School of PhysicsPHYC10006 Physics 2: Life Sciences and Environment Laboratory Manual Name: Lab Class: 2013 PHYC10006 Physics Laboratory Manual i Contents Introduction to Laboratory Work Laboratories in Physics I-1 Preparation I-1 Laboratory Work I-3 Help! I-5 Laboratory Safety – a brief summary I-6 Assessment of Practical Physics I-7 General Safety I-10 Semester 1 Laboratory Exercises Laboratory Exercise 1 Thermal Effects Laboratory Exercise 2 Buoyancy Laboratory Exercise 3 Flowing Fluids Laboratory Exercise 4 Fun with Charges Laboratory Exercise 5 Electrical Circuits Laboratory Exercise 6 Capacitors Laboratory Exercise 7 Magnetic Interactions Laboratory Exercise 8 Properties of Radiation Appendices Appendix A Uncertainties & Error Analysis Appendix B Graphs and How to Use Them Appendix C SI Units Appendix D Resistor Colour Codes Your Lab Schedule back cover PHYC10006 Physics Laboratory Manual I-1 Introduction to Laboratory Work Laboratories in Physics You will attend eight weeks of practical exercises as part of your learning and assessment in PHYC10006 Physics 2: Life Sciences and Environment. These laboratory exercises (also known as ‘Labs’, ‘Practical Classes’, or ‘Pracs’) will run alongside the lectures and tutorials, providing a practical exploration of ideas related to the course. Your physics demonstrator will supervise these exercises, and check that you achieve the ‘check points’ set. The aim is for you to broaden your understanding of the physics involved, and also to develop the skills needed to be a successful experimental physicist. Each weekly prac has two components: a Pre-Lab Exercise and the Lab itself (normally a combination of experiments and exercises, with a few questions to help guide the experimentation and interpretation of results). Completing all check points successfully within the lab will contribute 80% to your final mark for the laboratory exercise. Completing the Pre-Lab exercise will provide the remaining 20%. The Pre-Lab Exercise must be completed before you arrive. This routinely involves reading through the whole lab, answering any exercises labelled as pre-labs, and then completing the on-line questions that check your completion of this. The focus of the pre-labs will vary from week to week – sometimes they will relate more to the physics of the topic, and sometimes they will relate more to the experimental methods that will be used. In all cases your mark for the pre-labs will be given based on the answers on-line. You will be given a mark out of 10 for the pre-labs – 5 marks are allocated for the timely completion of the work and 5 marks are allocated for the correct answers. If the questions are not completed (and online answers submitted) before the lab (which means more than 10 minutes before lab is scheduled to begin), you will only be able to get up to half the marks allocated for the pre-labs. The Lab itself is normally a series of experiments and exercises designed to introduce you to important techniques of experimental physics and give some hands-on investigating of the physics taught in the lectures and tutorials. You will keep a record of your experimental notes and results in your Logbook. The Logbook remains in the physics laboratories at all times. Although the laboratory exercises investigate physics topics that are also covered in lectures, each lab is designed to be self-contained. Don’t be worried if your upcoming lab involves material that you have or haven’t seen before: the lab exercises are designed to be completed at any time during the course. Lectures will improve your understanding of labs, and labs will improve your understanding of lectures. No matter in what order you complete the exercises, any student who completes them all will be similarly advantaged. Preparation It is essential to be properly prepared for each lab exercise. The timetable at the back of this book will tell you exactly which laboratory your group is tackling each week (you will need to check which group you are in first (see below). You must read through the Lab Manual description of the Experiment for the week before you arrive, and complete any Pre-Lab Exercises that are required (including the online questions to ensure you get appropriate credit for your work at http://fyl.ph.unimelb.edu.au/prelabs). These need to be submitted at least 10 minutes before your lab class begins, otherwise the maximum mark possible for the pre- labs would be 5 out of 10 (assuming they are all correct). Before your first class, you must also read the Safety Notes (below). Laboratory exercises may involve radioactivity, toxic materials and/or hazardous equipment, and it is essential that you are fully aware of the safety issues involved. I-2 PHYC10006 Physics Laboratory Manual You should also read the rest of this Introduction to Laboratory Work, especially the sections below on Safety, on Assessment, and on logbook writing. You must read Appendix A to learn about uncertainty analysis. Appendix B discusses the creation and use of graphs. When do we start? Classes start in the second or third week of semester one. You will need to find out which lab group you are in, and also which section of the laboratory you have been assigned to for your first session. This information is available from the pre-labs web page (which is a link from the LMS page for the subject). http://fyl.ph.unimelb.edu.au/prelabs Where do I go? The first-year Physics laboratories are located on levels 3 & 4 of the Swanston Street extension to the Physics building, which is called the Physics Podium. The Physics 2: Life Sciences lab is on level 4. When arriving for your practical classes, you should enter the laboratories via the big ramp. Follow the ramp straight up into the Physics Podium, and once inside go forward (towards the Swanston St exit), left and then left again (near the noticeboard where the lab groups are posted). You are now on level 2. The entrance to the laboratories is via a stairwell, which looks like an emergency exit. Don’t be worried – up the concrete stairs (from level 2 up to level 4) is the way to go. When you arrive for your first class there will be signs posted to show you the way. PHYSICS labs: levels 3&4 western ramp Swanston Street bridge Students are assigned to lab groups, which are labelled with a code like ‘UPC2’. The letters and numbers describe your group: U is the day. M =Monday, U =Tuesday, W =Wednesday, and H =Thursday. P is the time of day. P =PM (afternoon), A =AM (morning), and E =Evening. C is the subject. C =PHYC10006 (this subject) (A, B, M are for the other subjects). 2 is the group number, which tells you which section of the lab you will be working in. There are up to four groups doing labs in your subject at the same time: groups 1, 2, 3 and 4. However not all groups will do the same experiment each week – the schedule is on the back of this book. What should I bring? To the first practical class, you should bring: your Physics 2 L.S.E Lab Manual (this book!) your Physics 2 lab notebook (which will be your Logbook) a calculator (if you have one) – but you should use Excel as much as possible pens (for written work), pencils (for graphs and diagrams) and a ruler All laboratory benches have a computer running Excel (and other useful software), and each laboratory has a printer. Any print-outs you create must be stuck into your logbook. You should write your name and details on the cover of your logbook, and also write your name on the two ends (so it can be read when the book is lying flat in a stack). PHYC10006 Physics Laboratory Manual I-3 Laboratory Work The laboratory exercises are designed to complement the lectures and tutorials. You will encounter some physics ideas for the first time in labs, and investigate them further in later lectures and tutorials. Other lab exercises will be exploring physics concepts you may have already seen in lectures. The first-year laboratory schedule runs for 8 weeks of classes, divided into 2 segments (see below). In each segment you will be supervised by a different demonstrator and will work with a different lab partner. Schedule Each lab takes place during a 3 hour laboratory