Secondary Physics 1 Student Textbook.pdf

South Sudan South Sudan 1 Secondary...

South Sudan South Sudan 1 Secondary 1 Secondary Physics Student’s Book Physics Secondary Physics has been written and developed by Ministry of General Education and Instruction, Government of South Sudan in conjunction with Subjects Student’s Book Secondary Physics experts. This course book provides a fun and practical approach to the subject of Physics, and at the same time imparting life long skills to the students. The book comprehensively covers the Secondary 1 syllabus as developed by Ministry of General Education and Instruction. Each year comprises of a Student’s Book and teacher’s Guide. The Student’s Books provide: Full coverage of the national syllabus. A strong grounding in the basics of Physics. Student's Book 1 Clear presentation and explanation of learning points. A wide variety of practice exercises, often showing how Physics can be applied to real-life situations. It provides opportunities for collaboration through group work activities. Stimulating illustrations. All the courses in this secondary series were developed by the Ministry of General Education and Instruction, Republic of South Sudan. The books have been designed to meet the secondary school syllabus, and at the same time equiping the students with skills to fit in the modern day global society. This Book is the Property of the Ministry of General Funded by: Published by: Funded by: Education and Instruction. This Book is the Property of the This Book is not for sale. Ministry of General Education Any book found on sale, either in print or electronic and Instruction. form, will be confiscated and the seller prosecuted. This Book is not for sale.  How to take care of your books. Do’s 1. Please cover with plastic or paper. (old newspaper or magazines) 2. Please make sure you have clean hands before you use your book. 3. Always use a book marker do not fold the pages. 4. If the book is damaged please repair it as quickly as possible. 5. Be careful who you lend your schoolbook to. 6. Please keep the book in a dry place. 7. When you lose your book please report it immediately to your teacher. Don’ts 1. Do not write on the book cover or inside pages. 2. Do not cut pictures out of the book. 3. Do not tear pages out of the book. 4. Do not leave the book open and face down. 5. Do not use pens, pencils or something thick as a book mark. 6. Do not force your book into your schoolbag when it is full. 7. Do not use your book as an umbrella for the sun or rain. 8. Do not use your book as a seat.  SECONDARY South Sudan 1 Physics Student’s Book 1 This book is the property of the Ministry of Funded by: General Education and Instruction. THIS BOOK IS NOT FOR SALE Published in 2018 by: Longhorn Publishers (K) Ltd., Funzi Road, Industrial Area, P.O. Box 18033 – 00500, Nairobi, Kenya. ©2018, THE REPUBLIC OF SOUTH SUDAN, MINISTRY OF GENERAL EDUCATION AND INSTRUCTION. All rights reserved. No part of this book may be reproduced by any means graphic, electronic, mechanical, photocopying, taping, storage and retrieval system without prior written permission of the Copyright Holder. Pictures, illustrations and links to third party websites are provided in good faith, for information and education purposes only.  Contents States of matter................................................................... 1 1.1 Matter and its composition....................................................... 2 1.2 Introduction to kinetic theory................................................... 4 1.3 Physical properties of matter..................................................... 6 1.4 Movement of particles in matter................................................ 13 1.5 Application of cohesive and adhesive forces between molecules.. 18 1.6 Surface tension......................................................................... 22 Topic summary and new words...................................... 28 Topic Test 1................................................................. 28 Types of forces and their measurement................................... 29 2.1 Definition of force.................................................................... 30 2.2 Effects of forces........................................................................ 32 2.3 Measurement of force.............................................................. 35 2.4 Representation of forces using vector diagrams.......................... 37 2.5 Combination of forces............................................................ 38 2.6 Types of forces......................................................................... 46 2.7 Weight and mass....................................................................... 66 Topic summary.......................................................... 70 Topic Test 2................................................................ 71 Pressure............................................................................. 74 3.1 Force acting on a surface.......................................................... 74 3.2 Definition of unit of pressure.................................................... 75 3.3 Pressure in solids...................................................................... 76 3.4 Pressure in liquids.................................................................... 81 3.5 Pressure in gases....................................................................... 87 3.6 Transmission of pressure in fluids.............................................. 88 3.7 Application of Pascal’s principle................................................ 91 iii 3.8 Atmospheric pressure............................................................... 93 Topic summary........................................................... 101 Topic Test 3................................................................ 102 Effects of temperature changes on matter............................... 105 4.1 Heat as a form of energy........................................................ 107 4.2 Temperature scales................................................................. 107 4.3 Thermal equilibrium.............................................................. 113 4.4 Measurement of temperature.................................................. 114 4.5 Types of thermometers........................................................... 116 4.6 Calibration of thermometers................................................... 121 4.7 Effects of temperature change on solids................................... 125 4.8 Effect of temperature change in liquids.................................... 128 4.9 Evaporation............................................................................ 137 4.10 Sublimation and deposition.................................................... 139 Topic summary........................................................... 143 Topic Test 4................................................................ 143 Reflection of light on plane surfaces........................................ 145 5.1 Nature of light........................................................................ 146 5.2 Rays and beams...................................................................... 148 5.3 Rectilinear propagation of light.............................................. 150 5.4 Formation of shadows and eclipses......................................... 151 5.4 Pinhole camera....................................................................... 156 5.5 Reflection of light at plane surfaces......................................... 161 5.6 Image formation by a plane mirror.......................................... 166 5.7 Applications of reflection at plane surfaces............................... 177 5.8 Project work.......................................................................... 179 Topic summary........................................................... 181 Topic Test 5................................................................ 182 iv Behavior of light at plane surfaces.......................................... 185 6.1 Phenomena of refraction of light............................................ 185 6.2 Refraction of light through a prism......................................... 208 Unit summary............................................................. 219 Topic Test 6................................................................ 220 Electricity........................................................................... 225 7.1 Types of electrostatic charges.................................................. 226 7.2 The law of electrostatics.......................................................... 228 7.3 Conductors and insulators...................................................... 230 7.4 Effects and application of electrostatics.................................... 232 Topic summary........................................................... 233 Topic Test 7................................................................ 234 Introduction to current Electricity......................................... 235 8.1 Simple electric circuit and its components............................... 235 8.2 Arrangement of bulbs and cells in an electric circuit................. 237 8.3 Electric current..................................................................... 243 8.4 Potential difference (p.d)......................................................... 250 8.5 Chemical cells........................................................................ 255 8.6 Project work.......................................................................... 264 Topic summary........................................................... 265 Topic Test 8................................................................ 