temperature Fig. 9.20: Bending effect of expansion and contraction 263 As the bimetallic strip is heated, brass expands more than iron. The large force developed between the molecules of brass forces the iron strip to bend downwards. On cooling below a room temperature, the brass contracts more than iron and the iron strip is forced to bend upwards. The force developed during expansion or contraction causes a bending of the metals. (b) Comparison of rates of expansion of different solids As we know from the kinetic theory of matter, the different states of matter expands when heated but at different rates. The following activity shows that different solids have different rates of expansion. Activity 9.14 To compare rates of expansion and contraction of different solids (Work in groups) Materials: • Thin metal rods of different metals • Source of heat • Rollers connected to a pointer • G - clamp Steps 1.
Clamp one end of a long thin metal rod tightly to a firm support, with the end of the rod resting on a roller fitted with a thin pointer (See Fig. 9.21). clamp pointer fixed to roller thin copper rod deflection of the pointer roller table heat Fig. 9.21: Expansion and contraction of thin metal rods. 2. Heat the metal rod for sometime. Observe and explain what happens to the rod. 3. Remove the burner and allow the rod to cool. What happens to the rod again after cooling. Does it reduce in size? Explain why. 4. Repeat the activity with thin rods of different materials. Observe and explain what happens, accounting for any differences. The pointer deflects in the clockwise direction on heating and in the anticlockwise direction on cooling. 264 The pointer deflects to different extents depending on the material. On heating, there is an increase in length (linear expansion) of the rods. The expanding rod moves the roller to the right making the pointer attached to the roller to deflects in a clockwise direction. On cooling, the rod contracts and decreases in length. The contracting rod moves the roller to the left hence the pointer deflects in the opposite direction (anticlockwise direction). When a different material e.g lead is used, the pointer deflects more to the right (clockwise). When cooled, the pointer deflects more to the left (anticlockwise). Different solids (e.g metals) expand and contract to different extents when heated by the same quality of heat. (c) Coefficient of linear expansion Consider a thin metal of length l0 in Fig. 9.22. l0 Δl Fig. 9.22: A thin rod showing increase in length. When the rod is heated, a temperature change of Δθ occurs and its length increases by Δl. The ratio of increase or decrease in length to original length ( Δl proportional to the change in temperature Δθ. l0 ) is directly Δl l0 ∝ Δθ ⇒ Δl l0 = α Δθ and α = Δl lθ Δθ where α is a constant called the coefficient of linear expansion. It is the value of the increase in length per unit rise in temperature for a given material. The SI units of α is K–1 Suppose: The temperature change = Δθ, l0 represents the original length of the rod l represents the new length for a temperature rise of �
� Then, Δl = l – l0 The above expression may be expressed in terms of l0, lθ, θ and α as follows. α = Δl l Δθ = l – l0 l Δθ Re-arranging l – l = l0 αΔθ l = l0 + l0 αΔθ l = l0(1 + αΔθ) 265 Example 9.1 A copper rod of length 2 m, has its temperature changed from 15 °C to 25 °C. Find the change in length given that its coefficient of linear expansion α = 1.7 × 10–6 K–1. Solution Δθ = (25 - 15) oC = 10 oC Δl = l0 = 3.4 × 10–5 m α Δθ = 2 × 1.7 × 10–6 × 10 = 0.000034 mm 9.3.1.2 Area and volume expansion (a) Demonstrations of area and volume expansions Activity 9.15 (Work in groups) Materials: To demonstrate volume and surface expansion and contraction using the ball and ring apparatus • A ball and a ring • Bunsen burner • A bowl of cold water Steps 1. Move the ball in and out of the metal ring at room temperature (see Fig. 9.23). What do you observe? 2. Keep the metal ball away from the ring and heat it for sometime. 3. Try to pass the ball through the ring. Does the ball pass through the ring this time? Why?. 4. Cool the metal ball in a bowl of cold water and try to pass the ball through the ring again. Does it pass through the ring? Explain why. metal ball metal ring Fig. 9.23: Ball and ring apparatus 266 A ball and ring apparatus consists of a ball and ring both made of the same metal. At a room temperature, the ball and the metal ring have approximately the same diameter, thus the ball just passes through the ring. On heating, the metal ball expands. There is an increase in volume and surface area of the ball. As a result, the ball cannot pass through the ring. On cooling, contraction occurs and the original volume is regained. The ball can now pass through the ring again. This activity shows volume and surface area expansion and contraction in solids. Most solids expand on heating and contract on cooling. Why solids expand on heating? In Secondary I, we learnt that