session. The work cannot be carried over between weeks. If you miss a class, you can only make it up during the same week (see Attendance, below). There are no lab classes in the first week of semester. The table on the outside back cover of this book tells you the schedule for each specific lab group semester one: Attendance Attendance is compulsory at all laboratory sessions. Laboratory work is a hurdle requirement: you must attend and complete your laboratory exercises satisfactorily in order to pass Physics 2 Life Sciences and Environment (see Assessment, below). If you are unavoidably absent from a laboratory session (or if you know that you are going to be), you need to contact Colin Entwisle as soon as possible (see the Help! section, below). If you present a medical certificate (or equivalent) you can be exempted from that prac. If you have a valid reason for missing the lab (but no medical certificate, or you have already missed 2 labs – see below) you will need to arrange (with Colin) to attend a catch-up lab session in the same week. If you ignore the absence, you will receive no marks for that week (and a lower final mark for the subject because of this). A maximum of 2 medical certificates in each semester will be accepted for absences. Any further medical certificates will require you to make up your lab session/s at another time (but only in very extraordinary circumstances can this be in a different week of semester). You must arrange for this as soon as possible after your absence. Contact Colin if you are unsure of what you need to do (
[email protected]). Lab Partners In every laboratory session, you will work with one or more lab partners (from the same subject). You will conduct the practical laboratory work together and produce a single set of experimental results. However, each of you must keep your own logbook. It is important to discuss the physics with your partner(s) as you work together, to ensure that you both understand what is going on. If you don’t agree with each other about your understanding of the physics involved, you need to resolve this with your demonstrator. At the start of the new lab segment, you will need to change partner(s). This policy is designed to develop your skills in working with a variety of people through the year. Demonstrators Each laboratory has a team of demonstrators, one of whom will be directly supervising your lab group. Most demonstrators are Physics Masters students – students who are completing their 4 th or 5 th Year of Physics studies. (Imagine yourself, three or four years from now.) Your demonstrator will instruct you in the correct use of the lab equipment, and assist you in understanding the physics concepts involved in the prac. Sometimes the demonstrator will talk to the entire lab group at once, to discuss an important concept or to give you all an overview of what you will be doing next. Most of the time, the demonstrator will be moving about the lab answering queries and offering advice to students (and confirming that you have achieved the check points specified). The demonstrators are not there to tell you all the answers. Their job is to encourage you to learn how to discover the answers for yourself: that is what experimental physics is for. Demonstrators are there to let you know if you are right or wrong, and to point you in the right direction. The purpose of laboratory work is not (only) to get the ‘right’ answer: it is to understand what your answers mean, even when they seem to be ‘wrong’. I-4 PHYC10006 Physics Laboratory Manual Demonstrators are also responsible for ensuring safety in the laboratory. You are required to obey your demonstrator’s instructions regarding safe practices in the lab (such as the correct use of equipment, evacuation in the event of an alarm, etc). Safety guidelines are extremely important: you must read the Safety section, below. Finally, demonstrators are responsible for checking your laboratory work and marking the checkpoint progress (see Assessment, below). Your demonstrator has the final say on what is expected from you each week, and will let you know if there are any changes to the lab exercise from what is shown in the manual. Remember to listen to the guidance from the demonstrators on what you need to do (since they determine the check point completion and therefore your mark). Help! During your laboratory session, questions should be directed to your demonstrator. Otherwise, the first-year laboratories are co-ordinated by the Teaching and Laboratory Coordinator, Mr Colin Entwisle. Any general problems or queries – especially about absences, timetables, or any other administrative issues – should be directed to Colin. His office is in the first-year labs, Room 3.11 (which is at the back of the third floor labs). If you are unable to contact Colin, send an email:
[email protected]. Equipment The equipment in the laboratories is under the care of the Laboratory staff. If you are having trouble with equipment, talk to your demonstrator and they will assess the need for further assistance. Concerns about teaching Any concerns you may have about the teaching in lab classes can be discussed with Colin or the academic co-ordinator of the first-year teaching, who is Dr Roger Rassool (email:
[email protected]). Lost Property See Colin Entwisle or other lab staff promptly. PHYC10006 Physics Laboratory Manual I-5 LABORATORY SAFETY – A BRIEF SUMMARY Laboratory exercises may involve radioactivity, toxic materials and/or hazardous equipment, and it is essential that you are fully aware of the safety issues involved. You are obligated to read and understand the General Safety Notes (later in this manual). You must understand and follow all safety instructions and warnings for each laboratory exercise. You must follow all the safety directions given by your demonstrator and other laboratory staff. At your first laboratory session, your demonstrator will provide you with a declaration form which you must sign, asserting these responsibilities. Much effort and thought goes into ensuring that the first-year laboratories are as safe as possible. If you have any safety concerns, you must immediately report these to your demonstrator or to another laboratory staff member. These are the three most basic safety rules: Adequate footwear and suitable clothing must be worn at all times. This means no sandals or thongs. If your shoes are not closed-toe, you will not be allowed to stay in the laboratory. Eating, drinking and smoking are not allowed in the laboratory. This is especially important in the Radiation laboratories. The radioactive materials you will encounter in first-year Physics are extremely dangerous if accidentally ingested. If you are thirsty, there is a drinking fountain at the eastern end of the laboratories. Mobile phones are not to be used in the laboratory. Hazardous equipment may be in use nearby, and mobile phones can be a dangerous distraction or source of interference. If you need to receive or make an essential call, you must leave the laboratory to do so. If there is an essential reason for your phone to be on in the laboratory, it must be set to ‘silent’ mode. REMEMBER: If you bring food or drink into the laboratory, or if you wear shoes which are not closed-toe, or if you answer your phone in the lab, you will be ejected and you will lose marks. I-6 PHYC10006 Physics Laboratory Manual Assessment of Practical Physics Laboratory work is an important and essential part of first-year Physics. Because of this, laboratory assessment makes up 25% of your final mark for the subject. This 25% comes from the sum of your laboratory session marks (based on satisfactory completion of check points and lab performance during the prac) and your pre-lab work which is submitted online before each lab (if you complete or alter your pre-lab answers online after you have had your lab you will not receive the marks allocated for timely completion). For each of the 8 weeks of laboratory sessions, you will get a mark out of 10 for the pre-labs (5 of which are for timely completion – that is submission more than 10 minutes before lab starts), a mark