265 v vi  UNIT 1 States of matter Topics in the unit Topic 1: States of matter Learning outcomes Knowledge and Understanding Understand that matter can exist in different states Skills Perform tests to investigate surface tension, osmosis and capillarity of fluids. Predict what might happen based on the particle theory Use appropriate measures Collect and present results appropriately Interpret results accurately Report findings appropriately Attitudes Show curiosity in carrying experiments. Key inquiry questions How can we explain why matter exists in three states? How do the forces interact in matter? What causes the change of states of matter? How could we determine the viscosity of a certain fluid in the lab? What causes surface tension? 1 TOPIC 1 States of matter Topic outline Describe the composition of matter. Simple kinetic theory. Evidence that matter is made up of small particles. Physical properties of solids. Physical properties of liquids. Physical properties of gases. Applications of physical properties of matter. Recognision of physical properties of matter. Introduction Matter is anything and everything that we come across in this world. Matter can be a piece of rock, a grain of maize, a piece of paper, water or air which we breath. In science ‘matter’ is defined as anything that occupies space and has mass. Matter can be classified into three states namely solids, liquids and gases. 1.1 Matter and its composition Activity 1.1 To describe matter (Work in pairs) Steps From your knowledge of science at the primary level: 1. Discuss with your class partner the examples of matter you can see or feel around you. 2. Compare and discuss your answers with other pairs in your class. 3. Take turns in a class discussion to present difference between solids, liquids and gases. As you learnt in your primary science, matter is anything that has weight and occupies space. Anything around us is matter. But what is matter made up of? Activity 1.2 will help us to understand this. 2 Activity 1.2 To investigate composition of matter (Work in pairs) Materials: a piece of chalk, a piece of paper Steps 1. Get a piece of chalk and a piece of paper. 2. Let one of you break the chalk and continue breaking until you cannot break it any further. What do you notice about the initial piece and the final particle in terms of size? Is the smallest size you have obtained the smallest possible? 3. Let your partner get the piece of paper and cut it into two halfs. 4. Continue cutting the paper into smaller pieces until you cannot cut it anymore. 5. Discuss your observations in step 2 and 4 with your colleagues. 6. Discuss with your colleague what you remember about an element, compound and mixture from what you learnt in primary 4. 7. Discuss the different methods used to separate mixtures. Are the methods you have discussed possible to separate all mixtures? Explain why? If you break a piece of chalk or paper, it will keep reducing to smaller paticles. If you could be able to keep on breaking the pieces you could arrive at the smallest particles of matter that can be separated by physical means. These smallest particle of matter that cannot be broken down further by physical means is called an atom. An atom is the smallest particle of matter that can take part in a chemical reaction. There are other smaller sub-atomic particles that are covered in other units. Matter can be made of particles (atoms) of the same kind or a group of particles of different kinds. Matter is made of an element, mixture or a compound. An element is a substance which cannot be splitted into a simpler substance. In other words, all the atoms in a substance have the same identity that substance is called an element e.g. copper, graphite in pencil (carbon). A compound is a substance made of two or more elements combined together in a fixed proportion. E.g. water is made up of oxygen and hydrogen, table salt is made of sodium and chloride, chalk is made up of calcium carbonate, that is, calcium, oxygen, and carbon. A mixture is a material made up of two or more substances that can easily be separated by physical means. e.g. salt and sand, iron and sulphur. Fig 1.1 illustrates the difference between a compound, an element and a mixture. 3  atoms of atoms of mixture of compound of iron sulphur iron and iron sulphide sulphur Fig 1.1 Iron and sulphur Warning Atoms may be small in size, but can be used to cause mass destruction through nuclear and atomic bombs. SAY NO TO WAR AS IT CAUSES A LOT OF DESTRUCTION. 1.2 Introduction to kinetic theory of matter Activity 1.3 (Work in groups) To differentiate between physical and chemical properties of matter Materials two beakers purple crystals of potassium permanganate water bunsen burner perfume straw Steps 1. Get a beaker and pour in water up to more than half its height and leave it to settle. 2. Get the crystals of potassium permanganate and drop them through the straw into the bottom of the beaker of water. What makes the colour of potassium permanganate spread? 3. What do you think would happen if you added the crystals of potassium permanganate into the water before it settled? 4. Repeat step 2 but this time heat the beaker gently. Compare your observations with that in step 2. How fast does the colour spread? 5. Stand in a row, from the front of the class to the back. Let the one in the front spray a perfume. Let each learner in the row raise his hand whenever he smells the spay. Do you all smell the perfume at the same time? In what pattern do you raise your hands? What do you think will cause the rate at which the spray spreads to change? 4  6. Discuss your observations in steps 2, 3 and 4 with other groups in class and use your conclusion to state the kinetic theory of matter. When a perfume is sprayed in one corner, it is smelt in the other corner because the particles of the perfume have moved from one point to the other. This shows that matter is made of particles that are constantly moving. If matter particles were not moving, then there could be nothing that could move about and mix with the water. The movement of these tiny particles is summed up in a model called the kinetic theory of matter. The kinetic theory makes the following assumptions. 1. Matter consists of small particles. All matter is made up of a large number of tiny particles either individual atoms or molecules. 2. Large separation between particles. The second assumption describes the separation of the particles. 3. Particles are in constant motion. The third assumption is that each particle in matter is in constant motion. The kinetic theory of matter The word kinetic is derived from the Greek word “kineo” which means “I move”. Particles in substance are in constant motion; they posses kinetic energy, which is the energy due to movement. Therefore, kinetic theory of matter states that matter is made up of tiny particles that are continuously in random motion. It says that the materials particles have greater kinetic energy and are moving faster at higher temperatures. When a fast moving particle collides with a slower moving particle, it transfers some of its energy to the latter, increasing the speed of that particle. If that particle collides with another particle that is moving faster, its speed will be increased even more. But if it then hits a slow moving particle, then it will speed up the third particle while its speed decreases. The theory explains how particles are packed in solids, liquids or gasses; the attractive forces between them; and the effect of temperature on them. The arrangement of particles in matter and the way they move determines the state of a substance, i.e. whether to be in solid, liquid or gaseous state. Note! One important fact explained by the kinetic theory is that the average molecular kinetic energy is proportional to the absolute temperature of the material. Such temperature is a measure of the average internal kinetic energy of an object. 5 1.3 Physical properties of matter 1.3.1 Solids Activity 1.4 To investigate physical properties of solids (Work in groups) Materials Internet Reference books Sand Solids of different shapes Marbles and a transparent square bowl Empty container Steps 1. Access the Internet or reference books and do a research on the physical properties of solids and their application. Discuss your findings in your group. 2. Now, put as many marbles into a transparent square bowl as you can. Incline the bowl a bit. 3. Continue adding more marbles into the bowl as many as possible. 4. Cover the bowl with a lid and note the pattern (arrangement) of marbles inside it. 5. Assuming the shape taken by the marbles in the fully parked container illustrates the arrangement of particles in solids, draw the arrangement of particles in solids. 6. Fill the bowl fully with the marble and cover it tightly with a lid. Try to shake the bowl while pressing the lid firmly. Do the marbles move easily? Explain the effect on their pattern of arrangement and the movement to your partner. 7. Pour out all the marbles from the bowl and fill it with sand. Cover it tightly with a lid. What can you note about number of sand particles and the number of marbles that fit into the container. Between the two which one are more packed? Use your conclusion to explain density in solids. 