Grade 12 Physical Sciences PDF

VERSION 1 CAPS VERSION 1 CAPS EVERYTHING SCIENCE BY GRADE 12...

VERSION 1 CAPS VERSION 1 CAPS EVERYTHING SCIENCE BY GRADE 12 GRADE 12 WRITTEN BY VOLUNTEERS PHYSICAL SCIENCEs PHYSICAL SCIENCEs WRITTEN BY VOLUNTEERS WRITTEN BY VOLUNTEERS THIS TEXTBOOK IS AVAILABLE PHYSICAL SCIENCEs GRADE 12 ON YOUR MOBILE Everything Science EVERYTHING SCIENCE This book is available on web, mobi and Mxit. Read, check solutions and practise intelligently at www.everythingscience.co.za EVERYTHING SCIENCE GRADE 12 PHYSICAL SCIENCES VERSION 1 CAPS WRITTEN BY VOLUNTEERS  COPYRIGHT NOTICE Your freedom to legally copy this book You are allowed and encouraged to copy any of the Everything Maths and Everything Science textbooks. You can legally photocopy any page or even the entire book. You can download it from www.everythingmaths.co.za and www.everythingscience.co.za, read it on your phone, tablet, iPad, or computer. You can burn it to CD, put on your flash drive, e-mail it around or upload it to your website. 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The physical universe really contains incredible complexity. Yet, what is even more remarkable than this seeming complexity is the fact that things in the physical universe are knowable. We can investigate them, analyse them and under- stand them. It is this ability to understand the physical universe that allows us to trans- form elements and make technological progress possible. If we look back at some of the things that developed over the last century ñ space travel, advances in medicine, wireless communication (from television to mobile phones) and materials a thousand times stronger than steel we see they are not the consequence of magic or some inexplicable phenomena. They were all developed through the study and systematic application of the physical sciences. So as we look forward at the 21st century and some of the problems of poverty, disease and pollution that face us, it is partly to the physical sciences we need to turn. For however great these challenges seem, we know that the physical universe is know- able and that the dedicated study thereof can lead to the most remarkable advances. There can hardly be a more exciting challenge than laying bare the seeming complexity of the physical universe and working with the incredible diversity therein to develop prod- ucts and services that add real quality to peopleís lives. Physical sciences is far more wonderful, exciting and beautiful than magic! It is every- where.  SPONSOR This textbook was developed with corporate social investment funding from MMI Holdings. Well structured, impactful Corporate Social Investment (CSI) has the ability to contribute positively to nation building and drive positive change in the communities. MMI’s commitment to social investment means that we are constantly looking for ways in which we can assist some of South Africa’s most vulnerable citizens to expand their horizons and gain greater access to life’s opportunities. This means that we do not view social investment as a nice to have or as an exercise in marketing or sponsorship but rather as a critical part of our contribution to society. The merger between Metropolitan and Momentum was lauded for the complementary fit between two companies. This complementary fit is also evident in the focus areas of CSI programmes where Metropolitan and Momentum together cover and support the most important sectors and where the greatest need is in terms of social participation. HIV/AIDS is becoming a manageable disease in many developed countries but in a country such as ours, it remains a disease where people are still dying of this scourge unnecessarily. Metropolitan continues to make a difference in making sure that HIV AIDS moves away from being a death sentence to a manageable disease. Metropolitan’s other focus area is education which remains the key to economic prosperity for our country. 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Your can check your progress and mastery for every topic in the book and use it to help you to manage your studies and target your weaknesses. You can also use your dashboard to show your teachers, parents, universities or bursary institutions what you have done during the year. Contents 1 Skills for science 6 1.1 The development of a scientific theory.................. 6 1.2 Scientific method............................. 7 1.3 Data and data analysis.......................... 13 1.4 Laboratory safety procedures....................... 16 2 Momentum and impulse 20 2.1 Introduction................................ 20 2.2 Momentum................................ 21 2.3 Newton’s Second Law revisited...................... 30 2.4 Conservation of momentum....................... 35 2.5 Impulse.................................. 53 2.6 Physics in action: Impulse........................ 62 2.7 Chapter summary............................. 65 3 Vertical projectile motion in one dimension 72 3.1 Introduction................................ 72 3.2 Vertical projectile motion......................... 72 3.3 Chapter summary............................. 101 4 Organic molecules 108 4.1 What are organic molecules?....................... 108 4.2 Organic molecular structures....................... 108 4.3 IUPAC naming and formulae....................... 131 4.4 Physical properties and structure..................... 162 4.5 Applications of organic chemistry.................... 179 4.6 Addition, elimination and substitution reactions............. 186 4.7 Plastics and polymers........................... 196 4.8 Chapter summary............................. 213 5 Work, energy and power 220 5.1 Introduction................................ 220 5.2 Work.................................... 220 5.3 Work-energy theorem........................... 230 5.4 Conservation of energy.......................... 239 5.5 Power................................... 245 5.6 Chapter summary............................. 250 6 Doppler effect 254 6.1 Introduction................................ 254 6.2 The Doppler effect with sound...................... 255 6.3 The Doppler effect with light....................... 263 6.4 Chapter summary............................. 266 7 Rate and Extent of Reaction 270 7.1 Introduction................................ 270 7.2 Rates of reaction and factors affecting rate................ 270 7.3 Measuring rates of reaction........................ 286 7.4 Mechanism of reaction and catalysis................... 291 7.5 Chapter summary............................. 295 8 Chemical equilibrium 300 8.1 What is chemical equilibrium?...................... 300 8.2 The equilibrium constant......................... 304 8.3 Le Chatelier’s principle.......................... 313 8.4 Chapter Summary............................. 331 9 Acids and bases 334 9.1 Acids and bases.............................. 334 9.2 Acid-base reactions............................ 349 9.3 pH..................................... 354 9.4 Titrations.................................. 359 9.5 Applications of acids and bases..................... 367 9.6 Chapter summary............................. 371 10 Electric circuits 376 10.1 Introduction................................ 376 10.2 Series and parallel resistor networks (Revision)............. 376 10.3 Batteries and internal resistance..................... 387 10.4 Evaluating internal resistance in circuits................. 392 10.5 Extension: Wheatstone bridge [Not examinable]............ 401 10.6 Chapter summary............................. 402 11 Electrodynamics 408 11.1 Introduction................................ 408 11.2 Electrical machines - generators and motors............... 408 11.3 Alternating current............................ 416 11.4 Chapter summary............................. 422 12 Optical phenomena and properties of matter 426 12.1 Introduction................................ 426 12.2 The photoelectric effect.......................... 