out of 8 for check point achievement and conclusion, and a mark out of 2 for Lab Performance. The final mark for lab assessment is 20% from pre-labs, 60% from the checkpoint and conclusion mark (which at its simplest means you have worked effectively during the lab session), and 20% for Lab Performance. The weekly checkpoint and lab performance mark out of 10 is based on the Four key aspects of laboratory work: 1. your logbook entry (see Logbooks, below) 2. your practical work during the session 3. your overall conduct during the session 4. the state of your lab bench at the end of the session. Each lab lists the check points at the beginning, and at each check point there is some indication of what the demonstrator will be looking for. As a general rule, if you follow this manual, and listen to your demonstrator, you should be able to get all the checkpoint marks! As well as contributing 25% to your final mark, the laboratory component of the first-year Physics course is a hurdle requirement. This means that if you fail to satisfactorily complete the laboratory component, you cannot pass. This is true no matter how well you do on the other components of the course. What does ‘satisfactorily complete’ mean? It means you must: Attend and satisfactorily participate in at least 6 of the 8 laboratory sessions in the semester Earn a final mark of at least 50% of the total possible marks. If you are unable to attend a laboratory session for any reason, you should talk to Colin Entwisle (or another laboratory staff member) as soon as possible. It is important to note that presenting a medical certificate for your absence does not waive the minimum attendance requirement. You cannot miss more than two of your lab sessions for any reason. If you do miss a lab session (or if you know that you are going to), you must see Colin as soon as possible in order to arrange a catch-up session. (Please read the Attendance section, above, for details.) Lab Performance An essential aim for laboratory work is that you demonstrate your understanding of what occurs. Being able to follow directions to produce a result is important, but results are meaningless unless you can explain how they relate to the physics involved. During your practical work, it is important to: Prepare for the laboratory – including reading the entire lab for that week, and submitting your answers to the online questions Use laboratory equipment carefully, respectfully and safely Set up equipment correctly (and don’t let your partner(s) do all the work!) Work with your lab partner(s) – share the workload including using the computer PHYC10006 Physics Laboratory Manual I-7 Talk to your partner(s) about the labs as you go along; if you are not sure that you understand the physics involved, you should also talk to your demonstrator together Ensure the accuracy and quality of your measurements. Think about how many measurements you should make, how best to use the available time, etc. Think about what you are doing – don’t follow directions blindly. Consider possible flaws in the experimental procedure, whether the equipment you are using is appropriate, etc. Pay attention to your results – do they seem ‘reasonable’, or are they obviously in error? For example, if your results say that the speed of light is only 2 metres per second, clearly you have made a mistake somewhere. Make sure your lab bench has the right equipment on it at the end of the lab session. If you borrow equipment from another bench, be sure to return it to the bench from which it was borrowed. TAKE NOTE: You may not always complete the entire laboratory exercise. But as long as the demonstrator is satisfied with your efforts, this is acceptable. It is better to keep a reasonable and well- considered logbook that covers 85% of the exercise, than to rush through 100% of the work without understanding anything and have a muddled, incomplete logbook record. It is always better to understand what you have done, rather than to just do it (it will make your job a lot easier when you are analysing, interpreting, or commenting on your results). The Lab Manual (this book) Pre-lab sections should be completed in this book (some space has been left) – and then the on-line questions answered. During the actual lab session you will record all your work straight into your logbook. Logbooks During each weekly Experiment, you will be writing in your logbook as you go along. Please note, your logbook stays in the laboratories at all times: you don’t get to take your logbook home to work on it later, so each week’s logbook entry must be finished by the end of each session. Keeping an effective logbook is very important in experimental science. An experimental log is not like an assignment, not like an essay, and not like the lab reports you may have written in secondary school. So, what is it? It is more like a diary – of your actions and thinking throughout the lab session. The idea of your experimental log is to keep a sequential record of your actions, thoughts and results during the experiment. Any other first-year Physics student should be able to read your log and recreate exactly your experiment(s). (Imagine that if you lost all your memory of the experiment, you could read your log again and be able to know and understand everything about it.) These are the KEY CRITERIA: The log needs to be self-contained. It must be complete in itself: it cannot say “refer to the lab manual”. It must read as if the manual does not exist. The log needs to be complete. It must include mention of all equipment used and procedures followed. All data & results should be recorded as they are taken – sometimes data will be entered directly into the computer, in which case you can stick print outs of tables and graphs into your logbook. The log needs to make sense. It needs to be clear, sensible, logical and readable. Remember that you and your peers should be able to read it! Results are not enough. Don’t just record your measurements in your logbook; you need to say something about what you are doing, why you are doing it, and what it all means. As you go along you must record all your analysis and discussion of the experiment, not only your ‘answers'. You should also analyse all numerical uncertainties and discuss any possible errors (see Appendix A for a thorough explanation of what this means). I-8 PHYC10006 Physics Laboratory Manual The log needs to follow some conventions. This includes putting the date, the title of the lab exercise, and the names of your partner(s) at the beginning of each new laboratory. You should always finish the lab with a summary of the day’s work (which can be brief). How to write your log Always use a pen to write your log, but use pencil (or Excel printouts) for graphs and diagrams. Your log does not need to be perfectly neat, only clear and readable. Never use white-out or correction fluid: simply put a line through what is incorrect and move on – apart from saving you time, this also shows your progress more correctly – making the logbook more useful to a reader. You should write fairly informally – you are not writing a paper for submission – it is an experimental diary for your own reference. At the start of each entry your log must clearly record the date, the title of the Experiment, and the names of your partner(s). Sometimes you may be able to write an ‘aim’ – which in later year’s laboratories will be mandatory, so it is a good skill to develop and practise – but do not worry about it if you aren’t sure. If you do write one, it should be short (a paragraph or two at most) and state the aims of the Experiment: what you are hoping to do, and why. (For this to make sense you might also need to discuss some theory, but try to make it brief; in-depth discussion of theory should be left to the Experiment section.) With or without an aim, the rest of the logbook is a chronological record of everything that you do and think, written as you go along. (Keep in mind the KEY CRITERIA listed above.) Think of it like a diary entry, or a story; it should describe everything that you do and explain why you did it and what you think about it. Don’t