8. Take the solids of different shapes i.e. cubes, cuboid and cylinders (see fig. 1.2). Fig. 1.2 6  9. Now put each of the solids you have into an empty container. Does their shape change? What can you conclude about the shape of solids? The particles in a solid are so tightly packed making them difficult to move. Solids have strong intermolecular forces in between the particles making the particles to be closely packed in fixed positions (rigidity). Fig 1.3 Arrangement of particles in solids Solids have a definite shape and volume. They are rigid and incompressible. They have the highest density compared to liquids and gases. A large force is needed to change the size and shape of a solid. Also, for a solid to melt into a liquid, it requires a lot of heat energy since the cohesive forces between the particles are strong. Particles or molecules in a solid are continuously vibrating in a fixed or mean position.When a solid is heated, the heat energy absorbed by the particles increases the kinetic energy; this makes the particles to vibrate more vigorously but in their fixed positions. When the temperature of a solid is increased, it undergoes thermal expansion.This happens because the mass of the solid stays the same but its volume increases. This results to decrease in density. When cooled down, solids undergo thermal contraction decreasing in volume and thus their density increases. Increase in heat energy increases the kinetic energy in the particles and weakens the cohesive forces between the molecules up to a point when the intermolecular forces are weak to allow the matter to flow. This point is referred to as melting point. The process of a solid changing into a liquid is called melting. 7 1.3.2 Liquids Activity 1.5 To investigate physical properties of liquids (Work in groups) Materials Water in a beaker Bunsen burner Chalk dust Steps 1. Put the chalk dust on the surface of the water in the beaker. Observe and explain the motion of the chalk particles. 2. Now, start heating the water to boil. Observe and explain the motion of the chalk particles. Does the motion change? What causes this change? 3. Draw the arrangement of particles in liquids. Compare and discuss your findings with other groups in your class. When dust particles in water are observed, they are seen moving in a random manner. Tiny invisible water molecules, moving in different directions at different speeds, collide with the chalk dust particles and force them to move. This activity suggests that the invisible, tiny molecules of water are in a constant random motion. As seen in Activity 1.5, the liquid molecules move freely, unlike the molecules in a solid. The distance between the molecules is slightly greater than the distance between molecules of a solid. The molecules of a liquid are loosely packed unlike those of the solid (Fig. 1.4). Fig 1.4: Arrangement of particles in liquids Activity 1.6 To investigate the shape of liquids (Work in groups) Materials A 250 ml beaker A 250 ml round bottom flask Water 8 Steps 1. Take a 250ml beaker and fill it with water. Note the shape taken by the water. 2. Pour the water from the beaker in step 1 into a 250ml round-bottom flask see Fig. 1.5. (a) Beaker (b) Round bottom flask Fig. 1.5 3. What shape does the liquid take? Why do you think the water takes the different shapes? Though liquids have definate size (volume), they have no particular shape. They take the shape of the container. Liquids expand when their temperatures increase. Increasing of temperature decreases the density of water. When the temperature increases, liquid molecules acquire more kinetic energy and hence move faster. This increase in kinetic energy of liquid molecules weakens the intermolecular forces between the particles. A further increase in kinetic energy makes the molecules to escape through the surface of the liquid. i.e., change into steam or gaseous state. The process of a liquid changing into the gaseous state is called evaporation. 1.3.2.1 Boiling point Activity 1.7 To investigate boiling of water (Work in groups) Materials Beaker water source of heat tripod stand wire guaze stirrer thermometer 9 Steps 1. Put some water into the beaker. Dip the stirrer and thermometer into the beaker. Record the temperature. Why do you think it is advisable to keep stirring the water? 2. Place the beaker and its content onto the stand and place the source of heat below it as shown in Fig. 1.6. Stirrer Beaker Thermometer Water Heat Fig 1.6: Boiling water 3. Continue heating the water as you observe the change in temperature. 4. The temperature reaches a point when the water will start boiling vigorously. Record the temperature. What is the name of this process? What do you think happens to the temperature of water as the water boils vigorously? 5. During this process is there a change in the temperature of the water? Try explaining what is happening to the molecules of water during this process. Boiling point is the temperature at which a liquid changes into a gas when the saturated vapor pressure of the liquid is equal to the external atmospheric pressure under one atmosphere. At this point, the liquid changes to gaseous state at constant temperature. Different liquids have different boiling points. 1.3.3 Gases Activity 1.8 To investigate the physical properties of gases (Work in groups) Materials Three marbles transparent dish a lid reference books Internet 10 Steps 1. Access the internet and reference books and do research on the physical properties of gases. Discuss your findings with other groups in your class. 2. Now, put three marbles in a transparent dish. Try as much as you can to move them further away from one another. 3. Cover the dish with a lid. Shake the dish. In what direction do the mables move? 4. Relate the movement of the marbles and the movement of air particles. Why do you think the air molecules are able to make such movement? When few marbles are put in a container and shaken they move freely in all directions in the dish. This is similar to the behaviour of particles in a gas. In gases, the intermolecular forces are so weak to be considered. Weak intermolecular forces only exist upon collision. A gas has no definite shape and volume, so they spread fill the container of any size and shape completely. Activity 1.9 To demonstrate that gases occupies space (Work in groups) Materials Polythene bag ( plastic bag) A straw Cello tape Heavy book. Steps 1. In groups of five, pick one plastic bag (polythene bag) and insert a straw into it. Leave part of the straw to protrude from the bag and then seal it with cello tape. 2. Place it on the table and then place a heavy book on it. 3. In turns, blow air into the bag. What do you think is the impact of the book as you blow? What do you observe? Explain your observation. 4. In turns, sketch the arrangement that you think the air molecules take.Give a reason for the shape you have sketched. CAUTION The material making up, plastic bags (polythene bags) determine, how easily it can be recycled. Some plastics can take years to decompose. But some companies and stores have begun using different types of biodegradable bags to avoid environmental pollution. If poorly disposed plastic pollutes the environment and can easily be ingested by livestock and wild animals thus possing a danger to them. 11 Activity 1.10 To investigate the shape of gases (Work in groups) Materials Solid carbon dioxide A 250ml beaker A glass lid A tumbler Steps 1. Place solid carbon dioxide at one of the bottom corner of a beaker covered with a glass lid. What happens to the solid carbon dioxide? 2. Place a tumbler that has a mouth the same size as the beaker on top of glass cover. 3. Remove the glass cover (see fig. 1.7). What happens to the fumes of carbon dioxide? What do you think causes the observation you have made? Tumbler Tumbler Glass lid Beaker Beaker Solid Solid carbon dioxide carbon dioxide (a) (b) Fig. 1.7 4. Do you think you will make the same observation if bigger tumblers were used? When air is blown into a polythene bag, it is seen to bulge and become inflated. This is because the number of gas molecules increased in the bag as one blew into it. This demonstrate that gases occupy space. Fig 1.8 shows the arrangement of gas particles. Fig. 1.8 Arrangement of gas particles 12 The distance between the molecules is large (see Fig 1.7) and the force of attraction between the molecules is very small (almost negligible). These molecules move about freely in all directions colliding with each other and with the walls of the container. The movement of molecules from a region of higher concentration to a region of lower concentration is called diffusion. From Activity 1.10 gases can diffuse into each other rapidly taking the shape of the container, this is because gases are light (less dense) compared to solid and liquid. This best explains what we learnt in activity 1.3 that when a gas is sprayed in one corner of the room, it spreads throughout the room. Gas particles are also smaller. Gases are compressible (they can be squeezed) into a small volume, like in a car tyres and bicycle tyres when pumped. This is because they have spaces in between them (Fig 1.8). 1.4 Movement of particles in matter 1.4.1 Viscosity Activity 1.11 To demonstrate viscosity in liquids (Work in groups) Materials House hold liquids (water, honey, oil, milk, paraffin) A sphere such as a steel ball 100 ml graduated cylinders Ruler Stopwatch. Steps 1. Measure equal amounts of water, honey, oil, milk and paraffin and pour them into different the graduated cylinders. What do you note about them? How is the flow of different liquids as you pour them into the cylinders? 2. Measure and record the depth of the liquids in the cylinders. 3. Place the sphere on the surface of water. Using a stopwatch, measure and record how long it takes for it to flow to the bottom of the liquid. 4. Remove the sphere and repeat step 3, two times for the same liquid. What do you observe? 5. Rinse and dry the sphere. Repeat steps 3,4 and 5 for the rest of the liquids. What do you observe? Explain your observation. What do you think makes the ball fall at different rates in the different liquids? 