molecules of a solid are closely packed and are continuously vibrating about their fixed positions. When a solid is heated, the molecules vibrate with larger amplitude about the fixed position. This makes them to collide with each other with larger forces which pushes them far apart. The distance between the molecules increases and so the solid expands. The reverse happens during cooling. (b) Coefficients of area expansion of solids Consider a solid whose surface area is A0. When the surface of the solid is heated or cooled to a temperature change of Δθ, its surface area increases or decreases by ΔA to a new value A. Experiments have proved that the ratio of the change in surface area to original area i.e ΔA is directly proportional to the change in temperature (Δθ). A0 ∝ Δθ ⇒ ΔA ΔA A0 A0 Hence β = = βΔθ (β is a constant called coefficient of area expansivity) A – A0 A Δθ ⇒ A –A0 = AθβΔθ ΔA A0Δθ Or β = (since ΔA = A – A0) A = A0 – A0βΔθ ∴ A = A0(1 - βΔθ) Note: Coefficient of area expansivity = 2 × coefficient of linear expansivity β = 2α Example 9.2 A round hole of diameter 4.000 cm at 0 °C is cut in a sheet of brass (coefficient of linear expansion is 19 × 10-6k-1(Co)-1. Find the new diameter of the hole at 40 °C. 267 Solution (θ 2 ) θ 2 - ΔA = βA0 Given: α = 19 × 10-6k-1, (θ2 – θ1) = 40°C, D = 4.000 cm so r = 2.000 cm, β = 2 α then Area (A0) = πr2 = 22 7 × 2.000 × 2.000 cm2 = 12.971 cm2 New area A = A0 + ΔA = (12.971 + 0.0197) cm2 = 12.991 cm2 = 12.987 Since A = πr2, the new radius r = A 3.141 π = 2.033 cm (c) Coefficients of volume expansion in solids When a solid is
heated or cooled to a temperature change of Δθ, its volume increases or decreases by ΔV to a new value V. The ratio of the change in volume to original volume i.e ΔV V0 to the change in temperature (Δθ). is directly proportional α Δθ ⇒ ΔV V0 ΔV V0 Hence ϒ = = ϒΔθ (ϒ is a constant called coefficient of volume expansivity) ΔV V0Δθ Or ϒ = V – V0 V Δθ (since ΔV =V – V0) ⇒ V –V0 = VθϒΔθ V =V0 – V0ϒΔθ ∴ V = V0(1 - ϒΔθ) Note: Coefficient of volume expansivity = 3 × coefficient of linear expansivity ϒ = 3α Example 9.3 A metal vessel has a volume of 800.00 cm3 at 0 °C. If its coefficient of linear expansion is 0.000014/K, what is its volume at 60 °C? Solution Given: V0 = 800.00 cm3, (θ2 – θ1) = 60 °C and α = 0.000014/K = 0.000014/ °C 268 Change in volume, (ΔV) = 3 α V0Δθ = 3(0.000014/°C) × 800.00 cm3 × 60°C = 2.016 cm3 New volume (at 60°C) = V0 + ΔV = (800.00 + 2.016) cm3 = 802.016 cm3 Exercise 9.2 1. What do you understand by the phrase 'coeficient of linear expansion'? 2. A vertical steel antenna tower is 400 m high. Calculate the change in height of the tower hence its new height that takes place when the temperature changes from –19 °C on winter day to 39 °C on a summer day. (Take α = 0.00000649/K 3. A 8 m long rod is heated to 90 °C. If the rod expands to 10 m after some time, calculate its coefficient of linear expansion given that the room temperature is 32 °C. 4. A rectangular solid of Brass has a coefficient of volume expansion of 96 × 10-6 /°C. The dimensions of the rectangle are 9 cm × 6
cm × 8 cm at 10 °C. What is the change in volume and the new volume if the temperature increases to 90 °C? 5. A solid plate of lead of linear expansion 29 × 10-6 /°C is 8 cm × 12 cm at 19 °C. What is the change in area and the new area of the lead if the temperature increases to 99 °C? 9.3.2 Thermal expansion and contraction in liquids Like solids, liquids expand on heating i.e volume increases and contract i.e Volume reduces on cooling. But liquids expand more than solids since they have relatively weak intermolecular forces. Activity 9.17 will help us to understand expansion and contraction in liquids. 