426 12.3 Emission and absorption spectra..................... 435 12.4 Chapter summary............................. 441 13 Electrochemical reactions 444 13.1 Revision of oxidation and reduction................... 444 13.2 Writing redox and half-reactions..................... 445 13.3 Galvanic and electrolytic cells...................... 449 13.4 Processes in electrochemical cells.................... 462 13.5 The effects of current and potential on rate and equilibrium...... 466 13.6 Standard electrode potentials....................... 467 13.7 Applications of electrochemistry..................... 481 13.8 Chapter summary............................. 488 14 The chemical industry 494 14.1 Introduction................................ 494 14.2 Nutrients.................................. 494 14.3 Fertilisers................................. 495 14.4 The fertiliser industry........................... 500 14.5 Alternative sources of fertilisers...................... 506 14.6 Fertilisers and the environment...................... 509 14.7 Chapter summary............................. 511 Solutions to exercises 513 List of Definitions 525 Image Attribution 527  CHAPTER 1 Skills for science 1.1 The development of a scientific theory 6 1.2 Scientific method 7 1.3 Data and data analysis 13 1.4 Laboratory safety procedures 16  1 Skills for science This book deals with the physical sciences - physics and chemistry. All the sciences are based in the use of experiment and testing to understand the world around us better. The scien- tific method requires us to constantly re-examine our understanding, by testing new evidence with our current theories and making changes to those theories if the evidence does not meet the test. The scientific method therefore is the powerful tool you will use throughout the physical sciences. In this chapter you will learn how to gather evidence using the scientific Figure 1.1: An ultraviolet image of the Sun. method. These skills will then be used throughout this textbook to test scientific theories and practices. 1.1 The development of a scientific theory ESCHQ The most important, and most exciting, thing about science and scientific theories is that they are not fixed. Hypotheses are formed and carefully tested, leading to scientific theories that explain those observations and predict results. The results are not made to fit the hypotheses. If new information comes to light with the use of better equipment, or the results of other experiments, this new information is used to improve and expand current theories. If a theory is found to have been incorrect it is changed to fit this new information. The data should never be made to fit the theory, if the data does not fit the theory then the theory is reworked or discarded. Although this changing of opinion is often taken for inconsistency, it is this very willingness to adapt that makes science useful, and allows new discoveries to be made. Remember that the term theory has a different meaning in science. A scientific theory is not like your theory of about why you can only ever find one sock. A scientific theory is one that has been tested and proven through repeated experiment and data. Scientists are constantly testing the data available, as well as commonly held beliefs, and it is this constant testing that allows progress, and improved theories. Gravity ESCHR The theory of gravity has been slowly developing since the beginning of the 16th century. Galileo Galilei is credited with some of the earliest work. At the time it was widely believed that heavier objects accelerated faster toward the earth than light objects did. Galileo had a hypothesis that this was not true, and performed experiments to prove this. Galileo’s work allowed Sir Isaac Newton to hypothesise not only a theory of gravity on earth, but that gravity is what held the planets in their orbits. Newton’s theory was used by John Couch Adams and Urbain Le Verrier to predict the planet Neptune in the solar system and this prediction was proved experimentally when Neptune was discovered by Johann Gottfried Galle. 6 1.1. The development of a scientific theory Although a large majority of gravitational motion could be explained by Newton’s FACT theory of gravity, there were things that did not fit. But although a newer theory that Robert Boyle should be a familiar name to better fits the facts was eventually proved by Albert Einstein, Newton’s gravitational you. Boyle’s law came theory is still successfully used in many applications where the masses, speeds and about from his air energies are not too large. pump experiments, where he discovered that pressure is Thermodynamics ESCHS inversely proportional to volume at a constant temperature The principles of the three rules of thermodynamics describe how energy works, on all (p ∝ V1 at constant T). size levels (from the workings of the Earth’s core, to a car engine). The basis for these three rules started as far back as 1650 with Otto von Guericke. He had a hypothesis that a vacuum pump could be made, and proved this by making one. In 1656 Robert Boyle and Robert Hooke used this information and built an air pump. Over the next 150 years the theory was expanded on and improved. Denis Papin built a steam pressuriser and release valve, and designed a piston cylinder and engine, which Thomas Savery and Thomas Newcomen built. These engines inspired the study of heat capacity and latent heat. Joseph Black and James Watt increased the steam engine efficiency and it was their work that Sadi Carnot (considered the father of ther- modynamics) studied before publishing a discourse on heat, power, energy and engine efficiency in 1824. This work by Carnot was the beginning of modern thermodynamics as a science, with the first thermodynamics textbook written in 1859, and the first and second laws of thermodynamics being determined in the 1850s. Scientists such as Lord Kelvin, Max Planck, J. Willard Gibbs (all names you should recognise) among many many others studied thermodynamics. Over the course of 350 years thermodynamics has devel- oped from the building of a vacuum pump, to some of the most important fundamental laws of energy. 1.2 Scientific method ESCHT The scientific method is the basic skill process in the world of science. Since the beginning of time humans have been curious as to why and how things happen in the world around us. The scientific method provides scientists with a well structured scientific platform to help find the answers to their questions. Using the scientific method there is no limit as to what we can investigate. The scientific method can be summarised as follows: 1. Ask a question about the world around you. 2. Do background research on your questions. 3. Make a hypothesis about the event that gives a sensible result. You must be able to test your hypothesis through experiment. 4. Design an experiment to test the hypothesis. These methods must be repeatable and follow a logical approach. 5. Collect data accurately and interpret the data. You must be able to take measure- ments, collect information, and present your data in a useful format (drawings, explanations, tables and graphs). 6. Draw conclusions from the results of the experiment. Your observations must be made objectively, never force the data to fit your hypothesis. 7. Decide whether your hypothesis explains the data collected accurately. 8. If the data fits your hypothesis, verify your results by repeating the experiment or getting someone else to repeat the experiment. 9. If your data does not fit your hypothesis perform more background research and Chapter 1. Skills for science 7 FACT make a new hypothesis. In science we never ’prove’ a hypothesis Remember that in the development of both the gravitational theory and thermody- through a single namics, scientists expanded on information from their predecessors or peers when experiment because developing their own theories. It is therefore very important to communicate findings there is a chance that you made an error to the public in the form of scientific publications, at conferences, in articles or TV somewhere along the or radio programmes. It is important to present your experimental data in a specific way. What you can say format, so that others can read your work, understand it, and repeat the experiment. is that your results SUPPORT the original 1. Aim: A brief sentence describing the purpose of the experiment. hypothesis. 