13 6. Tabulate your result in a table form as one shown in Table 1.1. Substance Trial Depth of liquid (cm) Time (s) Speed (s) Table 1.1: Table of results 7. In groups discuss and make notes on thickness of the liquids as illustrated by the steps 1-6. Different liquids have different thickness thus having different ability to flow. The state of a liquid being thick and sticky due to internal friction is called viscosity. Fluids resist the relative motion of immersed objects through them as well as the motion of layers with differing velocities within them. The sphere moved fastest in water and lowest in honey. This shows that, water has the lowest viscosity as compared to other liquids since it offers minimum resistance to the movement of the sphere through it. Honey has the highest viscosity as compared to the other liquids. 1.4.2 Diffusion Diffusion is the process in which the molecules of a fluid spread from regions of their higher concentration to regions of their lower concentration as we saw with the potassium permanganate crystals in activity 1.3. Activity 1.12 To investigate diffusion in liquids (Work in groups) Materials A bottle A glass container Concentrated solution of potassium permanganate Steps 1. Fill a bottle with a concentrated solution of potassium permanganate and leave the top open (Fig. 1.9(a)). 2. Place this bottle in a large glass container (Fig. 1.9(b)) and pour water carefully from the side till the water level is well above the open top of the bottle (Fig. 1.9(c)). Why do you think water should be above the bottle? 14  open top glass containers potassium permanganate water solution (a) (b) (c) Fig. 1.9: Diffusion in liquids 3. Leave the set-up undisturbed for some time. Observe what happens to the colour of the solution inside the bottle and to the water outside surrounding the bottle. You may have to observe this for a long time. 4. What do you think would happen if the concentrated potassium permanganate was used in place of water? The coloured solution of potassium permanganate rises upwards and spreads to the entire space occupied by the water. The spreading continues in such a way that the molecules of the solution move from a region of higher concentration to a region of lower concentration. This is diffusion in liquids.The spreading stops when the concentration of the entire solution becomes the same all over. Particles in liquids diffuse from one point to all other parts of the liquid. Activity 1.13 To demonstrate diffusion in gases Part 1 (Work in groups) Materials Two jars Carbon dioxide gas Blue litmus paper Two gas jars A glass plate Steps 1. Take two jars, one filled with carbon dioxide gas and the other with air. 2. Introduce a wet blue litmus paper into these jars and observe what happens in each case. Explain the observation made in each case? 15 Part 2 Procedure 1. Take two jars, one filled with carbon dioxide gas and the other with air. 2. Stick a blue litmus paper at the bottom of the beaker filled with air. 3. Arrange the two jars with a glass plate separating them as shown in Fig. 1.10. 4. Leave the set-up undisturbed for a few minutes and then carefully remove the glass plate. Does the litmus paper change colour before you remove the glass plate? 5. What happens to the litmus paper when the glass plate is removed? Explain your observation when the galss plate is removed? moist blue litmus paper B air jar B glass plate A carbon dioxide gas jar A Fig. 1.10: Diffusion in gases 6. Design an experiment to investigate effect of using gases of different mass in diffusion. 7. In your investigation write down the procedure you have followed, the assumptions made and the relevant illustration of your investigation. 8. Derive the relevant formulae to illustrate the effect of using different gases in diffusion. The blue litmus paper turns red in the jar containing carbon dioxide. It remains blue in the other jar. This is the test for the presence of carbon dioxide which will be used in part (b). The blue litmus paper turns red in air jar B. The above effect shows the presence of carbon dioxide gas in the top jar, which contained only air. That is why blue litmus paper turns red. As soon as the glass plate is removed, the dense molecules of carbon dioxide gas rise upwards and spreads to the region of air of low density. The molecules of the 16 two gases inter-mix with each other. The spreading continues until the mixture acquires a uniform density. The observation shows that molecules in a gas move from a region of higher concentration to the region of lower concentration. This is diffusion in gases. Diffusion in gases takes place more quickly than in liquids. The molecules of a gas move more freely than those of a liquid. This is the process by which volatile substances e.g. perfumes, spread through a room even when the air is parfectly still. In a solid, the molecules can only vibrate to and fro in their fixed positions. It is important to note that the rate of diffusion of gases depend on its molecular weight. Thus if molecular weight of gas A is four times that of gas B, then gas A would diffuse at half the rate of gas B. This is best explained using Graham’s law of diffusion which states that the rate of diffusion of a gas is inversely proportional to the square root of the mass of its particles. The formula can be written as: √ Rate A MB = MA Where: Rate A is the rate of diffusion of the first gas. Rate B Rate B is the rate of diffusion of second gas MA is the molar mass of gas A. MB is the molar mass of gas B. 1.4.3 Osmosis Activity 1.14 To investigate osmosis in semi-permiable membrane (Work in groups) Materials Straw/Capillary tube Salt solution Visking tube String Beaker with distilled water. Steps 1. Tie one side of the visking tube with a string. 2. Fill the tied visking tube with the salt solution. 3. Insert the straw into the visking tube and tie the visking tube around the straw. Note the level of the solution in the straw. 4. Deep the tied visking tube into the beaker containing distilled water. (see Fig 1. 11). Let it be in the water for few minutes. 5. What do you observe on the level of the solution in the capillary tube? 17 6. What happens to the level of water in the beaker? Explain what causes this change? 7. What do you think would happen if concentration of solution in both the beaker and the visking tubing was the same? Straw beaker visking tube distilled water Fig 1.11: Osmosis in semi-permiable membrane Osmosis is the process through which a solvent solution such as water moves through a semi-permiable membrane into a solution. Osmosis can be described in terms of kinetic theory, that is more massive molecules diffuse slower than the less massive ones at a similar temperature. A good example of osmosis is when an egg is put in a sugar solution. Water molecules pass through the semi-permiable shell into the egg. Sugar molecules that are bigger don’t pass through. 1.5 Application of cohesive and adhesive forces between molecules 1.5.1 Cohesive and adhesive forces Matter is made up of small particles called molecules. These particles are held together by force of attraction between them. The force of attraction between molecules of the same substance is called the force of cohesion (Fig. 1.12(a)). The force of attraction between molecules of different substances is called the force of adhesion (Fig. 1.12(b)). A free liquid drop is almost spherical. When a drop of water is placed on a glass plate, the glass molecules attract the water molecules strongly. The drop spreads out over the glass and hence its shape changes (Fig 1.12(b)). 18  Drop of water Drop of water glass plate Waxed surface (a) Force of cohesion (b) Force of adhesion (c) Drop of water on a waxed surface Fig. 1.12: Cohesive and adhesive forces When a drop of water is placed on a waxed surface (Fig. 1.12(c)), the drop is almost spherical. The force of adhesion between water molecules and wax molecules is less than the force of cohesion between water molecules. (The shapes of the drops described above is true for small drops. The large ones tend to spread a bit more due to their heaviness). The forces of cohesion and adhesion always exist in pairs whenever liquids are in contact with solids. Their effect on the liquid surface depends on which force is greater. The forces of cohesion and adhesion may be used to explain the liquid meniscus and the capillary action. Liquid meniscus When liquids are poured into containers, their surfaces are curved. In the case of water, the curved surface forms a concave shape (Fig. 1.13(a)). This is because the adhesive force between water molecules and glass molecules is more than the force of cohesion between the water molecules. For mercury the shape is convex (Fig. 1.13(b)). This is because cohesive force between the mercury molecules is greater than the adhesive forces between mercury molecules and glass molecules. concave convex meniscus meniscus (a) Water meniscus (b) Mercury meniscus Fig. 1.13: Liquid meniscus 19 1.5.2 Capillary action When a glass tube with a narrow bore in its centre (capillary tube) is dipped in a liquid, the liquid level rises or drops depending on the liquid used. The rise or fall of a liquid level in a tube is caused by capillary action. Capillary action can be defined as the ability of a liquid to rise or fall in narrow spaces due to the intermolecular forces between the liquid and sorrounding solid surfaces. Activity 1.15 To demonstrate capillary action using capillary tubes (Work in groups) Materials Beaker containing mercury Beaker containing water Three long tubes of different diameters. Steps 1. Observe as the teacher dips three long tubes, one of which is a capillary tube, open on both ends in a beaker containing water as shown in Fig. 1.14(a). Observe what happens to the level of water and the type of miniscus in the tubes. 2. What causes the different levels of miniscus? 