269 Activity 9.16 To demonstrate expansion and contraction in liquids (Work in pairsor in groups) Materials: • A glass flask • A rubber stopper • Long glass tubing Steps • Coloured water • Bunsen burner • Tripod stand • Wire guaze 1. Fill a glass flask with coloured water. 2. Fit the flask with a rubber stopper carrying a long narrow glass tubing. 3. Note the initial level of water in the glass tube before heating (Fig. 9.24). thin tube C A B glass flask coloured water wire gauze heat Fig. 9.24: Expansion of liquid 4. Heat the water in the flask. What happens to the level of water at A immediately the heating starts and after a few minutes? Explain your observation. In a similar activity, it was observed that at first the level of the coloured water in the tube drops to level B and then rises to level C. On heating, the glass flask is heated first and expands i.e its volume increases. The level of water immediately drops from A to B. On continuous heating, water starts to expand hence water level rises up the tube from B to C. If the setup is allowed to cool below room temperature, the water level drops to a point lower than A and B. This shows that liquids expand on heating and contract on cooling. Why liquids expand on heating? Molecules are loosely packed in liquids. The force of attraction between the molecules is weaker than in solids. The molecules move freely in the liquid. On 270 heating, the speed of the molecules increases. The collisions between the molecules increases the distance between them causing the liquid to expand. 9.3.3 Thermal expansion and contraction in gases Just like solids and liquids, gases expand on heating and contact on cooling. Gases expand more than
liquids and solid because their molecules move furthest on heating. The following activity will help us to study expansion and contraction in gasses. Activity 9.17 To demonstrate expansion of gases (Work in pairs or in groups) Materials: • A thin glass flask • A long narrow glass tube Steps • A rubber stopper 1. Take a thin glass flask with an open top. 2. Close the flask with a rubber stopper carrying a long narrow glass tube. 3. Invert the flask so that the glass tube dips into water in a container. What do you observe? (Fig. 9.25). 4. Place your hands over the flask to warm it for sometime. What happens in water. Explain your observation. 5. Remove your hands from the flask and wait for some time. What happens to the level of water in the tube of the flask. Explain your observation. When the flask is warmed by the warmth of the hands, the level of water in the tube drops and some bubbles are formed due to air escaping from the flask through the tube. 271 Fig. 9.25: Expansion of airairthin glass flaskcontainertubecoloured waterbubble On removing the hands from the flask, water level rises up the glass tube again due to contraction of air i.e volume of air reduces on cooling.This shows that gases expand on heating and contract on cooling.. The volume of air increases in the flask due to expansion. Why a gas expands on heating? The force of attraction between the molecules of a gas is very small (almost negligible) and the distance between the molecules is large compared to solids and liquids. The molecules move freely in all directions. When a gas is warmed, the molecules gain more energy and move far apart hence volume increases. Different gases expand by the same amount when heated equally. Gases contract on cooling and expand on heating. 9.3.4 Applications of thermal expansion and contraction Activity 9.18 To find out the applications of expansion and contraction (Work in pairs or in groups) Materials • Internet enabled devices (lab computers or tablets) • Reference books Steps 1. You have now learnt about expansion and contraction. Suggest any three applications of expansion and contraction in our daily lives. 2. Carry out a research from the internet on the applications of expansion and contraction. 3. Report your findings to the whole class. Thermal expansion and contraction, on one hand is a nuisance and on the other hand is quite useful. The following are some of the applications of thermal expansion and contraction. 1