2. Apparatus: A list of the apparatus. 3. Method: A list of the steps followed to carry out the experiment. 4. Results: Tables, graphs and observations about the experiment. 5. Discussion: What your results mean. 6. Conclusion: A brief sentence concluding whether or not the aim was met. A hypothesis A hypothesis should be specific and should relate directly to the question you are ask- ing. For example if your question about the world was, why do rainbows form, your hypothesis could be: Rainbows form because of light shining through water droplets. After formulating a hypothesis, it needs to be tested through experiment. An incor- rect prediction does not mean that you have failed. It means that the experiment has brought some new facts to light that you might not have thought of before. Activity: Analysis of the scientific method. Identify a problem or a question Conduct background research introduction / literature review Identify variables Three types of variables 1) Independent - changed by the investigator 2) Dependent - changes according to the independent variable 3) Controlled - kept constant throughout the experiment Make a hypothesis Generate aim/prediction Revise and modify the original hypothesis Design an experiment or generate a new one Observation and collection of data Analysis and presentation of data (tables, Repeat graphs, drawing, written explanations) Make conclusions Data supports hypothesis Data does not support hypothesis Accept hypothesis Reject hypothesis Figure 1.2: Overview of scientific method. 8 1.2. Scientific method Break into groups of 3 or 4 and study the flow diagram provided, then discuss the questions that follow. 1. Once you have a problem you would like to study, why is it important to conduct background research before doing anything else? 2. What is the difference between a dependent, independent, and controlled vari- able and why is it important to identify them? 3. What is the difference between identifying a problem, a hypothesis, and a scien- tific theory? 4. Why is it important to repeat your experiment if the data fits the hypothesis? Activity: Designing your own experiment Recording and writing up an investigation is an integral part of the scientific method. In this activity you are required to design your own experiment. Use the information provided below, and the flow diagram in the previous experiment to help you design your experiment. The experiment should be handed in as a 1 - 2 page report. Below are basic steps to follow when designing your own experiment. 1. Ask a question which you want to find an answer to. 2. Perform background research on your topic of choice. 3. Write down your hypothesis. 4. Identify variables important to your investigation: those that are relevant, those you can measure or observe. 5. Decide on the independent and dependent variables in your experiment, and those variables that must be kept constant. 6. Design the experiment you will use to test your hypothesis: State the aim of the experiment. List the apparatus (equipment) you will need to perform the experiment. Write the method that will be used to test your hypothesis – in bullet format – in the correct sequence, with each step of the experiment numbered. Indicate how the results should be presented, and what data is required. Reading instruments ESCHV Before you perform an experiment you should be comfortable with certain apparatus that you will be using. The following pages give some commonly used apparatus and how to use them. 1 cm 10 mm Most rulers you find have two sets of lines. z}|{. z}|{ on them. You can ignore those with the numbers spaced further apart. We only work in the metric system and those are for the imperial system. The closest together lines are for millimetres, the thicker lines are for 5 mm and the thicker, longer lines Figure 1.3: The end of a ruler. with numbers next to them mark off every 10 mm (1 cm). Chapter 1. Skills for science 9  A thermometer can have one, or two sets of numbers on it. If it has two sets of numbers one will be in Celsius, and one will be in Fahrenheit. We use Celsius, so you can ignore the side with a larger temperature range. In Figure 1.4 you can ignore the right-hand side. Looking on the left you can see that the red line (coloured ethanol here) is next to the fourth line above 0 ◦ C. Each small line is 1 ◦ C, so the temperature is 4 ◦ C. Figure 1.4: Reading a thermometer. Laboratory thermometers will go to much higher temperatures than those used for measuring the temperature outside, or your body temperature. It is important to make sure that the thermometer you are using can handle the temperature you will be measuring too. If not, do not use that thermometer as you will break it. Make sure your thermometer is upright whenever you use it in an experiment, to avoid incorrect results. Figure 1.5: A laboratory style thermometer. See video: 27HM at www.everythingscience.co.za Different scales have different functions. However, a basic function of all scales is a tare button. This zeros the balance. It is important that you zero the balance before you take any measurements. If you are weighing something on a piece of paper you should tare the bal- ance with the piece of paper on it, and weigh the sub- stance. Make sure you check the units that your scale is weighing in. If you want your value to be accurate to ,00 g then the scale must measure to that accuracy. A scale that measures in mg would be best. Figure 1.6: A scale (also referred to as a balance). The surface of the water (the meniscus) is slightly higher at the edges of a container than in the middle. This is due to surface tension and the interaction between the water and the edge of the container (Figure 1.7). When measuring the volume in a burette or measuring cylinder or pipette you should look at the bottom of the meniscus. Where that lies is where you measure the volume. So in this example the meniscus is on the fifth line below the large line that represents 1 ml. Therefore the volume is 1,5 ml. It is also possible that the liquid being measured has greater internal forces than those between it and the container. Then the meniscus would be higher in the middle than at the sides, and you would use the top of the meniscus to measure your volume. Figure 1.7: The meniscus of water in a burette. 10 1.2. Scientific method  A burette is used to accurately measure the volume of a liquid added in an experiment. The valve at the bottom allows the liquid to be added drop-by-drop, and the initial and final volume can be measured so that the total volume added is known. More information about burettes is given to you in your first titration experiment this year in Chapter 9. Figure 1.8: A burette. A measuring cylinder is used to measure volumes that you want accurate to the nearest millilitre or so. It is not a highly accurate way of measuring volumes. The volume in a measuring cylinder is measured in the same way as for a burette, the dif- ference is that in a measuring cylinder the smallest volume would be at the bottom, while the largest would be at the top. Figure 1.9: A measuring cylinder with water. There are two types of pipettes you might encounter this year. A volumetric pipette has a large bulb, marked with the set volume it can measure. Above the bulb on these pipettes there is a line. For a 5 ml volumetric pipette, when the meniscus of your liquid sits on the line, then the volume in that pipette is 5 ml. A graduated pipette has the same type of marking you see on a burette. The top is 0 ml, and the volume increases as you move down the