3. Now observe as he removes the tubes from the beaker containing water, dry them and dip them in the beaker containing mercury as shown in Fig 1.14(b). 4. Observe what happens to the level of mercury and the type of miniscus formed in the tubes. Give a reason for the difference in level of the miniscus. capillary capillary tube tube (a) Water (b) Mercury Fig. 1.14: Capillary action in water and mercury The level of water rises in the tubes. The greatest rise is observed in the narrowest capillary tube (Fig. 1.14(a)). If mercury is used instead of water, the levels fall as shown in Fig. 1.14(b). The greatest fall is observed in the narrowest capillary tube. 20 Activity 1.16 To demonstrate capillary action using chalk bricks. Materials Two chalk bricks Shallow tray Waxed paper Coloured water Steps 1. Pour a little coloured water into a shallow tray so that it submerges half of one of the chalk bricks (fig. 1.15(a)). 2. Place a second chalk brick on top of the first and observe what happens. 3. Repeat the steps 1 and 2 but with a piece of waxed paper between the two chalk bricks (fig. 1.15(b)). Why do you think a waxed paper was used? chalk bricks waxed paper coloured water (a) Capillary action takes place (b) No capillary action Fig 1.15: Capillary action on chalk bricks 4. Explain the forces that are leading to the observation made. Chalk is a porous substance. The tiny air spaces in it form the capillary tube needed for the capillary action to take place. The coloured water rises up into the top brick (Fig. 1.15(a)). However, when waxed paper is used, Fig. 1.15(b), the adhesive force between the water molecules and the wax is small. The coloured water is therefore not able to cross over to the other chalk brick on top. Applications of capillary action Capillary action is applied in many situations. Here are some of the situations. 1. The spreading of ink over a blotting paper: The air spaces provide fine tubes. 2. Kerosene rises up the wick of a lamp: The fibres act like capillary tubes of fine bore. 3. The rise of water from the soil in the plants: Tissues of plants provide narrow tubes. 4. Towels used for drying. The air spaces in a towel provide fine tubes. 21 Capillary action might also become a nuisance. It causes dampness through the walls and floors of houses. To prevent this, a waterproof sheet of polythene is laid in the concrete base as shown in Fig. 1.16. concrete waterproof polythene damp course quarry chips Fig. 1.16: Water proof material prevents dampness 1.6 Surface tension Activity 1.17 To demonstrate surface tension Materials Tissue paper Greased steel pin Water in a beaker Steps 1. Place a tissue paper on the surface of clean water contained in a beaker. What happens to the tissue? Explain the observation. 2. Carefully place a greased steel pin on top of the tissue paper. Take care not to touch the water. Observe what happens (fig. 1.17). What do you think will happen if you touch the water. Explain. pin water tissue paper Fig.1.17: Surface tension 3. Put a drop of oil near the steel pin and observe what happens. Explain your observation. What is the effect of the drop of oil? 22 The tissue paper absorbs water and sinks to the bottom, leaving the steel pin floating on the surface of the water. How does the steel pin which is denser than water float? Use a hand lens to observe the surface under the steel pin. The surface of water behaves like a stretched, thin elastic skin that is under tension. The force that causes a liquid to behave this way is called surface tension. When a drop of oil is put near the steel pin, it immediately sinks. The oil has reduced the surface tension of water which supported the steel pin and hence the pin sinks. This shows that surface tension of a liquid can be reduced by introducing impurities. Raising the temperature of the liquid also reduces surface tension. Surface tension enables insects to walk on water surface. It provides a force which supports them. Activity 1.18 To show that a liquid will tend to have its surface as small as possible Materials Funnel Liquid soap or detergent Steps 1. Dip an inverted filter funnel in a liquid soap or detergent solution. 2. Take it out and blow a soap bubble on the wider end as shown in Fig. 1.18(a). Observe closely what happens to the bubble. funnel soap film soap film (a) (b) (c) soap bubble Fig. 1.18: Bubble moves up the funnel The bubble flattens to a film and slowly moves up the funnel Fig. 1.18(b) until it reaches the narrowest end of the funnel Fig. 1.18(c). The soap film acts as an elastic skin in forming the soap bubble. By moving up it makes its surface as small as possible. 23 Activity 1.19 To show surface tension in soap film. Materials Cotton wool Wire frame Liquid soap Steps 1. Tie a loose loop of cotton thread onto the wire frame. 2. Slowly dip the wire frame into a liquid soap or detergent solution. 3. Withdraw it slowly so that a film is formed across the wire frame as shown in fig. 1.19(a). Break the film inside the loop and observe what happens. cotton loop wire frame film (a) (b) Fig. 1.19: Film on a wire loop Once the film is broken from the inside of the loop, it forms a perfect circle (Fig. 1.19(b)). The film makes its surface as small as possible by pulling the thread into a circle. Activity 1.20 To show surface tension in clean water Materials Tambler Dropper Water Steps 1. Fill a tumbler with clean water (Fig. 1.20(a)). 2. Add a few more drops of water slowly in the tumbler as shown in Fig. 1.20(b). What happens to the water surface? 24  (a) (b) Fig. 1.20: Surface of water behaves like an elastic skin The water forms a convex shape. The surface of the liquid behaves as if it were an elastic skin. However if more water is added the skin breaks and the water overflows. Surface tension of different liquids Different liquids exhibit different surface tensions. e.g. water has a bigger surface tension than soap solution. Activity 1.21 To show the effect of two tensions Materials Matchstick Soap Water in a beaker Steps 1. Apply some soap on one end of a matchstick. 2. Place the matchstick on water (Fig. 1.21). Does the matchstick move? In what direction does it move? What causes the movement? soaped end motion Fig 1.21: Effect of different surface tensions 25 The matchstick immediately starts to move in such a way that the soaped end is behind. The soaped end lowers the surface tension of water (soap dissolves and makes a soap solution). The other end being in a region of higher surface tension is pulled and moves in the direction shown. The cleaning power of a detergent Place a drop of oil on the surface of clean water (Fig. 1.22). Observe what happens. oil patch water Fig. 1.22: Oil drop spreads into a circular patch The surface tension of oil is less than that of water. Water pulls oil in all directions and spreads it in a thin circular patch. Collect a few grains of detergent powder and drop them on the oil patch formed and observe.­The oil patch breaks up and forms circles round each grain. The cleaning action of detergents depends on their ability to weaken the elastic skin. When it comes in contact with grease and dirt, it spreads into all corners and thoroughly wets the dirty objects instead of forming drops. Explaining surface tension Molecules in a liquid attract each other (cohesion) (Fig. 1.23(a)). Molecules that are inside the liquid are attracted equally in all directions. The net force on a molecule inside a liquid is therefore zero (Fig. 1.23(b)). However molecules on the liquid surface have no molecules above them. The attractive force is therefore due to the molecules that are inside the liquid. Consequently the molecules on the surface layer experiences an inward pull from the molecules below them (Fig. 1.23(c)). The free surface of a liquid is therefore under tension which tends to stretch it. 26  molecule elastic skin (a) (b) (c) net force net force on molecules net force is the inward inside the liquid is zero. pull downwards Fig. 1.23: Explaining surface tension Exercise 1.1 1. Give scientific reasons for the following statements: (a) Water wets glass. (b) Mercury meniscus is convex. (c) Small drops of mercury form spherical drops when in contact with a clean glass plate. (d) Capillarity is more pronounced in very narrow bored glass tubes. (e) Towels are used to dry wet hands. 2. The diagram in Fig. 1.24 shows a cracked drainage pipe. Explain the formation of the drops shown and how water is able to run along the underside of the pipe. drop of water water running down Fig. 1.24: A leaking drainage pipe 3. Describe an experiment to explain surface tension in liquids. 27 Topic summary Matter is anything that has mass and occupies space. Kinetic theory of matter states that matter is made up of of tiny particles that are in constant random motion. Matter can be classified into three states: solids, liquids and gases. A gas has neither definite volume nor shape. Its molecules are free to move randomly. Solids have definite volume and shape. The molecules of solids are closely packed hence they just vibrate to and fro about their fixed positions. Liquids molecules move freely inside the container. Liquids take the shape of the container vessels. They have definite volume. Melting is the process by which a solid is converted to a liquid at a constant temperature. Viscosity is a measure of how much a fluid resists movement of objects through it. Gases are compressible because they have molecular spaces in between them. Topic Test 1 1. Explain why the density of a gas is much less than that of a solid or a liquid. 2. Draw a diagram to show how air molecule moves in a closed container. 3. Explain why it is easier to compress a gas than a liquid or a solid? 4. State one similarity between particles of a liquid and those of a gas. 5. Describe the difference between solids, liquids, and gases in terms of the arrangement of the molecules throughout the bulk of the material. 