leave writing this until the end – it is very important (and time-saving!) to record your work as you go along. This skill (to write a sensible, brief, and effective record of your work as you do it) is one of the main aims in the first year laboratory program. Be accurate, and be honest! If you make a mistake in your setup and have to start again, your log should record this. If you misinterpret results and have to go back and re-analyse them, discuss your mistake in your log and explain where you went wrong. Keep your description of the experimental procedure simple and clear. Do not copy the manual word- for-word. You need to include all relevant details; you should be able to recreate the experiment entirely from your log, without the manual. When the manual has a question, you need to answer it in your log in a way that makes sense (i.e. combine the question and answer into a self-contained sentence). Use diagrams to show configurations of equipment. Don’t be photographic – rather than draw an electronic detector the way it actually looks, just draw a square box and label it ‘detector’. Remember that all numerical results should be presented with their ‘plus-or-minus’ uncertainty values – this is essential! There are some checkpoints and some labs that draw particular attention to this – the skill to include an uncertainty or error for any experimental quantity is another key aim of undergraduate labs. It can seem painful, hard and unnecessary at first, but we hope to make it a routine part of your experimental work. You must read Appendix A: Uncertainties & Error Analysis. If you are still unsure about what this means, talk to your demonstrator. Finish with a Summary. Every lab should have a brief summary at the end. This is a brief paragraph discussing how the Experiment’s actual outcomes (as recorded in the Experiment section) related to the original aims (as described in the Aim). As with all logbook keeping – this does not need to be formal – just a ‘wrap- up” of what you did – in your own words! PHYC10006 Physics Laboratory Manual I-9 General Safety Notes To ensure a safe and environmentally friendly workplace for all staff, students, and visitors, the University of Melbourne has adopted the internationally recognised systems Safety MAP (ISO12001) and Environmental Management System (ISO14001). As a student of the University you are responsible for adopting safe work and study practices, and you are required to comply with all relevant University and Departmental rules and procedures. Detailed information on University policy and procedures is provided in the Environment, Health and Safety Manual at http://www.unimelb.edu.au/ehsm The Laboratory Rules and Safe Work Procedures set out below must be adhered to at all times. You must follow the safety directions of all demonstrators and other staff. Any injuries or other incidents must be immediately reported to a laboratory staff member. If you have any concerns about the safety or environmental impact of any aspect of the laboratory classes, please raise them with your demonstrator. Emergency Procedures If the emergency alarm bell sounds continually, the building must be evacuated. Switch off all equipment, clear walkways and leave by the suggested emergency exit route. This route is: Go through the door at the East (Swanston St.) end of the laboratory, and then down the stairs to the grassy knoll area next to the Potter cafe. You must not re-enter the laboratories until your demonstrator or evacuation controller directs that it is safe to do so. If this exit is not accessible, leave instead by the usual Western stairway. If a fire occurs in the laboratory, alert people near you and also others on your level. Turn off all equipment and leave the area immediately. Do not get in the way: your demonstrator will take control. Using the wrong type of fire extinguisher can be very dangerous. The two most common types of extinguishers are: Water (or Soda Acid), which is most effective on ordinary combustibles (paper, wood, etc.). These extinguishers should NOT be used on electrical, oil or grease fires. Carbon Dioxide (CO2), which can be used on combustible, electrical and flammable liquid fires. The first-year laboratories use dry powder type fire extinguishers, which are safe to use in the laboratories. In case of fire, remember that it is very easy to be overcome by smoke and fumes. These fumes may be extremely toxic, especially if electrical equipment is involved. Accidents If you are first on the scene of an accident and the casualty is in danger of further injury, observe the area for hazards and, only if it is safe, pull the casualty clear. Do not move the casualty unnecessarily. Once the casualty is out of immediate danger, summon aid immediately by reporting the accident to your demonstrator and to any lab staff (offices in the eastern end of the labs), or to the Physics building front office (ground floor). There are a number of people available who are qualified in First Aid: attempt to find one of them by asking your demonstrator. Electrical Hazards The mains electrical supply is alternating current at 240 volts. This supply is hazardous and can be lethal. Care must be taken at all times. When working with electrical equipment, always remember the following: Be aware of live parts and take appropriate precautions Make sure all connections are clean, dry and secure I-10 PHYC10006 Physics Laboratory Manual Always connect the supply voltage to your circuit last, and (at first) only connect it for an instant Do not attempt to service any electrical equipment yourself (this includes changing fuses). If an accident occurs, act quickly. Ensure that you will not be in danger of electric shock by attempting to help the casualty. If it is safe to do so, switch off the electrical supply at the wall and pull out the plug. Otherwise, free the person by using something non-conductive (e.g. dry wood, rubber, etc.). Do not touch the casualty (you may receive a shock if you do). If there are any injuries or other incidents, alert your demonstrator immediately. Radiation Hazards All types of ionising radiation produce changes in living cells, but actively dividing cells (e.g. blood- forming and reproductive cells) are particularly susceptible to damage. All doses of radiation, therefore, must be kept as low as possible. All radioactive sources are sealed and shielded, to prevent the active material from dispersing into the surroundings (where it could be inhaled, ingested or absorbed). Take care not to break these seals and shields. If any sources appear to be damaged, alert your demonstrator immediately. A dose of radiation received is directly proportional to the exposure time and inversely proportional to the distance squared. Therefore, the main safety procedures are: Minimise your exposure time Maximise the distance between yourself and the source Where appropriate, use shielding to reduce the intensity of radiation (e.g. lead blocks) Wash hands thoroughly after handling sources (or touching any lead shielding), and again after leaving the laboratory When the sources are not in use, return them to the demonstrator and sign off. Radioactive sources must never leave the laboratory. Medical status – voluntary notification If you have any allergies or medical conditions that you think might be affected by any of the chemicals, materials or procedures in these laboratories, you must fill in a Medical Status – Voluntary Notification for Laboratory Classes form and give it to your demonstrator. This is so that any risks can be assessed and the laboratory procedures modified. This form is available from your demonstrator, or online at http://fyl.ph.unimelb.edu.au/medform.pdf Safety Rules In all of the laboratories, the following rules should be remembered. Maintain a neat and clean bench and work area. Keep aisles and doors clear. Switch off and tidy up the equipment after use. Your work area will be checked by your demonstrator at the end of each session, before you leave. If you do not follow these instructions you will be penalised. Never run or throw objects in the laboratory. Don’t adopt a casual