. Electric thermostats A thermostat is a device made from a bimetallic strip that is used to maintain a steady temperature in electrical appliances such as electric iron boxes, refrigerators, electric geysers, incubators, fire alarms and the automatic flashing unit for indicator lamps of motor cars. Fig. 9.26 show two such devices. 272 cell iron D C A brass bell iron B A brass resistance wire (a) Fire alarm (b) Electric iron box Fig. 9.26: Electric appliances with thermostat The bimeltalic, as discussed earlier, bends on expansion and relaxes on cooling, connectin and disconnecting the circuit to regulate temperature. Be responsible and take care! Conserve energy by switching off the socket after using electrical appliances. Be careful when using electrical devices to avoid electric shocks. 2. Ordinary and pyrex glasses You may have observed that when boiling water is poured into a thick-walled glass tumbler it may break suddenly. This is because the inside of glass gets heated and expands even before the outside layer becomes warm. This causes an unequal expansion between the inside and the outside surfaces. The force produced by the expanding molecules on the inside produces a large strain in the glass and the tumbler breaks. This is the reason why pyrex glass tumblers are recommended for use while taking hot liquids. 3. Rivets In industries, steel plates are joined together by means of rivets. Hot rivets are placed in the rivet holes and the ends hammered flat. On cooling the force of contraction pulls the plates firmly together (Fig. 9.27). rivet rivet holes steel plates hot rivet rivet hammered flat Fig. 9.27: Rivets 273 4. Expansion of joint loops Metal pipes carrying steam and hot water are fitted with expansion joint or loops. These allow the pipes to expand or contract easily when steam or hot water passes through them or when the pipes cool down. The shape of the loop changes slightly allowing necessary movement of the pipes to take place (Fig. 9.28). Expansion Expansion Fig. 9.28: Expansion joint 5. Loosely fitted electric cables Telephone and electricity cables are loosely fitted between the poles to allow room for contraction in cold weather and expansion in hot weather. 6. Use of alloys The measuring tape used by surveyors for measuring land is made of an alloy of iron and nickel called invar. Invar has a very small change in length when temperature changes. 7. Gaps
in railway tracks Gaps are left between the rails when the railway tracks are laid. The rails are joined together by fish-plates bolted to the rails. The oval shaped bolt holes allow the expansion and contraction of the rails when the temperature changes (Fig. 9.29). rail rail gap Bolts Oval shaped bolts holes fish plate rigid supports Fig. 9.29: Gaps left between rails In very hot weather, the gaps may not be enough if the expansion is large. The rails may buckle out. Modern methods use long welded lines rigidly fixed to the beds of the track so that the rails cannot expand. Expansion for the rails is provided by overlapping the plane ends (Fig. 9.30). 274 Fig. 9.30: Overlapping joints 8. Rollers on bridges The ends of steel and concrete bridges are supported on rollers. During hot or cold weather, the change in length may take place freely without damaging the structure (See Fig. 9.31). steel bridge fixed point wall rollers Fig. 9.31: Steel and concrete bridges are supported on rollers To demonstrate causes of expansion and contraction • Water 9. Breakages Activity 9.19 (Work in pairs) Materials: • A beaker • An immersion heater • A measuring cylinder • A thermometer • Stop watch 275 Steps the final temperature θ 1. Take 200 g of water in a beaker and note its initial temperature θ 2. Heat the water with an immersion heater for 10 minutes (Fig. 9.32 (a)). Note 1. 3. Repeat (2) above by taking 400 g of water in the same beaker and same initial 1 (Fig. 9.32 (b)). Note the time taken to produce the same 2 and calculate the change in temperature, Δθ = θ temperature θ change in temperature as before. Is it more or less? 2 – θ 1. 4. Compare the time taken to produce the same change in temperature in 200g and 400g of water. What is your conclusion? (a) (b) Beaker Thermometer Heating element 200 g of water Heating element Fig. 9.32: Relationship between heat energy and mass of the substance Beaker Thermometer 400 g of water Sudden expansion and contraction can lead to breakages of things like glasses and egg shells. This behaviour is mitigated against in the manufacture of glass items such as the drinking glass. They are made of thin walls to allow even expansion and contraction thus minimising chances