pipette. In this pipette you should fill the pipette to near the 0 ml line and make a note of the volume. You can then add the desired volume, stopping when the volume in the pipette has decreased by the required amount. Figure 1.10: A 5 ml volumetric pipette. Figure 1.11: A graduated pipette. Chapter 1. Skills for science 11  Performing experiments ESCHW A learner wondered whether the rate of evaporation of a substance was related to the boiling point of the substance. Having done background research they realised that the boiling point of a substance is linked to the intermolecular forces within the substance. They know that greater intermolecular forces require more energy to overcome. This led them to form the following hypothesis: The larger the intermolecular forces of a substance the higher the boiling point. There- fore, if a substance has higher boiling point it will have a slower rate of evaporation. Perform the following experiment that the learner designed to test that hypothesis. Experiment: Boiling points and rate of evaporation: Part 1 Aim: To determine whether the rate of evaporation of a substance is related to its boiling point. Apparatus: You will need the following items for this experiment: 220 ml water, 20 ml methylated spirits, 20 ml nail polish remover, 20 ml water, 20 ml ethanol One 250 ml beaker, four 20 ml beakers, a thermometer, a stopwatch or clock Method: WARNING! All alcohols are toxic, methanol is particularly toxic and can cause blindness, coma or death. Handle all chemicals with care. 1. Place 200 ml of water into the 250 ml beaker and move the beaker to sunny spot. Place the 1 2 thermometer in the water. 2. Label the four 20 ml beakers 1 - 4. These beakers should be marked. 20 ml 20 ml 3. Place 20 ml methylated spirits into beaker 1, methylated nail polish 20 ml nail polish remover into beaker 2, 20 ml spirits remover water into beaker 3 and 20 ml ethanol into 3 4 beaker 4. 4. Carefully move each beaker to the warm (sunny) spot. 5. Observe each dish every two minutes. Note the 20 ml 20 ml water ethanol volume in the beaker each time. 6. Continue making observations for 20 minutes. Record the volumes in a table. Results: Record your observations from the investigation in a table like the one below. Methylated Nail polish Substance Water Ethanol spirits remover Boiling point (◦ C) 78,5 56,5 100 78,4 Initial volume (ml) 20 20 20 20 2 min 4 min 6 min 12 1.2. Scientific method 1.3 Data and data analysis ESCHX In order to analyse the data obtained during experiments it is often necessary to convert that data into different representations. One type of representation is a graph. A few examples are given here. How to draw graphs in science ESCHY For all graphs plotted from experimental data it is important to remember that you should never connect the dots. Data will never follow a line or curve perfectly. By obtaining multiple experimental data points any discrepancies in each data point can be removed. The line added after the points are plotted should be a best fit line that can then be used to more accurately determine further information. Features of graphs you plot: An appropriate scale is used for each axis so that the plotted points use most of the axis/space (work out the range of the data and the highest and lowest points). The scale must remain the same along the entire axis and should use easy inter- vals such as 10’s, 20’s, 50’s. Use graph paper for accuracy. Each axis must be labelled with what is shown on the axis and must include the appropriate units in brackets, e.g. Temperature (◦ C), time (seconds), height (cm). The independent variable is generally plotted along the x-axis, while the depen- dent variable is generally plotted along the y-axis. Each point has an x and y co-ordinate and is plotted with a symbol which is big enough to see, e.g. a cross or circle. A best fit line is then added to the graph. Do not start the graph at the origin unless there is a data point for (0,0), or if the best fit line runs through the origin. The graph must have a clear, descriptive title which outlines the relationship between the dependent and independent variable. If there is more than one set of data drawn on a graph, a different symbol (and/or colour) must be used for each set and a key or legend must define the symbols. Use line graphs when the relationship between the dependent and independent variables is continuous. For a line graph, you can draw a line of best fit with a ruler. The number of points are distributed fairly evenly on each side of the line (see Figure 1.12). With an exponential graph (when the points appear to be following a curve) you can draw a best fit line freehand (see 1.13). Change in temperature with time Change in distance (due to acceleration) with time 10 8 Temperature (◦ C) distance (meters) 6 6. 4 4 2 2 0 2 4 6 8 10 0 10 20 30 time (seconds) time (seconds) Figure 1.12: A straight line graph of the change in Figure 1.13: A graph with an exponential best temperature with time. fit line. Chapter 1. Skills for science 13  Remember that without units much of our work as scientists would be meaningless. We need to express our thoughts clearly and units give meaning to the numbers we measure and calculate. Depending on which units we use, the numbers are different. For example if you have 12 water, it means nothing. You could have 12 ml of water, 12 litres of water, or even 12 bottles of water. Units are an essential part of the language we use. Units must be specified when expressing physical quantities. Qualitative and quantitative analysis ESCHZ Qualitative analysis In qualitative research you look at the quality of a substance. At how it looks compared to other cases. You do an in-depth analysis of a specific case, and then make an informed decision about similar cases. For example, a qualitative study of the study habits of university students could include only a few people, or over twenty. Each person would be asked in-depth questions about how they study, and what works for them, and a general, informed assertion can then be made about these study habits. Quantitative analysis In quantitative research you look at specific numbers. You study a large group (data sample) and do statistical analyses of the group, with experimental controls, manipu- lation of variables, and the modelling and analysis of your data. For example, a quantitative study of those same study habits of university students would include a large number of people, for statistical relevance. The questions asked would include raw data of actual studying hours, and the most productive study times. These data points would then be analysed using graphical models. Experiment: Boiling points and rate of evaporation: Part 2 Results: Now that you remember how to plot graphs, go back to the data you obtained during the previous experiment. On the same set of axes, plot a graph of the volume (ml) versus the time (min) for each substance. Analysis of results or discussion: Analyse the results plotted on the graphs and the table. Which substance has the fastest decrease in volume? Which has the slowest decrease? Discuss if there are any relationships between your independent (time) and de- pendent (volume) variables (what type of graph did you plot?). It is important to look for patterns/trends in your graphs or tables and describe these clearly in words. Compare the different graphs and the different rates of evaporation to the boiling points of the substances. Evaluation of results: This is where you answer the question Is the rate of evaporation of a substance related to its boiling point? You need to carefully consider the results: 14 1.3. Data and data analysis  – Were there any unusual results? If so then these should be discussed and possible reasons given for them. – Discuss how you ensured the validity and reliability of the investigation. Was it a fair test (validity) and if the experiment were to be repeated would the results obtained be similar (reliability)? The best