attitude: be aware of the potential hazards and act accordingly. Never work alone in a laboratory. A colleague should always be within call. Adequate footwear (closed-toe) and suitable clothing must be worn at all times. Eating, drinking and smoking are forbidden. After leaving the laboratory, always wash your hands thoroughly (especially if working in the Radiation labs). All accidents, injuries, mishaps and ‘near misses’ must be reported to your demonstrator immediately. This also includes breakages, faulty equipment, etc. If you are involved in a mishap or accident, don’t cover it up: tell your demonstrator immediately. Remember, by speaking up you may save someone else from being injured. REMEMBER: If you bring food or drink into the laboratory, or if you wear shoes which are not closed-toe, you will be ejected and you will lose marks. PHYC10006 Physics Laboratory Manual Exercise 1 – 1 Laboratory Exercise 1 Thermal Effects SAFETY Make sure that you have read the General Safety Notes, in the Introductory section of this manual, before you begin. Do not, under any circumstances attempt to repair any of the equipment. If you suspect equipment to be faulty, turn it off at the power point and talk to your demonstrator. In this exercise, the surface of the lamps and globes will become EXTREMELY HOT: do not touch them, or you will burn yourself. You should handle the globe by using the attached wooden block. Marks Breakdown: - Check point #1 - 2 marks - Check point #2 - 2 marks - Check point #3 - 2 marks - Conclusion - 2 marks - Lab Performance - 2 marks Outline of Laboratory Exercise In Section A you will investigate the concept of black-body radiation, observing how the radiation spectrum of an incandescent light globe filament varies with temperature. You will also observe some discrete elemental spectra. In Section B you will observe and analyse how the energy transference of thermal energy (via conduction, convection and radiation) depends on the temperature difference between an object and its surroundings. Pre-Lab Exercise: Read the entire laboratory exercise. Read the appropriate section of your textbook (detailing thermal energy and its transference) before coming to class. Then complete the exercises after the discussion of blackbody radiation below, before answering the questions for the pre-lab task online (http://fyl.ph.unimelb.edu.au/prelabs) for this experiment. [Your marks for the pre- lab will be based on the answers to the online questions, which are taken from the pre-lab work in the manual.] Temperature Units – Important! Remember that when dealing with temperature in the thermal equations discussed below, you must always use units of Kelvin (K). Negative temperatures don’t work when we relate temperature to energy (and ‘no negatives’ means no Celsius). Although each Kelvin unit is the same ‘size’ as a Celsius degree, Kelvin is never negative – the coldest temperature possible in Kelvin is absolute zero (i.e. –273.15° Celsius). Remember: always use Kelvin! Exercise 1 – 2 PHYC10006 Physics Laboratory Manual Introduction Our bodies interact with our surroundings in many ways. One of the most important ways is through thermal energy. For our bodies to function, it is vital that we maintain our internal blood temperature at around 37° C – if our core temperature is more than a few degrees away from this, the chemical processes that keep us alive will stop working properly. Although our internal temperature is near 37°, our surface temperature is usually less – around 33° C. 33 °C 37 °C Energy is produced in our bodies from exothermic chemical reactions. This energy output can be transferred to our surroundings via conduction, convection and radiation, as well as evaporation. We also receive energy from our surroundings – in particular from the sun, via its electromagnetic radiation. In the pre-lab below you will focus on thermal energy transference via radiation. Blackbody Radiation In thermal physics, we often talk about the concept of a black body – this is a theoretical object that fully absorbs 100% of the radiation that hits it, and then emits pure thermal radiation according to its surface temperature. Our sun produces a radiation spectrum that is approximately the same as an ideal blackbody radiator at a temperature of 6000 K. 0 2 4 6 8 10 0.0 1.0 2.0 3.0 4.0 wavelength (micron) intensity 6000 K 3000 K ì max,6000K ì max,3000K (Note that the intensity scale on the inserted graph is a logarithmic scale.) The graphs above illustrate the two main effects of temperature on the radiated spectrum: 1. The wavelength emitted with the most intensity is inversely proportional to the temperature: 1.0E-07 1.0E-06 1.0E-05 1.0E-04 1.0E-03 1.0E-02 1.0E-01 1.0E+00 1.0E+01 0.0 2.0 4.0 6.0 8.0 10.0 12.0 wavelength (micron) intensity 6000 K 3000 K 1500 K 750 K 375 K 188 K PHYC10006 Physics Laboratory Manual Exercise 1 – 3 ì max = 2.90 ×10 ÷3 Km T This is called Wien’s Law: the most intense wavelength ì max (in metres) is 2.90 x 10 -3 (in Kelvin metres) divided by the temperature T (in Kelvin). 2. The total power emitted (i.e. the rate of emission of energy) is proportional to the temperature to the power of four: Q rad t = Power =coAT 4 This is the Stefan-Boltzmann equation. Here c is the emissivity of the object’s surface, o is the Stefan-Boltzmann constant (which = 5.670 x 10 -8 Wm -2 K -4 ), A is the object’s surface area, and T is the surface temperature of the object (in Kelvin). The emissivity c is a value between 0 and 1, where 1 represents a perfect emitter. For a tungsten filament wire (as in an incandescent light globe), c is generally less than half. Calculate the wavelength of the most intense radiation emitted by: • A body with a surface temperature of 33°C • Inside an oven at 200°C • An incandescent light globe filament at 2300°C To convert between Kelvin (K) and degrees Celsius (°C), use K = 273 + C. Wavelength and Colour Recall that colour indicates wavelength. An approximate relationship between the colour and wavelength of visible light is given below: 400 nm 500 nm 600 nm 700 nm IR violet blue green yellow orange red UV Exercise 1 – 4 PHYC10006 Physics Laboratory Manual Section A – Thermal energy transference Radiator Spectra SAFETY WARNING Never look directly at the sun – direct sunlight will cause long-term damage to your eyes. Also, electric light sources will become very hot. This is normal. However, do not leave a light on and unattended for too long, or overheating may occur. Be careful! Look through a spectroscope at sunlight reflected off a sheet of white paper (see diagram below). sunlight white paper spectroscope eye Hold the spectroscope so that the colours range from violet on the left to red on the right. Adjust the tube of the spectroscope until the upper and lower edges of the spectrum are sharp – at this point it should be roughly in focus. In your logbook, sketch an approximate bar graph of intensity versus colour for the continuous spectrum you see, estimating the relative intensities across four regions of colour (see example below): violet - blue green yellow- orange red Now use the spectroscope to examine the light from an incandescent light globe filament. Sketch an approximate intensity-vs-colour bar graph for the light from the globe. The electric current through the incandescent filament can be changed using the variable transformer. Reducing the current should reduce the filament’s temperature. Examining the filament light with a spectroscope as before, steadily reduce the current. What do you observe? Sketch intensity-vs-colour graphs for three lower levels of current in the filament. Be sure that your graphs all have the same scale (i.e. each segment of colour in the same position on each graph). Considering the spectra of the sun and of the incandescent light, what can you say about the relationship between temperature and the kind of light emitted? Do your observations agree with the solar spectrum graphs shown in the Introduction section (under the Blackbody Radiation heading), above? If not, how and why are they different? Using your own solar spectrum results, estimate the brightest wavelength in the