of breakage. Exercise 9.3 1. Use particles model to explain thermal expansion of solids. 2. Explain why: (a) Steel bridges are usually supported by rollers on one loose side. (b) Metal pipes carrying steam and hot water are fitted with loops. 3. Describe how shrink fitting is done. 4. State two applications of contraction of solids. 5. Name three physical properties that change when heating a solid. 276 Topic summary • Heat is a form of energy which is transferred from a region of higher temperature to a region of lower temperature. • The SI unit of heat energy is Joule (J). • Two substances of equal masses can be at the same temperature but contain different amounts of heat energy and vice-versa. • Heat energy can be transferred by three different modes: conduction, convection or radiation. • Solids are heated by conduction and fluids by convection. Radiation can take place through vacuum. • We get heat energy from the sun by radiation. Topic Test 9 For questions 1 – 9, select the correct answer from the choices given. 1. Radiation in a thermos flask is minimized by A. Cork C. Felt pad 2. A dull black surface is a good (i) Absorber of heat energy (ii) Emitter of heat energy (iii) Reflector of heat energy B. Vacuum D. Silvered glass water (i) only (ii) and (iii) only B. (i) and (ii) only D. (i), (ii) and (iii) A. C. 3. Radiation is the transfer of heat _______ A. B. C. D. 4. The mode of transfer of heat between the boiler and the storage tank of a hot in a liquid which involves the movement of the molecules. from one place to another by means of electromagnetic waves. through a material medium without the bulk movement of the medium. through a fluid which involves the bulk movement of the fluid itself. water supply system is A. radiation C. convention B. conduction D. evaporation 277 5. The transfer of heat by the actual movement of molecules of matter takes place B. only in gases D. A. only in liquid C. in solids and liquid 6. Match each heat transfer mechanisms to its description Conduction Evaporation Radiation Convection Electromagnetic waves. Transfer of vibrational energy from particle to particle. Escaping of particles from the surface of a liquid.
Movement of particles due to changes in density. in liquids and gases 7. Explain the following statements: (a) A metallic seat seems to be hotter during the day and colder during the night than a wooden seat under the same conditions. (b) The bottom of cooking vessels are usually blackened. (c) It is safer to hold the other end of a burning match stick. 8. In a experiment requiring storage of heat energy, water is preferred to other liquids. Give two reasons for this. 9. A cup made of pyrex glass has a volume of 200 cm3 at 0 °C. If the coefficient of linear expansion is 0.000003/K, what will be its volume if it holds hot water at 92 °C? 278 UNIT 7 Magnetism Topics in the unit Topic 10: Magnetism Learning outcomes Knowledge and Understanding • Understand the theory of magnetism and explain the properties of magnets. Skills • Design investigations to determine the polarities of magnets, methods of magnetization and demagnetization, and how to distinguish between magnets and non-magnets. • Carry out accurate observation. • Recording results accurately in appropriate way. • Analysis of results in groups. • Explain analysis and consider applications. Attitudes • Appreciate the properties of magnets in construction of simple compass. Key inquiry questions • Why a compass needle does always points to the north? • Why that some magnets are classified as strong? • Why that a point is identified as neutral in magnetic field lines? • Why would you shield a small compass needle from earth’s magnetic field? • Why do we use soft iron keeper? 279 TOPIC 10 Magnetism Unit Outline • Definition of a magnet • Magnetic and non-magnetic materials • The poles of bar magnet • Test for magnetism • Types of magnets Introduction The people of Magnesia in Asia Minor observed that certain kinds of naturally occurring iron ores possessed an iron-attracting property. The ore was discovered near the city of Magnesia and hence it was named as Magnetite. Huge lumps of magnetite were often called lodestone meaning “ leading” stone or natural magnet. Chemically lodestone consists of iron oxide. Dr. William Gilbert (1540-1603) did a lot of work with the natural magnets. He published a book called De magnete in 1600 in which he gave an account of his research into the magnets and their properties. In one of his work he concluded that the earth was itself magnetic and that is why compasses point