way to ensure reliability is to repeat the experiment several times and obtain an average. – Discuss any experimental errors that may have occurred during the experi- ment. These can include errors in the methods and apparatus. Make sug- gestions on what could be done differently next time. – Did this experiment yield qualitative or quantitative results? Conclusions based on scientific evidence ESCJ2 Experiment: Boiling points and rate of evaporation: Part 3 Conclusion: You have your results, and the analysis of your results. Now you need to look back at your hypothesis. The conclusion needs to link the results to the aim and hypothesis. In a short para- graph, write down if what was observed supports or reject the hypothesis. If your original hypothesis does not match up with the final results of your experiment, do not change the hypothesis. Instead, try to explain what might have been wrong with your original hypothesis. What information did you not have originally that caused you to be wrong in your prediction. Activity: Conclusions and bias Read the following extract on bias taken from radiology.rsna.org (01/09/13), and an- swer the questions that follow: Bias is a form of systematic error that can affect scientific investigations and distort the measurement process. A biased study loses validity in relation to the degree of the bias. While some study designs are more prone to bias, its presence is universal. It is difficult or even impossible to completely eliminate bias. In the process of attempting to do so, new bias may be introduced or a study may be rendered less generalizable. Therefore, the goals are to minimize bias and for both investigators and readers to comprehend its residual effects, limiting misinterpretation and misuse of data. In the light of the above quotation, why is it important for you to clearly state all your experimental parameters? Why is it important never to try and make the data fit your hypothesis? Look again at the conclusions you drew during your experiment. – Are they biased? – Did you make any assumptions based on preconceived ideas? – Is the data presented in a clear way that does not force a reader to agree with your conclusions? Chapter 1. Skills for science 15  Activity: Different explanations for the same set of experimental data. To prevent bias, it is important to be able to look at the same information in different ways, to make sure your conclusion is the most logical one. Divide into groups of three or four and compare the conclusions you drew from the boiling points and rate of evaporation experiment, and answer the questions that fol- low: Did anyone in the group draw a different conclusion from the one you drew? If yes, discuss the merits and short-falls of the different conclusions. Did your conclusion match what you were expecting to find from the hypothesis? Can you think of any other explanation that would explain your data? Activity: Methods of knowing used by non-scientists. Research one of the following topics and report your findings to the class in a five minute oral presentation: Traditional medicines. Navigation and knowledge of the seasons, from the stars. Designing a model ESCJ3 Sometimes a system is too large to be studied, or too difficult to recreate experimen- tally. In these cases it is possible to design a model based on a smaller system, that fits the data observed for the larger system. Here are some key points to remember when designing a model: A model is a testable idea that describes a large system that is not easily testable. The model should be able to explain as many observations of the large system as possible, and yet be relatively simple. An example of a model was the spherical model of the Earth, rather than a flat one. Many educated people of the day (in the late 1400s) knew that the Earth could not be flat due to observations that did not fit. A spherical Earth model was proposed, which was testable on a small scale. The model explained many previously unexplained phenomenon (such as that ships appeared to sink over the horizon, regardless of the direction of travel). The model was further verified by the shape of the Earth’s shadow on the moon during lunar eclipses. 1.4 Laboratory safety procedures ESCJ4 Laboratories have rules that are enforced as safety precautions. These rules are: Before doing any scientific experiment make sure that you know where the fire extinguishers are in your laboratory and there should also be a bucket of sand to extinguish fires. You are responsible for your own safety as well as the safety of others in the laboratory. Never perform experiments alone. 16 1.4. Laboratory safety procedures  Do not eat or drink in the laboratory. Do not use laboratory glassware to eat or drink from. Ensure that you are dressed appropriately whenever you are near chemicals: – hair tied back – no loose or flammable clothing – closed shoes – gloves – safety glasses Always behave responsibly in the laboratory. Do not run around or play practical jokes. Always check the safety data of any chemicals you are going to use. Never smell, taste or touch chemicals unless instructed to do so. Do not take chemicals from the laboratory. Only perform the experiments that your teacher instructs you to. Never mix chemicals for fun. Follow the given instructions exactly. Do not mix up steps or try things in a different order. Care needs to be taken when pouring liquids or powders from one container to another. When spillages occur you need to call the teacher immediately to assist in cleaning up the spillage. Care needs to be taken when using strong acids and bases. A good safety pre- caution is to have a solution of sodium bicarbonate in the vicinity to neutralise any spills as quickly as possible. If you spill on yourself wash the area with lots of water and seek medical attention. Never add water to acid. Always add the acid to water. When working with chemicals and gases that are hazardous, a fume cupboard should be used. Always work in a well ventilated area. When you are instructed to smell chemicals, place the container on a laboratory bench and use your hand to gently waft (fan) the vapours towards you. Be alert and careful when handling chemicals, hot glassware, etc. Never heat thick glassware as it will break. (For example, do not heat measuring cylinders). When lighting a Bunsen burner the correct procedure needs to be followed: securely connect the rubber tubing to the gas pipe, have your matches ready, turn on the gas, then light a match and the bunsen burner. Do not leave Bunsen burners and flames unattended. When heating substances in a test tube do not overheat the solution. Remember to face the mouth of the test tube away from you and members of your group when heating a test tube. Always check with your teacher how to dispose of waste. Chemicals should not be disposed of down the sink. Ensure all Bunsen burners are turned off at the end of the practical and all chem- ical containers are sealed. Hazard data ESCJ5 Before starting any experiment, research the chemicals and materials you will be using in that experiment. Laboratory chemicals can be dangerous, and you should study the safety data sheets should before working with a chemical. The data sheets can be found at http://www.msds.com/. Before working with a chemical, you should also make sure that you know how to, and have the facilities available to, dispose of those chemicals correctly and safely. Many chemicals cannot simply be washed down the sink. If you follow these few simple guidelines you can safely carry out experiments in the laboratory without endangering yourself or others around you. Chapter 1. Skills for science 17  CHAPTER 2 Momentum and impulse 2.1 Introduction 20 2.2 Momentum 21 2.3 Newton’s Second Law revisited 30 2.4 Conservation of momentum 35 2.5 Impulse 53 2.6 Physics in action: Impulse 62 2.7 Chapter summary 65  2 Momentum and impulse 2.1 Introduction ESCJ6 In Grade 10 we studied motion but not what caused the motion, in