solar spectrum. Use this value to estimate the sun’s surface temperature. If the temperature of the incandescent filament were raised even higher (do not attempt to do this), its light would appear to be a blue-white colour. Why? PHYC10006 Physics Laboratory Manual Exercise 1 – 5 Elemental Spectra Some glowing bodies do not behave like black-bodies. Instead of producing light that is a continuous spread of colours, they only emit light of certain particular wavelengths. When an atom of a particular element is heated until it glows, it will emit a unique spectrum of certain particular wavelengths of light. This spectrum is unique to each element: just as every element has some particular boiling point, melting point, density etc, so it also has a particular emission spectrum. Unlike a continuous black body spectrum, these spectra are discrete. By analysing the emission spectra from light sources (such as distant stars), we can figure out which elements are glowing to produce the light. Many gases can be made to glow by passing electric current through them in discharge lamps. (This is basically how neon lights and fluorescent tubes work.) Use a spectroscope to examine the light emitted by a standard fluorescent light, a mercury discharge lamp (i.e. uncoated fluorescent), and a compact fluorescent. Sketch the spectra of these lights. In what ways are these spectra different to the spectra from hot solid bodies (as examined in the Radiator Spectra section)? Comparing the standard fluorescent light to the uncoated fluorescent light, how does the coating change the spectrum? Check Point #1: Show your demonstrator your sketched graphs and your answers to the questions above (from the Radiator Spectra and Elemental Spectra sections). [Make sure you’ve labelled all your graphs properly, so that your demonstrator can distinguish between them.] Thermal energy Transfer When there is a difference in temperature between an object and its environment, thermal energy will flow from one to the other. Thermal energy (labelled Q) is the thermal energy transferred between a body and its environment. Because thermal energy is a form of energy, it is measured in the SI unit for energy – joules (J) (See Appendix – SI Units). However, another common unit is the calorie (cal). Unit Conversion: 1 cal = 4.186 J There are three ways of transmitting thermal energy: Conduction, Convection, and Radiation. Conduction Conduction is the transfer of thermal energy via direct touch – when you touch something hot with your hand, the thermal energy is conducted to your hand. Consider an object (e.g. a rectangular slab) which has a length L, and two flat faces (each of surface area A) at each end of its length. One face is maintained at temperature T H and the other at temperature T C (where T H > T C ) so that thermal energy is conducted from the T H face to the T C face along the length of the object L. dQ cond dt ~ Q cond t = k A L T H ÷T C ( ) Here Q cond is the amount of thermal energy conducted, t is the time taken, and k is the thermal conductivity of the material. The rate of thermal energy transfer is proportional to the difference in temperature, the dimensions of the object (A and L), and the thermal conductivity constant (which depends on the material involved). Exercise 1 – 6 PHYC10006 Physics Laboratory Manual Convection Convection is a special form of conduction – it is the transfer of thermal energy due to motion within a fluid (such as air). When parts of a fluid are at different temperatures, the hot parts will tend to rise, transferring energy to the cooler parts as they do – until they become cooler than the parts below, and so they start to fall while the ‘new’ hot parts rise instead. This creates a cycle of rising and falling that transfers thermal energy around and around the fluid. The complexity of our weather is largely driven by convection processes in the atmosphere. Radiation Radiation is the transfer of thermal energy via electromagnetic radiation (light). We have already seen that the rate at which an object emits energy via thermal radiation is: dQ rad dt ~ Q rad t =coAT 4 This is the very same Stefan-Boltzmann equation discussed earlier for black-body radiation. In general, this equation describes the ideal transformation between thermal radiation and an object’s temperature (i.e. in either direction). If T is made to be the temperature of the environment (instead of the temperature of the object), then the equation also demonstrates the rate at which an object will absorb energy via thermal radiation from its environment. Section B — Energy Absorption and Cooling You should have the following apparatus setup on your desk: Lamp Thermometer Copper disc The lamp acts as a source of radiant thermal energy. This radiation from the lamp illuminates a painted copper disc, which supports a thermometer. The disc will warm up as it absorbs the energy radiated by the lamp. Its temperature will increase according to the balance between the energy it absorbs and the energy that it emits. There are two copper discs: one with a black surface and one with a white surface. You will measure the energy absorption rate of the two discs by recording the change in temperature of each disc over three minutes. PHYC10006 Physics Laboratory Manual Exercise 1 – 7 Directions: - Place the white-surface disc (with thermometer) on the peg on the board, about 10 cm away from the face of the lamp. - Turn on the lamp. (It should be connected to a 12 V power supply.) - Using the thermometer and a stopwatch, record the temperature of the disc every 15 seconds over a period of five minutes. Record your data in Excel. - Replace the white-surface disc with the black-surface disc. Do not burn yourself by touching anything too hot! - Repeat the recording of temperature as before, this time with the black-surface disc. - Turn off the lamp. As the black-surface disc cools, continue recording its temperature every 15 seconds for a further 5 minutes. Analysis — Answer all the following questions in your logbook. Now graph your data using Excel (both black-surface and white-surface heating data on the same graph). Use Excel to fit curves to your data points. Each disc absorbs radiant energy from the lamp while at the same time losing thermal energy to its surroundings. What are the processes by which the disc is losing energy? Look at the shape of the heating curves on your graph (temperature-vs-time). Think about how the process of absorption of energy will change as the temperature increases, and think about how the loss of energy will change as the temperature increases. With this in mind, try to explain the shape of the heating curves. At a certain temperature, the heating curve becomes horizontal. (Your results may not have reached this point.) Why does the curve become horizontal? What is happening at this point? Compare and explain the different results for the black-surface and white-surface discs. Consider the different gradients (slopes) of the different heating curves. Check Point #2: Show your demonstrator your heating graphs and discuss the questions above. [Make sure you justify your choice of curve to fit to your data.] Newton’s Law of Cooling Newton’s Law of Cooling states that an object’s rate of thermal energy loss is proportional to the difference in temperature between an object and its environment: dQ dt = hA(T obj ÷T env ) = hA AT ( ) Here Q is the thermal energy transferred over time t, h is the thermal energy transfer coefficient, A is the surface area of the object losing thermal energy, T obj is the surface temperature of the object and T env is the temperature of the environment surrounding the object. ∆T is just another way of writing the difference in temperature between an object and its environment. Although this equation is accurate and useful, it can be difficult in practice to calculate the thermal energy transfer coefficient h. But if the temperature difference between object and environment is not too great, we can simplify the equation as follows: dT dt = ÷r AT ( ) Exercise 1 – 8 PHYC10006 Physics Laboratory Manual The cooling rate (change in the temperature over