6. Explain why tyres burst when left outside during hot weather? 7. According to the kinetic theory, what is temperature? 8. State and explain two applications of physical properties of solids, liquids and gases and show how they have improved our lives. 28  Types of forces and their UNIT 2 measurement Topics in the unit Topic 2: Introduction to forces Topic 3: Pressure Learning outcomes Knowledge and Understanding Understand the types of forces and their measurement. Skills Carry out practical investigations using meters into the effect of friction and pressure Use appropriate measures Collect and present results appropriately Interpret results accurately Report findings appropriately Attitudes Show curiosity in carrying experiments. Key inquiry questions How do we classify forces? How can we distinguish between weight and mass of a body? Why are frictional forces important to an object? 29 TOPIC 2 Introduction to forces Topic outlines Definition of force. Types of forces and differenciate between contact and non-contact forces. Effects of forces. Representation of forces using vector diagrams. Measurement of forces. Weight and mass. Combination of forces. 2.1 Definition of force In our daily lives, it is common to see things being pushed or pulled. Activity 2.1 gives us some of the instances where things are either being pulled or pushed. Activity 2.1 Demonstration of force (Work in pairs) Materials Charts A stone Rope Classroom table Steps 1. Push a table in your classroom slightly to displace it. Take care not to damage the legs of the table due to dragging. 2. Tie a stone or brick using a rope and pull it to other positions. (Take care not to be hurt by the stone).What will you notice if you used a bigger Fig. 2.1 : Pushing a table stone? 3. Now, study the pictures shown in Fig 2.2 and discuss with your class partner what is happening in each of them. 30  (a) (b) (c) (d) Fig. 2.2 : Pushing or pulling objects 4. Tell your partner where a push or a pull is occurring. 5. Discuss with your partner other examples where a push or a pull occurs in our daily lives. List them down in your exercise book. 6. Compare and discuss your findings with different groups in your class. These activities and many more involve either pushing or pulling. In physics, a pull or a push is called a force. Force is an action that causes the motion of an object in its direction of application or causes an object to change shape. However not all forces causes bodies to move. The SI unit of force is the newton (N), named after the famous physicist Sir Isaac Newton (1642 –1727). Force is a vector quantity. It has both magnitude and direction. The magnitude is represented by a straight line while the direction is shown using an arrow as shown in Fig 2.3. Fig. 2.3: Force exerted to the right 31 2.2 Effects of forces The effect of a force depends on the size, nature, how and where the force is applied. The following activities illustrate the effect of forces on bodies. Activity 2.2 To demonstrate the effect of a force on objects (Work in groups) Materials A chart showing the different pictures Steps 1. Look at the pictures in Fig 2.4. 2. Identify the effects of forces shown in the figures. (a) Catching a moving ball (b) Spiking a volleyball (d) Cars colliding. (e) A girl sitting on a balloon. Fig. 2.4: Effects of forces 3. Discuss other cases where the effects you have identified in step 1 are also experienced. 4. What do you think will happen if the amount of force in each picture was increased? 32 A force can make a body at rest to start moving or a moving body to come to rest. It can also change the direction of motion of a body. Therefore, force can change the state of motion of a body. A force can distort or change the shape of an object. For example, stretching a rubber band or a spring when compressed by a force and squeezing a balloon. Clay and plasticine are also other examples of substances whose shapes change easily when a force acts on them. A force due to an earthquake can also cause massive destruction such as death of people and animals. It can also cause land deformation which leads to soil erosion and consequently contribute to pollution. Activity 2.3 To show that force produces a turning effect on an object (Work in pairs) Materials A seesaw A bottle opener Unopened bottle Steps 1. With your partner, try to balance on a seesaw (Fig. 2.5(a)). Now try to lift your partner on the seesaw. What do you observe? How can you balance on the seesaw? 2. Observe the activity in Fig. 2.5 (b). (a) Seesaw (b) A bottle opener Fig. 2.5: Forces causing turning and rotation 3. Discuss with your class partner the effects of force shown in Fig. 2.5(b). When forces are suitably applied can make a body to turn about a point or cause a rotation. 33 Activity 2.4 To demonstrate tear and wear as caused by force Materials Different tyres Steps 1. Take a close look at different tyres of vehicles within the school compound or roadside. What can you comment about their treads? Suggest a reason for their appearance. 2. Now, compare and discuss the state and condition of the tyres shown in Fig. 2.6. (a) (b) Fig. 2.6: Conditions of tyres 3. Name the effect of the force demonstrated in Fig 2.6 (b). Explain how the effect demonstrated is brought about by force. The tyres wear and sometimes tear because of friction between the road and the tyre when in use. This shows that, forces can cause wear and tear. In summary, the following are the effects of forces: Force can cause change in the state of motion of a body, i.e. force can start, stop, increase or reduce motion and change the direction of a body in motion. Force can change the shape of a body i.e. force can distort, stretch or compress a body. Force can cause turning effect. Examples are a seesaw and a beam balance. Force can cause rotation in the bodies e.g a steering wheel. Force can cause heating effect, i.e. frictional force cause heating, e.g. lighting a matchstick. Frictional force causes noise when rough surfaces are rubbed together. 34 2.3 Measurement of force Activity 2.5 To determine the force of an object using a force meter Materials Force meter Masking tape Unknown masses of between 0.5kg and 1.0 kg Steps 1. Using the masking tape cover the scale of the force meter to have a blank strip along the scale. 2. Hold the force meter vertically without any mass on the hanger. Make a mark on the blank strip of the force meter and that will be the 0 mark of your force meter scale. 3. Hang a 100 g mass from the force meter (100 g is equivalent to 1 newton). This force stretches the spring. Make a mark on the blank strip that will be the 1 newton of the scale. 4. Add another 100 g mass to the force meter. The force pulling the spring of the force meter now becomes approximately 2 newtons. Make 2 newton mark on your force meter scale. 5. Repeat step 3 up to 10 newtons mark. You have now ‘calibrated’ your force meter so that it has a scale for taking measurements. 6. Take the masses off the force meter and hang the unknown mass from it. Record the approximated force that acts on this mass. Fig 2.7. sketch of mass on a force meter. 7. Now remove the making tape from the force meter scale and repeat step 6. Record the force that acts on the different masses. What is the difference between the approximated force and the accurate force? 35 Activity 2.6 To determine your own strength (Work in pairs) Materials Spring balance Wall/ Rigid support Steps 1. Hook the spring balance onto the wall. 2. Pull the other end of the spring as shown in fig 2.8. Spring A Pull Rigid support Fig 2.8 Measuring force 3. Let your patner read and record the reading on the spring 4. Exchange roles with your partner. What is the difference between your strengths? Forces can be measured using a device called force meter. Force meters come in many forms and designs. The most common ones are the ones that make use of elastic materials like springs and rubber bands. An example of a force meter is Spring force metre.(see Fig. 2.9(a)). This is a device that measures the magnitude of a force. The spring stretches when a force is applied to the hook, and a reading is taken from the scale. Fig 2.9(b) shows a digital force meter. a) Spring force metre b) Digital force metre Fig 2.9: force meters 36 2.4 Representation of forces using vector diagrams Activity 2.7 To demonstrate representation of force Material Marbles Steps 1. Arrange the marbles on top of your desk in a straight line (Fig. 2.10). Fig. 2.10: Movement of marbles 2. Give one marble a slight push toward others. As it moves and hits the next one, what happens? 3. Does it stop after the others start moving? Explain why. 4. What do you think would happen if the first marble hit the second at an angle and not just straight ahead? 5. Discuss with your group members your observations and suggest how forces are represented. We have already learnt that, force is a vector quantity, that is, it has both magnitude (size) and direction. A vector is normally represented by a line with an arrow head ( ). The length of the line represents the magnitude and the arrow head shows the direction. We therefore need a way of representing both magnitude and direction on a diagram in order to represent forces. A diagram showing all the forces acting on a body in a certain situation is called a free body diagram or simply a vector diagram. A free body diagram shows only the force acting on the object under consideration, not those acting on other objects. Fig. 2.11 shows forces acting on a body falling in a liquid. v v, is the viscous drag of the liquid. w, is the weight of the object. u, is the upthrust in the liquid. w u Fig. 2.11: A moving object in a liquid 37 Fig. 2.12 shows a body moving toward right on a rough surface. N Motion N is the normal reaction. Fs Fa Fa is the applied force. Fs is the friction force. A A is the action force or (weight). Fig. 2.12: Normal, applied force and friction force Fig. 2.13 shows a person pushing a wheelbarrow. R P D W Fig. 2.13: Shows a wheelbarrow being pushed towards left R is the reaction force of earth on the wheelbarrow. This force acts at right angle (or normally) to the ground. It is also referred to as the normal reaction force. P is the forward force exerted by the worker on wheelbarrow. W is the pull of earth on wheelbarrow (its weight). D is the drag force acting on the wheelbarrow. 