Grade 11 we learnt about forces and how they can alter the motion of an object. In this chapter we will focus on what happens when two bodies undergo a contact interaction and how their motion is affected. We learn more about how force and motion are related. We are introduced to two new concepts, momentum and impulse. We can begin by considering some scenarios to set the context. Most people have some intuition for physics based on their everyday experiences but they haven’t for- malised it. We can use our intuitive answers to lead into more structured thinking about physical events. Everyone has experienced a mosquito landing on their arm and it can happen quite unnoticed. Consider the case of a falcon landing on your arm (ignore the sharp claws for now). You would definitely notice, why? What makes a mosquito different to a falcon? Would you still notice if the mosquito flew the same way as a falcon, or if the falcon copied the flight of a mosquito before landing? You probably would still notice, but try to think about what makes them so different. Look at a motorcycle, motorcar and truck. Which of them is more likely to result in less damage in a collision situation, why? What factors would you change to reduce potential damage. The factors that come up in these considerations are how fast things are moving and how massive they are. A falcon moving at the same speed as a mosquito still has a much larger mass. Even if a mosquito moved as fast as a falcon it wouldn’t bother us because the mass of a mosquito is so small. If a motorcycle, motorcar and truck were all moving at the same speed then it would be much safer to be in a collision with the motorcycle but a truck doesn’t have to be moving as fast as a motorcycle to have a huge impact in a collision because of its large mass. 20 2.1. Introduction Why is the Moon’s orbit largely unaffected when TIP it is hit by asteroid? Momentum transfer doesn’t require a contact interaction but There is an interplay between mass and speed (ve- we won’t consider any locity to be precise) that governs what would hap- non-contact scenarios pen if these objects came into contact with an- in this chapter. other object. There are two quantities that depend on mass and velocity, kinetic energy and momen- tum. Kinetic energy is something that we learnt about previous. Momentum is different to kinetic energy and is what we will focus on in the first part of this chapter. In the second part we will cover some of the differences between kinetic en- ergy and momentum. Key linked concepts Units and unit conversions — Physical Sciences, Grade 10, Science skills Equations — Mathematics, Grade 10, Equations and inequalities Techniques of vector addition — Physical Sciences, Grade 10, Vectors and scalars Newton’s laws — Physical Sciences, Grade 11, Forces 2.2 Momentum ESCJ7 Momentum is a physical quantity which is closely related to forces. Momentum is a property which applies to moving objects, in fact it is mass in motion. If something has mass and it is moving then it has momentum. DEFINITION: Momentum The linear momentum of a particle (object) is a vector quantity equal to the product of the mass of the particle (object) and its velocity. The momentum (symbol ~p ) of an object of mass m moving at velocity v is: ~p = m~v Momentum is directly proportional to both the mass and velocity of an object. A small car travelling at the same velocity as a big truck will have a smaller momentum than the truck. The smaller the mass, the smaller the momentum for a fixed velocity. If the mass is constant then the greater the velocity the greater the momentum. The momentum will always be in the same direction as the velocity because mass is a scalar not a vector. Vector nature of momentum ESCJ8 A car travelling at 120 km·hr−1 will have a larger momentum than the same car travel- ling at 60 km·hr−1. Momentum is also related to velocity; the smaller the velocity, the smaller the momentum. Different objects can also have the same momentum, for example a car travelling slowly can have the same momentum as a motorcycle travelling relatively fast. We can easily demonstrate this. Chapter 2. Momentum and impulse 21 TIP Consider a car of mass 1000 kg with a ve- Now consider a motorcycle, also travel- A vector multiplied by locity of 8 m·s−1 (about 30 km·hr−1 ) East. ling East, of mass 250 kg travelling at a scalar has the same direction as the The momentum of the car is therefore: 32 m·s−1 (about 115 km·hr−1 ). The mo- original vector but a mentum of the motorcycle is: magnitude that is scaled by the ~p = m~v ~p = m~v multiplicative factor. = (1000) (8) = 250 kg 32 m·s−1

= 8000 kg·m·s−1 East = 8000 kg·m·s−1 East Even though the motorcycle is considerably lighter than the car, the fact that the motor- cycle is travelling much faster than the car means that the momentum of both vehicles is the same. From the calculations above, you are able to derive the unit for momentum as kg·m·s−1. Momentum is also vector quantity, because it is the product of a scalar (m) with a vector (~v ). This means that whenever we calculate the momentum of an object, we should include the direction of the momentum. See video: 27HN at www.everythingscience.co.za Worked example 1: Momentum of a soccer ball QUESTION A soccer ball of mass 420 g is kicked at 20 m·s−1 towards the goal post. Cal- culate the momentum of the ball. SOLUTION Step 1: Identify what information is given and what is asked for The question explicitly gives: the mass of the ball, and the velocity of the ball. The mass of the ball must be converted to SI units. 420 g = 0,42 kg We are asked to calculate the momentum of the ball. From the definition of momen- tum, ~p = m~v we see that we need the mass and velocity of the ball, which we are given. 22 2.2. Momentum Step 2: Do the calculation We calculate the magnitude of the momentum of the ball, ~p = m~v = (0,42) (20) = 8,40 kg·m·s−1 Step 3: Quote the final answer We quote the answer with the direction of motion included, ~p = 8,40 kg·m·s−1 in the direction of the goal post. Worked example 2: Momentum of a cricket ball QUESTION A cricket ball of mass 160 g is bowled at 40 m·s−1 towards a batsman. Calculate the momentum of the cricket ball. SOLUTION Step 1: Identify what information is given and what is asked for The question explicitly gives the mass of the ball (m = 160 g = 0,16 kg), and the velocity of the ball (~v = 40 m·s−1 towards the batsman) To calculate the momentum we will use ~p = m~v. Step 2: Do the calculation ~p = m~v = (0,16) (40) = 6,4 kg·m·s−1 = 6,4 kg·m·s−1 in the direction of the batsman Chapter 2. Momentum and impulse 23  Step 3: Quote the final answer The momentum of the cricket ball is 6,4 kg·m·s−1 in the direction of the batsman. Worked example 3: Momentum of the Moon QUESTION The centre of the Moon is approximately 384 400 km away from the centre of the Earth and orbits the Earth in 27,3 days. If the Moon has a mass of 7,35 × 1022 kg, what is the magnitude of its momentum (using the definition given in this chapter) if we assume a circular orbit? The actual momentum of the Moon is more complex but we do not cover that in this chapter. SOLUTION Step 1: Identify what information is given and what is asked for The question explicitly gives the mass of the Moon (m = 7,35 × 1022 kg) the distance to the Moon (384 400 km = 384 400 000 m = 3,844 × 108 m) the time for one orbit of the Moon (27,3 days = 27,3 × 24 × 60 × 60 = 2,36 × 106 s) We are asked to calculate only the magnitude of the momentum of the Moon (i.e. we do not need to specify a direction). In order to do this we require the mass and the magnitude of the velocity of the Moon, since ~p = m~v. Step 2: Find the magnitude of the velocity of the Moon ∆x The magnitude of the average velocity is the same as the speed. Therefore: v = ∆t We are given the time the Moon takes for one orbit but not how far it travels in that time. However, we can work this out from the distance to the Moon and the fact that the Moon has a circular orbit. 