time) is proportional to the difference in temperature. This is an important principle. The proportionality factor r is called the cooling constant. Cooling Analysis Look at your temperature-vs-time data from the black-surface disc as it cooled. This is a cooling curve. The gradient of the cooling curve will be the instantaneous cooling rate dT/dt (see the equation above). Which points on the curve do you think will produce a good estimate of the cooling constant r? Select three widely-spaced points on the curve. For each of these points, make a tangent line (or use Excel) to calculate the gradient at that point: T disc time 200 100 0 30 40 50 60 T 1 t 1 T 2 t 2 T 3 t 3 From the cooling rate equation above, the gradient at any point on the graph (i.e. dT/dt) should always be equal to the cooling constant r multiplied by the temperature difference ∆T at that point. Using the gradients for the temperature points you have chosen; calculate the cooling constant r from the cooling curve. Do you get the same value of r from each data point? Do your results confirm that the rate of cooling of the disc is proportional to the temperature difference between the disc and its surroundings? If not, why? Does Newton’s Law of Cooling make sense? Discuss and explain. If you were walking through the desert on a sunny day, what colour clothes would you like to wear? Explain why. Check Point #3: Show your demonstrator your cooling graph, analysis and answers to the questions above. [Make sure you discuss Newton’s Law of Cooling and whether your results support it.] Conclusion: Write a brief conclusion summarising what you did in today’s lab and your results. Remember to discuss whether your results were what you expected and include any sources of error. PHYC10006 Physics Laboratory Manual Exercise 2 – 1 Laboratory Exercise 2 Buoyancy SAFETY Make sure that you have read the General Safety Notes, in the Introductory section of this manual, before you begin. Do not, under any circumstances attempt to repair any of the equipment. If you suspect equipment to be faulty, turn it off at the power point and talk to your demonstrator. WATER AND ELECTRICITY DO NOT MIX In this experiment you must be aware of the danger of using electrical equipment near water. If any container breaks, please turn off the electrical equipment at the power point and immediately consult your demonstrator. Ensure that you use the drip trays provided, to minimise the possibility of any spillage reaching the electrical apparatus. Marks Breakdown: - Check point #1 - 2 marks - Check point #2 - 2 marks - Check point #3 - 2 marks - Conclusion - 2 marks - Lab Performance - 2 marks Outline of Laboratory Exercise In Section A you will observe the principle of buoyancy (Archimedes’ Principle) in action. Using your theoretical knowledge of buoyancy you will predict and test the apparent weight of a partially submerged object. In Section B you will determine the density of an unknown solution by observing the flotation of an object of known density. Pre-Lab Exercise: Read the entire laboratory exercise. Read the appropriate section of your textbook (detailing buoyancy and Archimedes’ Principle) before coming to class. Then complete the exercises below, before answering the questions for the pre-lab task online (http://fyl.ph.unimelb.edu.au/prelabs) for this experiment. [Your marks for the pre-lab will be based on the answers to the online questions, which are taken from the pre-lab work in the manual.] Exercise 2 – 2 PHYC10006 Physics Laboratory Manual 1. If a ball floats in water, partially submerged, is the density of the water more or less than the density of the ball? 2. A small wooden block floats on water. Will a wooden block with a hole in it also float? Explain. Section A Introduction When part (or all) of an object is submerged in a fluid, the fluid exerts an upward force on the object (against the pull of gravity). The discovery of this buoyancy force is credited to Archimedes (287– 212 BC), from whom we have Archimedes’ Principle: The buoyant force on an object immersed in a fluid is equal to the weight of the volume of fluid displaced by that object. This can be shown by considering the case of an ‘object’ immersed in the fluid is actually made of the fluid itself (e.g. a particular volume of water immersed within a larger body of water). Obviously, any volume of water must experience a pull of gravity due to its own weight. However, we know that water floats on water – it does not sink through itself! Since our volume of water is not accelerating downwards, a buoyancy force must somehow exist to exactly cancel the gravitational force of its weight. This buoyancy force is due to the pressure of the rest of the water surrounding and below our volume. It should now be clear that if our volume of water (or any other fluid) is replaced by another object that takes up the same volume, the buoyancy force due to the fluid does not go away. Therefore, any object in a fluid must experience the same buoyancy force that the fluid itself experiences – a force to cancel out the weight of the fluid of that volume. For example, consider the following situation. A ball is held under water: PHYC10006 Physics Laboratory Manual Exercise 2 – 3 A ball of mass M ball and volume V ball will experience a gravitational force equal to M ball g (directed downwards). Submerged in water, the ball also experiences a buoyant force equal to the weight of displaced water (directed upwards). The weight of displaced water is the weight of water that would be there if the ball was not – i.e. the volume of the ball multiplied by the density of water. The object therefore experiences a net force of gravity minus buoyancy: F net = M ball g ÷ µ water V ball g F net = µ ball V ball g ÷ µ water V ball g F net = µ ball ÷ µ water ( ) V ball g As a result of this, the ball appears to weigh less underwater than out of the water – the force it feels is as if the ball is less dense. This is why people feel ‘lighter’ when they swim. If the density of the ball is less than the density of the water, then the net force is negative and the ball will float upwards, until it is only partially submerged. (As it goes from being completely submerged to only partially submerged, the buoyancy decreases, because the volume of fluid displaced is less – only the parts of the object that are underwater are actually displacing fluid.) According to legend, Archimedes discovered this principle when taking a bath, and was so excited at his discovery that he ran naked through the streets, shouting ‘Eureka!’ (Greek for ‘I have found it!’). Archimedes was considering how to determine if a king’s crown was pure gold or not. If the crown is weighed first in air and then underwater, Archimedes’ Principle can be used to determine its relative density – i.e. whether or not the crown has the same density as pure gold. And of course, Archimedes’ Principle is especially useful for determining whether ships will sink or float. Complete the following activities. Record your observations and answers to any questions in your logbook. Melting Ice Due to increasing temperatures in the Earth’s atmosphere, it seems that our polar ice caps are currently melting. There are two kinds of ice in the world: ice that rests on the ground (e.g. glaciers), and ice that floats in the ocean (e.g. icebergs and ice shelves). In your laboratory are two beakers, each filled to the brim with water. One beaker has an ice cube outside of the water (simulating a glacier) and the other beaker has an ice cube in the water (simulating an iceberg). Predict which beaker/s will overflow when the ice cubes melt, and explain your reasoning. Will melting icebergs cause global sea levels to rise? What about melting glaciers? Explain. Check Point #1: Show your demonstrator your predictions. [Make sure you explain your reasoning.] Exercise 2 – 4 PHYC10006 Physics Laboratory Manual Weight of an object immersed in water You are given an aluminium cylinder, a container of water, and some measuring scales. The cylinder has an external scale on its side, as shown: external scale 5 4 3 2 1 0 Using vernier callipers, measure