to the north of the earth. 10.1 Definition of a magnet Activity 10.1 To identify magnets (Work in groups) Materials: Cooking stick, steel nail, a bar magnet, a spanner, a cork Steps 1. Identify a magnet from the materials provided (see Fig. 10.1). Suggest a reason why you think the material you have identified is a magnet. 280 (a) `(b) (c) (d) (e) Fig. 10.1: Magnetic and non-magnetic materials 2. Discuss in your group what a magnet is. From Activity 10.1, you observed that Fig. 10.1 (d) is a magnet. A magnet is a piece of metal with either natural or induced properties of attracting another metal objects e.g. steel. The common type of a magnet used in school laboratory is a bar magnet (Fig. 10.1 (d)). We shall learn about types of magnets later. 10.2 Magnetic and non-magnetic materials Materials may be classified according to their magnetic properties. There are those that are attracted by magnets and others that are not. Identifying magnetic and non-magnetic substances Activity 10.2 To identify magnetic and non-magnetic substances (Work in groups) Materials: Iron and steel nails, bar magnet, copper metal, cobalt, wood, zinc, glass rods 281 Steps 1. Place some iron nails on the table. Bring a bar magnet close to the iron nails and observe what happens. Explain your observations. 2. Repeat the activity with other material such as copper, cobalt, steel, sulphur, brass, wood, cork, nickel, plastic, pens, wax, zinc, glass rods, carbon, aluminium, paper, chalk etc. 3. Record your observations in tabular form as shown in Table 10.1. Table 10.1: Magnetic and non-magnetic materials Substances attracted by a bar magnet Substances not attracted by a bar magnet 1. 2. 3. 4. 1. 2. 3. 4. 4. Discuss your observations in step 3 in your group and suggest the name given to substances that are attracted by a magnet and those that are not. The results from Table 10.1 shows that some materials are attracted by the bar magnet while others are not. The materials which are attracted by a magnet are called magnetic materials while those which are not attracted are called non-magnetic materials. The magnetic materials that are strongly attracted by a magnet are called ferrom
agnetic materials. These include nickel, iron, cobalt and steel. Materials that are not attracted by a magnet are called non-magnetic materials. Examples of non-magnetic materials include copper, brass, aluminium, wood, cork, plastic etc. When metals are mixed together, they form alloys. Some alloys are ferromagnetic materials. An example is Al-ni-co which composed of aluminium (Al), nickel (Ni) and cobalt (Co) hence the name Al-ni-co. Another example of alloys which are those composed of nickel, iron, copper, chromium or titanium; they are also ferromagnetic. 282 10.3 Properties of magnets (a) Polarity property of magnets Activity 10.3 (Work in groups) To identify the poles of a magnet Materials: A bar magnet, iron filings in a container, a paper Steps 1. Lay a bar magnet on a bench and cover it with a piece of paper. 2. Sprinkle the iron filings over the paper. What happens to the iron filings? Explain your observations. 3. Which parts have attracted more iron filings? 4. Suggest the name given to the ends of a magnet. From Activity 10.3, you must have noted that the iron filings were attracted by a bar magnet. Most iron filings remained clustered around the ends of the magnet as shown in Fig. 10.2. Bar magnet Iron filings Iron filings Fig. 10.2: Distribution of iron filings around a bar magnet. The ends of a magnet where the attraction is strongest are known as the magnetic poles. Magnetic poles are the places in a magnet where the total attractive force seems to be concentrated. A straight line drawn passing through these ends is called the magnetic axis of the magnet (see Fig. 10.3). Magnetic pole Fig. 10.3: Magnetic poles and magnetic axis of a bar magnet. A bar magnet has the strongest attraction at the poles. Magnetic pole 283 (b) Directional property of a magnet Activity 10.4 (Work in groups) To observe the directional property of a magnet Materials: A bar magnet, 1 metre long thread Steps 1. Suspend a bar magnet freely at its centre by a length of a cotton thread from a support (Fig. 10.4 (a)). Make sure there are no steel or iron objects near the magnet. N S (a) Magnetic meridian Fig. 10.4: A freely suspended magnet i n e l N - S 2. Displace the magnet slightly so that it