24 2.2. Momentum Using the equation for the circumference, Combining the distance travelled by the C, of a circle in terms of its radius, we Moon in an orbit and the time taken by can determine the distance travelled by the Moon to complete one orbit, we can the Moon in one orbit: determine the magnitude of the Moon’s velocity or speed, C = 2πr   ∆x = 2π 3,844 × 108 v= ∆t = 2,42 × 109 m C = T 2,42 × 109 m = 2,36 × 106 s = 1,02 × 103 m·s−1. Step 3: Finally calculate the momentum and quote the answer The magnitude of the Moon’s momentum is: ~p = m~v p = mv    = 7,35 × 1022 1,02 × 103 = 7,50 × 1025 kg·m·s−1 The magnitude of the momentum of the Moon is 7,50 × 1025 kg·m·s−1. As we have said, momentum is a vector quantity. Since momentum is a vector, the techniques of vector addition discussed in Vectors and scalars in Grade 10 must be used when dealing with momentum. Change in momentum ESCJ9 Particles or objects can collide with other particles or objects, we know that this will often change their velocity (and maybe their mass) so their momentum is likely to change as well. We will deal with collisions in detail a little bit later but we are going to start by looking at the details of the change in momentum for a single particle or object. Case 1: Object bouncing off a wall Lets start with a simple picture, a ball of mass, m, moving with initial velocity, ~vi , to the right towards a wall. It will have momentum ~pi ~pi = m~vi to the right as shown in this picture: Chapter 2. Momentum and impulse 25  The ball bounces off the wall. It will now be moving to the left, with the same mass, ~pf but a different velocity, ~vf and therefore, a different momentum, ~pf = m~vf , as shown in this picture: We know that the final momentum vector must be the sum of the initial momentum vector and the change in momentum vector, ∆~p = m∆~v. This means that, using tail- to-head vector addition, ∆~p , must be the vector that starts at the head of ~pi and ends on the head of ~pf as shown in this picture: We also know from algebraic ad- ~pf ~pi dition of vectors that: b ~pf = ~pi + ∆~p ∆~p ~pf − ~pi = ∆~p ∆~p = ~pf − ~pi If we put this all together we can show the sequence and the change in momentum in one diagram: ~pi ~pf ~pf ~pi b ∆~p = ~pf − ~pi We have just shown the case for a rebounding object. There are a few other cases we can use to illustrate the basic features but they are all built up in the same way. Case 2: Object stops In some scenarios the object may come to a standstill (rest). An ex- ample of such a case is a tennis ball hitting the net. The net stops the ball but doesn’t cause it to bounce back. At the instant be- fore it falls to the ground its ve- locity is zero. 26 2.2. Momentum This scenario is described in this image: ~pi ~pf = 0 ~pf ~pi b ∆~p = ~pf − ~pi Case 3: Object continues more slowly In this case, the object continue in the same direction but more slowly. To give this some context, this could happen when a ball hits a glass window and goes through it or an object sliding on a frictionless surface encounters a small rough patch before carrying on along the frictionless surface. ~pi ~pf ~pf ~pi b ∆~p = ~pf − ~pi Important: note that even though the momentum remains in the same direction the change in momentum is in the opposite direction because the magnitude of the final momentum is less than the magnitude of the initial momentum. Case 4: Object gets a boost In this case the object interacts with something that increases the velocity it has without changing its direction. For example, in squash the ball can bounce off a back wall Chapter 2. Momentum and impulse 27  towards the front wall and a player can hit it with a racquet in the same direction, increasing its velocity. If we analyse this scenario in the same way as the first 3 cases, it will look like this: ~pi ~pf ~pi ~pf b ∆~p = ~pf − ~pi Case 5: Vertical bounce IMPORTANT! For this explanation we are ignoring any effect of gravity. This isn’t accurate but we will learn more about the role of gravity in this scenarion in the next chapter. All of the examples that we’ve shown so far have been in the horizontal direction. That is just a coincidence, this approach applies for vertical or horizontal cases. In fact, it applies to any scenario where the initial and final vectors fall on the same line, any 1-dimensional (1D) problem. We will only deal with 1D scenarios in this chapter. 28 2.2. Momentum For example, a stationary basketball player bouncing a ball. ~pf ~pi b ∆~p = ~pf − ~pi ~pi ~pf To illustrate the point, here is what the analysis would look like for a ball bouncing off the floor: Exercise 2 – 1: 1. a) The fastest recorded delivery for a cricket ball is 161,3 km·hr−1 , bowled by Shoaib Akhtar of Pakistan during a match against England in the 2003 Cricket World Cup, held in South Africa. Calculate the ball’s momentum if it has a mass of 160 g. b) The fastest tennis service by a man is 246,2 km·hr−1 by Andy Roddick of the United States of America during a match in London in 2004. Calculate the ball’s momentum if it has a mass of 58 g. c) The fastest server in the women’s game is Venus Williams of the United States of America, who recorded a serve of 205 km·hr−1 during a match in Switzerland in 1998. Calculate the ball’s momentum if it has a mass of 58 g. d) If you had a choice of facing Shoaib, Andy or Venus and didn’t want to get hurt, who would you choose based on the momentum of each ball? 2. More questions. Sign in at Everything Science online and click ’Practise Science’. Check answers online with the exercise code below or click on ’show me the answer’. 1. 27HP www.everythingscience.co.za m.everythingscience.co.za Chapter 2. Momentum and impulse 29  2.3 Newton’s Second Law revisited ESCJB In the previous section we considered a number of scenarios where the momentum of an object changed but we didn’t look at the details of what caused the momentum to change. In each case it interacted with something which we know would have exerted a force on the object and we’ve learnt a lot about forces in Grade 11 so now we can tie the two together. You have learnt about Newton’s Laws of motion in Grade 11. We know that an object will continue in its state of motion unless acted on by a force so unless a force acts the momentum will not change. In its most general form Newton’s Second Law of motion is defined in terms of mo- mentum which actually allows for the mass and the velocity to vary. We will not deal with the case of changing mass as well as changing velocity. DEFINITION: Newton’s Second Law of Motion (N2) The net or resultant force acting on an object is equal to the rate of change of momen- tum. p Mathematically, Newton’s Second Law can be stated as: ~Fnet = ∆~ ∆t If a force is acting on an object whose mass is not changing, then Newton’s Second Law describes the relationship between the motion of an object and the net force on the object through: ~Fnet = m ~anet We can therefore say that because a net force causes an object to change its mo- tion, it also causes its momentum to change. ~Fnet = m ~anet ~Fnet = m ∆~v ∆t ~pf ~pf ~Fnet = m∆~ v ∆t b ∆~p = ~pf − ~pi ~Fnet = ∆~p ∆t Let us apply this to the last case from the previous section, consider a tennis ball ~pi ~pi (mass = 0,1 kg) that is thrown and strikes the floor with a velocity of 5 m·s−1 down- wards and bounces back at a final veloc- ity of 3 m·s−1 upwards. As the ball ap- proaches the floor it has an initial mo- mentum ~pi. When it moves away from the floor it has a final momentum ~pf. The bounce on the floor can be thought of as a collision taking place where the floor exerts a force on the tennis ball to change its momentum. 