2.5 Combination of forces Parallel forces Activity 2.8 To demonstrate parallel forces Materials A block of wood Two identical springs Steps 1. Place a block of wood on a rough surface. 38 2. Pull the block using a string attached to a spring balance until the block just starts to move Fig. 2.14(a). Record the value of the force applied. 3. Repeat the activity but use two identical springs parallel to each other. (Fig.2.14(b)). Record the force applied in each of the springs. wooden block (a) Pulling a block using one spring wooden block (b) Pulling a block using two springs Fig. 2.14: Measuring force using spring balance 4. Compare the value of the forces applied in steps 2 and 3. Explain the difference if any. 5. What will happen if the springs were used to pull the wooden block in opposite direction from each other? When pulling together two springs, the same value is recorded on both springs. This value is half of that recorded by the single spring. Let the force applied by the single spring A values = y Force applied by each one of the two spring = x Therefore, x + x = y 2x = y y x= 2 When several parallel forces act together on the same body in the same direction the combined or resultant force can be added by the ordinary rules of arithmetic. If the Activity 2.9 is repeated with two equal forces pulling the wooden block at the same time but in opposite direction, one force cancels or counters the other one. If the force in one direction is taken as positive, then the force in the other direction is taken as negative. 39  When a number of parallel forces act on a single body, the resultant force acting on the body can be found by adding all the forces taking considerations of the directions (+ or –). Example 2.1 Two oxen are pulling a heavy block along a floor in the same direction. One exerts a horizontal force of 800 N and the other a force of 1000 N. If the frictional force between the crate and the floor is 430 N. (a) Draw the force diagram. (b) Find the total horizontal force in (a) above. (c) Find the direction of the force in (a) above. Solution (a) 800 N 430 N 1000 N Fig. 2.15: Addition of parallel forces (b) We shall chose the forward direction as positive since the frictional force opposes motion i.e acts backwards in the negative direction. Force exerted by the oxen = 800 N + 1000 N Force exerted by friction = -430 N The total sum of force on the crate = 800 + 1000 – 430 N = 1370 N The resultant force on the crate = 1370 N (c) Since the force is positive its direction is forward. 40 Exercise 2.1 1. Name all the forces acting on the following: (a) A book resting on a table. (b) A book which is being pushed across a flat rough table by a student’s finger. (c) A stone resting on a rough sloping board. (d) A box supported on a tall thin pillar. 2. Draw force diagrams for the cases in question 1. 3. Find the resultant of the following sets of forces: (a) A force of 35 N backwards and a force of 35 N forward. (b) A force of 120 N upwards and a weight of 150 N. (c) A force of 29 N upward, a force of 34 N upward, and a force of 50 N downwards. Non-parallel forces Activity 2.9 To demonstrate non-parallel forces (Work in groups of three) Materials A ring 3 ropes/strings Steps 1. Tie three ropes at different points on the ring as shown in Fig 2.16. Rope Ring Fig. 2.16: Strings tied to a ring 2. Let three of you pull each rope in different directions. 3. Do all of you pull the ropes with the same force? 4. What happens when you all pull the ropes? 41 When one rope is pulled by a greater force than the rest, the other two, move towards its direction. However, when the ropes are pulled with the same force, neither of you moved to any particular direction since the forces are balanced. These three forces in this activity act on the ring in different directions. Such forces are called non-parallel forces. Addition of non-parallel forces Activity 2.10 To illustrate addition of non-parallel forces (Work in groups) Materials 3 - identical spring balances A ring Plane paper 3 - heavy wooden blocks Part A 1. Cover the top of a table with a plane paper. 2. Hook the spring balances to wooden blocks. 3. Hook the springs to the ring by means of loose loops of the string as shown in Fig 2.17. Wooden block A String A B O String B String C C Wooden block Fig. 2.17: Addition of non-parallel forces 42 4. Move the wooden blocks outwards until each spring balance is showing appreciable reading. Record the readings of the spring balances. 5. Tap the ring and the strings so as to be in their true position. Is the ring balanced? Give a reason. Mark the centre of the ring as point O. 6. Draw a straight line along each string. Mark points A, B and C along the lines representing the respective strings as shown in Fig. 2.17. From Activity 2.10 part A, the ring is observed to be in equilibrium i.e. state of balance. Therefore, the total force acting upon it must be zero. This can be shown by adding together the forces exerted by spring balances A, B and C as shown in part B below. Part B Steps 1. Remove the set ups. 2. Produce the lines through A, B and C inwards to meet at O. 3. Using a suitable scale, mark off distances OA, OB and OC accurately and proportional to the readings you recorded for the respective springs. 4. Construct a parallelogram OBRA and draw the diagonal OR (see Fig 2.19). 5. Find the length OR and compare it with the length OC. What can you say about forces OC and OR. What is the relationship between Forces OA, OC and OR. The magnitude force OR and OC are equal in magnitude but opposite in direction (Fig. 2.18). R A B O C Fig. 2.18: Construction of parallelogram This force OR represent the resultant force exerted by OA and OB. This method of obtaining the resultant of two forces is called the parallelogram law method which says that; 43 If two forces are represented in magnitude and direction by two sides OA and OB of the parallelogram OARB, then the resultant is represented in magnitude and direction by the diagonal OR. Example 2.2 A wooden crate is pulled horizontally by two forces of 250 N and 150 N at an angle of 70º to each other. (Fig. 2.19). Determine the resultant force on the box. A 150N 70º B 250N Fig. 2.19: Wooden crate being pulled by two forces Solution Using a scale of 1.0 cm represent 50 N Draw a line OA to represent 250 N Draw a line OB to represent 150 N Let O be the common point and the angle between the two lines be equal to 70º A R O OA = 5.0 cm 70º OB = 3.0 cm B Fig 2.20: Parallelogram of forces acting on a crate Construct the parallelogram OARB using these lines OA and OB as adjacent sides and measure the diagonal OR = 6.9 cm. Using the scale of 1.0 cm = 50 N, we find the resultant force is 345 N. 44  NB: When the angle between two forces is very close to 0º or close to 180º, the parallelogram of forces folds down into a flattened form lying almost along a single straight line. The parallelogram rule of addition of slanting forces then gives the same result as the simple addition rule for parallel forces. Equilibrium of three non-parallel forces Consider a balloon suspended from a rigid support (Fig. 2.21). T W Fig. 2.21: Suspended balloon Supposing the wind exerts a horizontal force on the balloon. The balloon moves and stops with the string making an angle with the vertical line. The balloon is in equilibrium under the force due to the wind, the force due to the baloons own weight, and the tension in the string. The resultant of the wind force and the weight in the string is therefore equal and opposite to the tension in the string. Hence, the net resultant force is equal to zero at equilibrium. A O Ɵ Ɵ T Resultant of wind Weight force and weight Wind force R Force due to wind B W Fig. 2.22: Determining resultant force of suspended balloon The resultant force is known to act in the same straight line as the tension in the string. 45 Exercise 2.2 1. State the parallelogram law. 2. Explain the term equilibrium. 3. A box is moving constantly across a rough horizontal floor, pulled by two horizontal ropes. One of the ropes has a tension of 150 N and makes an angle 20º with the direction of motion of the box. The other rope with a tension force of 90 N makes an angle 40º with the direction of motion of the box. (a) Sketch the arrangement. (b) By scale drawing find the resultant forward force acting on the box. 2.6 Types of forces 2.6.1 Contact forces Contact forces are those forces that act at the point of contact between two objects, in contrast to body forces. Examples of contact forces are tension, normal action reaction force, air resistance, upthrust and frictional force. (a) Tension force Activity 2.11 To demonstrate the existence of tension forces in strings (Work in pairs) Materials: A string A pail with water Rigid support Steps 1. Hold one end of a string and your friend the other end. 2. Let both of you pull the ends away from each other as shown in Figure 2.23. What makes the string stiff? String Fig. 2.23: Pulling a string 46 3. Discuss your observations in step 2 with your Rigid support class partner. 4. Tie a string to the pail and hang it as shown in Figure 2.24. Tension 5. Discuss with your class partner any forces acting on the string and the pail in fig 2.24. 