swings in a horizontal plane. 3. Note the direction in which the magnet finally comes to rest. Suggest a reason why it rests in that direction. 4. Repeat the activity at different places and note the resting direction of the magnet. What do you observe about the resting direction of the magnet? Explain the direction of the magnet when it rests. In Activity 10.4, you observed that the bar magnet swings to and fro and finally rests in a north-south (N-S) direction of the earth. The magnet comes to rest with its axis in a vertical plane called the magnetic meridian (Fig. 10.4 (b)) i.e. a bar magnet rests in a north-south direction. The pole that points towards the north pole of the earth is called the north seeking pole or simply the north pole (N). The other pole is called the south seeking pole or south pole (S). 284 Identifying the poles of a magnet by colour Activity 10.5 (Work in groups) To identify the poles of a magnet by colour Materials: A bar magnet, 1 metre long thread Instructions 1. In this activity you will conduct an investigation to identify the poles of a magnet. 2. Write a brief procedure of the investigation. Execute the procedure and conduct the investigation. After the activity answer the following questions. 3. Compare the direction shown by the compass and that of the suspended bar magnet. 4. Note the pole of the suspended bar magnet that is pointing in the same direction as north pole or south pole of the magnetic compass. Deduce the poles of the magnet. 5. Write a report on poles of magnets and present it in a class discussion. From Activity 10.5, you noted that the pole that points in the direction of the north of the compass is the north pole and the other pole is the south pole. In order to easily identify the poles of a magnet, the ends are usually painted in different colours. For example, the N-pole is painted red while the S-pole is painted blue or white Fig 10.5 (a). In other cases the whole bar is painted blue with a red dot or spot on one end to identify the north pole. (See Fig. 10.5 (b)). Red (North pole) (a) Blue (South pole) Red (North pole) (b) Fig. 10.5: Colours used to identify poles of a bar magnet Blue (South pole) Hey!! Do you know that the red colour in our national flag symbol
ises the blood that was shed for the independence of our country. Let us always live happily with one another and keep peace in our beautiful country. 10.4 Test for magnetism Basic law of magnetism Activity 10.6 (Work in groups) To establish the basic law of magnetism Materials: Two bar magnets, cotton thread. 285 Steps 1. Suspend a bar magnet using a light cotton thread with its north and south pole clearly marked. 2. Bring a S-pole of a second bar magnet slowly towards the S-pole of the suspended magnet (Fig. 10.6(a)). What happens to the magnets. 3. Repeat the activity using the S-pole of the suspended magnet and the N-pole of the second magnet (Fig. 10.6 (b)). What happened to the magnets? N repulsion S S N attraction N S N S (a) (b) Fig. 10.6: Action of magnets on each other. 4. Repeat using the other poles and record your observation in a tabular form as shown in table 10.2. Poles of suspended magnet Pole of second magnet Observation South South North North South North South North _______________ _______________ _______________ _______________ 5. Why does some poles attract whereas others repel each other? Table 10.2: Test for magnetism From Activity 10.6, you must have discovered that a north pole attracts a south pole, a north pole repels a north pole and a south pole repels a south pole. Therefore, unlike poles attract each other while like poles repel each other. This is called the basic law of magnetism. In the previouus class, we learnt about charges. Like charges repel whereas unlike charges attract. The same concept is applied in the basic law of magnetism. Like poles repel whereas unlike poles attract. 286 Testing the polarity of magnets using the basic law of magnetism Activity 10.7 To test for polarity of magnets using the basic law of magnetism (Work in groups) Materials: A nail, two bar magnets, a cotton thread Steps 1. Freely suspend a bar magnet as shown in Fig. 10.7. 2. Bring one pole of the magnet close to a nail placed on a table. What happens to the nail?. cotton thread nail S N Fig. 10.7: Testing the polarity of a magnet. 3. Repeat with the other pole close to the nail and record your observations. 4. Repeat steps 2 and 3

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