30 2.3. Newton’s Second Law revisited Remember: momentum and velocity are vectors so we have to choose a direction as positive. For this example we choose the initial direction of motion as positive, in other words, downwards is positive. ~pi = m~vi = (0,1) (+5) = 0,5 kg·m·s−1 downwards When the tennis ball bounces back it changes direction. The final velocity will thus have a negative value because it is in the negative direction. The momentum after the bounce can be calculated as follows: ~pf = m~vf = (0,1) (−3) = −0,3 = 0,3 kg·m·s−1 upwards Now let us look at what happens to the momentum of the tennis ball. The momentum changes during this bounce. We keep our initial choice of downwards as positive. This means that the final mo- mentum will have a negative number. ∆~p = ~pf − ~pi = m~vf − m~vi = (−0,3) − (0,5) = −0,8 = 0,8 kg·m·s−1 upwards You will notice that this number is bigger than the previous momenta calculated. This should be the case as the change has to cancel out the initial momentum and then still be as large as the final momentum over and above the initial momentum. Worked example 4: Change in Momentum QUESTION A tennis ball of mass 58 g strikes a wall perpendicularly with a velocity of 10 m·s−1. It rebounds at a velocity of 8 m·s−1. Calculate the change in the momentum of the tennis ball caused by the wall. SOLUTION Step 1: Identify the information given and what is asked The question explicitly gives a number of values which we identify and convert into SI units: the ball’s mass (m = 58 g=0,058 kg), the ball’s initial velocity (~vi = 10 m·s−1 ) towards the wall, and Chapter 2. Momentum and impulse 31  the ball’s final velocity (~vf = 8 m·s−1 ) away from the wall We are asked to calculate the change in momentum of the ball, ∆~p = m~vf − m~vi ~pi ~pf ~pf ~pi b ∆~p = ~pf − ~pi We have everything we need to find ∆~p. Step 2: Choose a frame of reference Since the initial momentum is directed to- Let us choose towards the wall as the pos- wards the wall and the final momentum is itive direction. away from the wall, we can use the alge- braic method of subtraction discussed in Vectors in Grade 10. Step 3: Do the calculation Step 4: Quote the final answer The change in momentum is ∆~p = m~vf − m~vi 1,04 kg·m·s−1 away from the wall. = (0,058) (−8) − (0,058) (+10) = (−0,46) − (0,58) = −1,04 = 1,04 kg·m·s−1 away from the wall Worked example 5: Change in momentum QUESTION A rubber ball of mass 0,8 kg is dropped and strikes the floor with an initial velocity of 6 m·s−1. It bounces back with a final velocity of 4 m·s−1. Calculate the change in the momentum of the rubber ball caused by the floor. 32 2.3. Newton’s Second Law revisited SOLUTION Step 1: Identify the information given and what is asked The question explicitly gives a number of values which we identify and convert into SI units: the ball’s mass (m = 0,8 kg), 6 m·s−1 the ball’s initial velocity (~vi = 6 m·s−1 ) downwards, and the ball’s final velocity (~vf = 4 m·s−1 ) upwards We are asked to calculate the change in momentum of the ball, 4 m·s−1 ∆~p = m~vf − m~vi Step 2: Do the calculation Step 3: Quote the final answer Let us choose down as the positive direc- The change in momentum is tion. 8,0 kg·m·s−1 upwards. ∆~p = m~vf − m~vi = (0,8) (−4) − (0,8) (+6) = (−3,2) − (4,8) = −8 = 8,0 kg·m·s−1 upwards Worked example 6: Change in momentum QUESTION A regulation squash ball weighs 24 g. In a squash match a ball bounces off the back wall in the direction of the front wall at 1 m·s−1 before a player hits it with a racquet. After being struck towards the front wall the ball is moving at 20 m·s−1. What is the change in momentum? SOLUTION Step 1: Identify the information given and what is asked The question explicitly gives a number of values which we identify and convert into SI Chapter 2. Momentum and impulse 33  units: the ball’s mass (m = 24 g=0,024 kg), the ball’s initial velocity (~vi = 1 m·s−1 ) towards the front wall, and the ball’s final velocity (~vf = 20 m·s−1 ) towards the front wall We are asked to calculate the change in momentum of the ball, ∆~p = m~vf − m~vi ~pi ~pf ~pi ~pf b ∆~p = ~pf − ~pi We have everything we need to find ∆~p. Step 2: Choose a frame of reference Let us choose towards the front wall as the positive direction. Step 3: Do the calculation ∆~p = m~vf − m~vi = (0,024) (20) − (0,024) (+1) = (0,48) − (0,024) = 0,456 = 0,46 kg·m·s−1 towards the front wall Step 4: Quote the final answer The change in momentum is 0,46 kg·m·s−1 towards the front wall. 34 2.3. Newton’s Second Law revisited Exercise 2 – 2: 1. Which expression accurately describes the change of momentum of an object? ~ F a) m ~ F b) ∆t c) ~F · m d) ~F · ∆t 2. A child drops a ball of mass 100 g. The ball strikes the ground with a velocity of 5 m·s−1 and rebounds with a velocity of 4 m·s−1. Calculate the change of momentum of the ball. 3. More questions. Sign in at Everything Science online and click ’Practise Science’. Check answers online with the exercise code below or click on ’show me the answer’. 1. 27HQ 2. 27HR www.everythingscience.co.za m.everythingscience.co.za 2.4 Conservation of momentum ESCJC In this section we are going to look at momentum when two objects interact with each other and, specifically, treat both objects as one system. To do this properly we first need to define what we mean we talk about a system, then we need to look at what happens to momentum overall and we will explore the applications of momentum in these interactions. Systems ESCJD DEFINITION: System A system is a physical configuration of particles and or objects that we study. For example, earlier we looked at what happens when a ball bounces off a wall. The system that we were studying was just the wall and the ball. The wall must be con- nected to the Earth and something must have thrown or hit the ball but we ignore those. A system is a subset of the physical world that we are studying. The system exists in some larger environment. In the problems that we are solving we actually treat our system as being isolated from the environment. That means that we can completely ignore the environment. In reality, the environment can affect the system but we ignore that for isolated systems. We try to choose isolated systems when it makes sense to ignore the surrounding Chapter 2. Momentum and impulse 35  environment. DEFINITION: Isolated system An isolated system is a physical configuration of particles and or objects that we study that doesn’t exchange any matter with its surroundings and is not subject to any force whose source is external to the system. An external force is a force acting on the pieces of the system that we are studying that is not caused by a component of the system. It is a choice we make to treat objects as an isolated system but we can only do this if we think it really make sense, if the results we are going to get will still be reasonable. In reality, no system is competely isolated except for the whole universe (we think). When we look at a ball hitting a wall it makes sense to ignore the force of gravity. The effect isn’t exactly zero but it will be so small that it will not make any real difference to our results. Conservation of momentum ESCJF There is a very useful property of isolated systems, total momentum is conserved. Lets use a practical example to show why b this is the case, let us consider two bil- liard balls moving towards each other. ~vB1 Here is a sketch alongside (not to scale). When they come into contact, ball 1 ex- erts a contact force on the ball 2, ~FB1 , and the ball 2 exerts a force on ball 1, ~FB2. We also know that the force will result in a change in momentum: ~vB2 ~Fnet = ∆~p ∆t b We also know from Newton’s third law that: ~FB1 = −~FB2 This says that if you add up all the changes in mo- mentum for an isolated system the net result will be ∆~pB1 ∆~pB2 =− zero. If we add up all the momenta in the system ∆t ∆t the total momentum won’t change because the net ∆~pB1 = −∆~pB2 change is zero. ∆~pB1 + ∆~pB2 =0 Important: note that this is because the forces are internal forces and Newton’s third law applies. An external force would not necessarily allow momentum to be con- served. In the absence of an external force acting on a system, momentum is con- served. 36 2.4. Conservation of momentum Activity: Newton’s cradle demonstration Momentum conservation: A Newton’s cradle demonst