6. Sketch a diagram to show the direction in which the forces in step 2 and 4 are acting and state where this forces are applied. Pull of gravity 7. Compare your findings in step 5 and 6 with Fig. 2.24: Pail with water those of other pairs in the class. (b) Action and reaction forces Activity 2.12 To demonstrate action and reaction forces (Work in groups) Materials: A rigid support Two identical spring balances Steps 1. Hook one end of a spring balance A to a rigid support e.g a wall. Pull the other end until the spring shows a reading (see Fig 2.25(a)). 2. Discuss with your partner what happens to the rigid support. 3. Repeat the activity by using a similar spring B instead of a rigid support. 4. Pull the two springs until the reading on spring A is the same as before (see fig 2.25(b)). What reading is shown by spring B? What is the relationship between reading A and reading B? Explain. Spring A Pull Rigid support (a) 47  Pull Spring A Spring B Pull (b) Fig. 2.25: To demonstrate action and reaction forces When two springs are pulled in opposite direction they will show same reading. This implies that there are two equal forces which are acting in opposite directions in the two springs. Similarly, when a spring fixed on a rigid support is pulled, the support also pulled it with an equal and opposite force. These two equal forces that act in opposite directions are called action and reaction force. Another example that shows action and reaction force is when a book is placed on a table. The weight of the book provides action force while the table supporting the book provides reaction (Fig. 2.26) Reaction Table Book Action Fig. 2.26: A book on a table Activity 2.13 To demonstrate action and reaction forces (Work in groups) Materials A bench A wooden block Steps 1. Press the bench downwards with your thumb (Fig. 2.27). What do you feel? Suggest the kind of force acting on your thumb. Fig 2.27: Thumb pressing on a table 48 2. Place a wooden block on the bench. Suggest the forces that are acting on the wooden block and the direction in which it is acting. 3. Lift one side of the bench top upwards at an angle Ɵ. Ensure that the wooden block does not fall down.(see Fig 2.28) Bench top Wooden block Ɵ Fig 2.28: Wooden block at an angle 4. Identify the forces that are acting on the block of wood in step 3. When you press with some force on a wall with your thumb, the force you feel acting on your thumb by the table is called reaction force and the one acted by the thumb on the table is called action force. This activity has shown that the reaction and action forces are always perpendicular (normal) to the surface of the body exerting the reaction (Fig 2.29) Normal reaction Normal action Fig. 2.29: Normal reaction and action perpendicular to the surface Normal reaction and action also acts on the wooden block resting on the bar (step 2). The force due to the block is called the action force, while that due to the table is called normal reaction force. Since the block is at rest the two forces must be equal though acting in opposite directions. (Fig. 2.30). 49  Normal reaction Wooden block Table Action Fig. 2.30: Action and reaction forces The forces that are acting on a wooden block when the bench top is lifted at an angle Ɵ are shown in Fig 2.31. Normal reaction n ctio Fri el Centre dot ( ) a r all p e r c e an Fo the pl to Weight Action Ɵ Fig 2.31: Forces acting on a wooden block at an angle Note: The normal action force is the component of weight in an inclined body. Exercise 2.3 Give explanation to the following observations: (a) A balloon will start moving when the air inside it is released. (b) A garden sprinkler starts rotating immediately the water starts to jet out of nozzles. (c) When a gun is fired, the holder shakes as the gun tends to move backwards(recoil). 50 (c) Upthrust Activity 2.14 To demonstrate upthrust force (Work in groups) Materials Resort stand A spring balance Metre rule Beaker with water A solid mass. Steps 1. Suspend a solid in air using a spring balance (Fig 2.32(a). Note its weight. 2. Push the solid upwards gradually with your hand (Fig 2.32(b).What happens to the reading of the balance? Explain. 3. Release the solid and submerge it in a fluid such as water as shown in Fig 2.32(c). What is the weight of the solid? Note it down. Water (a) (b) (c) Fig. 2.32: To demonstrate upthrust force 4. Compare the weight of the solid in air and water. Note it down. Suggest the reason for your observation. 5. Use the observation you have made to explain why a ball held under water will jump into the air when released. 6. How will the weight compare if a different liquid e.g honey was used in place of water? Explain. When a solid hung on a spring balance is pushed upwards, the pointer moved upwards. Similary when the solid is submerged in water while still hanging on a spring balance, the pointer moves upwards due to upward force in water which acts from below the solid submerged in it. This upward force due to a fluid is called upthrust. 51 The difference between weight in air and weight in water (a liquid) is known as apparent loss in weight of a body. Apparent loss in weight = upthrust = wair - w liquid Example 2.3 A metal block weighs 20 N when in air and 14 N when submerged in water. Determine the upthrust on the block. Solution Upthrust = Weight in air - Weight in fluid = 20 N - 14 N =6N Example 2.4 A body weighs 3.5 N in air. When the body is completely immersed in water the upthrust on the body is 1.6 N. Find the weight of the body in water. Solution Upthrust = Wair – Wwater Wwater = Wair – upthrust = 3.5 – 1.6 = 1.9 N Factors affecting the magnitude of upthrust Magnitude of the upthrust depends on the following factors: Density of the liquid. As the density of the liquid increases, the upthrust increases and vice versa i.e a denser liquid exerts greater upthrust on an object than the less dense liquid. The volume of the body immersed in the liquid. The greater the height, and hence the volume of the portion of the object submerged into liquid, the greater the upthrust exerted on the body. 52 Upthrust and archmedes principle Activity 2.15 To investigate the relationship between upthrust and the weight of water displaced Materials An iron bar Wood block An overflow can (eureka can) A compression balance Steps 1. Weigh a uniform iron bar in air. Fill an overflow can (eureka can) with water. Allow the excess water to flow out through the spout. 2. Place an empty beaker on a compression balance under the spout and record its weight. 3. Immerse a quarter of the length (0.25 l) of the iron bar into water (Fig. 2.33). What happens to the water in the eureka can? Weight in water (Wwater) Upthrust Weight in air (Wair) Weight of displaced water + beaker 0 N Fig. 2.33: Effect of the weight of liquid displaced on upthrust 4. Record the upthrust and the weight of the liquid displaced as read from the spring balance and compression balance respectively. 5. Repeat the experiment with half length 0.5 l, three quarter length 0.75 l and full length l, of the iron bar immersed in the water. Tabulate your results as in the Table 2.1. 53  Table 2.1 Portion immersed Upthrust = Wair – Wwater (N) Weight of displaced water (N) 0 0.25 l 0.5 l 0.75 l 1l 6. Plot a graph of upthrust against weight of the water displaced. 7. Calculate the slope of the graph. What does the slope represent? What is the relationship between the water displaced and upthrust? 8. Now replace the iron bar with a block of wood and lower it into the water. What happens to the spring as you lower the block into the water? What is the reading on the spring balance when the block comes to rest? Whats the relationship between the weight of the block and the weight of the displaced fluid? The iron bar displaces some water which goes into the beaker. The graph is a straight line graph passing through the origin (Fig. 2.34). This shows that upthrust is directly proportional to the weight of liquid displaced. Upthrust (N) Weight of water displaced (N) Fig. 2.34: A graph of upthrust against weight of water displaced The slope of graph is 1. Therefore upthrust is equal to the weight of water displaced. Similar experiment with other liquids show similar results i.e. Upthrust = weight of liquid displaced 54  Experiments involving gases instead of liquids give results similar to ones obtained using liquids. Therefore for all fluids upthrust = weight of fluid displaced. Activity 2.15 is a verification of what is called Archimedes’ principle, which states states that: When a body is wholly or partially immersed in a fluid, it experiences an upthrust which is equal to the weight of the fluid displaced. Upthrust = weight of fluid displaced = Apparent loss in weight If a block of volume, v, hung from a spring balance using a thin string is lowered gradually into water of density ,ρ, in an overflow can, it displaces some water. The string becomes slack when the block of wood comes to rest, i.e the block is in equilibrium. Since the weight of the block in air minus upthrust is equal to the tension in the string, when the tension in the string is 0, the weight of the block in air is equal to the weight of the fluid displaced. Hence weight of the floating body = weight of fluid displaced. This is the law of floatation which is a special case of Archimedes' principle in that the apparent weight of a body is zero in the fluid. Note 1. The same effect is observed for a partially immersed cube. 2. The forces on the sides are equal but act in opposite directions hence the is no net force on the sides of the cube is zero. Example 2.5 A concrete block of mass 2.7 × 103 kg and volume 0.9 m3 is totally immersed in sea water of density 1.03 × 103 kg/m3. Find: (a) Weight of the block in air. (b) Weight of the block in sea water. Solution (a) Weight in air = mg = 2.7 ×