the diameter of the cylinder as accurately as you can. Use this diameter and the cylinder’s external scale markings to fill in the first two empty columns of a table in excel with the following headings: External scale marking Distance (to mark) Volume (to mark) Mass of displaced water Weight force of displaced water Expected apparent weight Measured apparent weight Given that water has a density of 1.0 g cm -3 , calculate the weight of water that will be displaced by the cylinder when it is submerged in water (up to each of its external markings). Enter this data in your table. Weigh the cylinder (in air). Using this value with Archimedes’ Principle, calculate the expected apparent weight of the cylinder submerged in water (up to each of its external markings). Enter this in the table as well. Immersion Fill the container with water up to approximately 10 cm from the top. Attach the cylinder to the scales and hang the scales from the jaws of a clamp, fixed to a stand above the container of water as shown: Adjust the position of the clamp on the stand, and the scales on the clamp, so that the cylinder is immersed in the water up to its first scale marking. The scale reading is a measurement of the cylinder’s apparent weight. Enter this value in the table above. Immerse the cylinder in the water up to each successive scale marking, recording each apparent weight measurement in the table as above. PHYC10006 Physics Laboratory Manual Exercise 2 – 5 How do the measured weight values compare to your predicted values? Do the differences between measured and predicted values (if any) seem reasonable, given the accuracy of the measurements? If you used a cylindrical (hollow) cup of aluminium instead of a solid cylinder of aluminium, how would the results differ? What about an aluminium object of a different shape? How is it that enormous ships made of heavy steel and concrete – e.g. aircraft carriers, cruise liners – do not sink? Check Point #2: Show your demonstrator your completed table and your answers to the questions above. [Make sure you stick your table into your logbook.] Section B — Density of an unknown solution In this section you will determine the density of an unknown solution (i.e. water with something unknown dissolved in it) by comparing its buoyancy force to the buoyancy of pure water. As in Section A, this is an application of Archimedes’ Principle. Recall that a balanced floating object is at rest: its gravitational weight is exactly balanced by the buoyancy force. Consider a hydrometer tube, partially submerged in water as shown: Mg 0 2 4 6 8 10 l sub d F B = V sub sol g Here V sub is the volume of the submerged part of the hydrometer, l sub is the length submerged and µ sol is the density of the unknown solution. The volume of the cylinder must be: V sub = l sub t d 2 | \ | . | 2 = l sub td 2 4 Using Archimedes’ Principle, write an expression for the ratio µ sol / µ water . Your task is to take measurements that will enable you to calculate µ sol . Directions: - Carefully place the hydrometer in the container of distilled water, making sure that it does not sink. - Let the hydrometer tube come to equilibrium (this should only take about 20 seconds). - Record the water level (according to the hydrometer’s scale on its side), and measure the distance from this level to the bottom of the hydrometer. This value is l sub . Exercise 2 – 6 PHYC10006 Physics Laboratory Manual - Using the scales provided, measure the mass of the hydrometer (with the ball bearings still inside). - Now place the hydrometer in the container of unknown solution. Measure the water level l sub of the floating hydrometer as before. Analysis Using your results, calculate the density of the unknown solution. (Assume that the density of pure water is 1.00 g cm -3 .) Ask your demonstrator for the actual density of the unknown solution and compare with your measured value. How well do the measured and ‘actual’ values agree? If they do not agree, what could be the cause of this? Explain and consider. Check Point #3: Show your demonstrator your results. Do they agree with the “actual” value? [Make sure you include a discussion of possible sources of error.] Conclusion: Write a brief conclusion summarising what you did in today’s lab and your results. Remember to discuss whether your results were what you expected and include any sources of error. PHYC10006 Physics Laboratory Manual Exercise 3 – 1 Laboratory Exercise 3 Flowing Fluids SAFETY Make sure that you have read the General Safety Notes, in the Introductory section of this manual, before you begin. Do not, under any circumstances attempt to repair any of the equipment. If you suspect equipment to be faulty, turn it off at the power point and talk to your demonstrator. WATER AND ELECTRICITY DO NOT MIX In this experiment you must be aware of the danger of using electrical equipment near water. If any container breaks, please turn off the electrical equipment at the power point and immediately consult your demonstrator. Ensure that you use the drip trays provided, to minimise the possibility of any spillage reaching the electrical apparatus. Marks Breakdown: Check point #1 - 2 marks Check point #2 - 2 marks Check point #3 - 2 marks Conclusion - 2 marks Lab Performance - 2 marks Outline of Laboratory Exercise In the Section A you will begin to explore the phenomenon of surface tension – the “skin-like” behaviour of the surfaces of fluids. In Section B you will investigate Bernoulli’s equation. In Section C you will use capillary tubes to measure surface tension. You will investigate differences between the surface tension of water and the surface tension of a soap solution. Pre-Lab Exercise: Read the entire laboratory exercise. Read the appropriate section of your textbook (detailing fluids and flow) before coming to class. Then complete the exercise below, before answering the questions for the pre-lab task online (http://fyl.ph.unimelb.edu.au/prelabs) for this experiment. [Your marks for the pre-lab will be based on the answers to the online questions, which are taken from the pre-lab work in the manual.] Exercise 3 – 2 PHYC10006 Physics Laboratory Manual Pre-lab Exercise Venturi Meter A manometer is a U-shaped tube containing fluid. A Venturi meter is a tube with a constriction in one part, connected to a manometer (see diagram below): Manometer Air blown in here y x P 2 P 1 P1 , v1, A1 P2 , v2, A2 The height of the fluid in the manometer arms can be used to determine the pressure difference between the constricted and non-constricted parts of the Venturi meter. According to the Continuity Equation A 1 v 1 = A 2 v 2 (see above) – therefore air should travel more quickly through the narrow part of the Venturi meter than through the wider parts. Go to the following website. Experiment and play with the Venturi Flowmeter Calculator located there: http://www.efunda.com/formulae/fluids/venturi_flowmeter.cfm Does it matter in which direction the air is blowing? Will there be any change to the pressure difference measured by the Venturi meter? Why? Section A — Surfaces and Tension Background Molecules that form the surface of a liquid exert forces on each other. As a result, the surface of a liquid can be imagined to behave like a slightly elastic ‘skin’. The forces between molecules of the liquid near the surface allow the surface to resist significant changes in shape: This elastic ‘resistance to change’ is called surface tension. It has the symbol and it is defined as the force per unit length along a line across the surface, where the force is parallel to the surface but perpendicular to the line: PHYC10006 Physics Laboratory Manual Exercise 3 – 3 F F force length This is also equivalent to the energy required to ‘stretch’ the area of the surface by a certain amount: work done increase in area The following example illustrates how these two definitions are equivalent. Consider a soap film being stretched in the x direction by a uniform force F: F x d force length F 2d work done increase in area Fx 2dx F 2d Note that in the first definition the length is 2d rather than d because the soap film has two sides. Soap Bubbles and Detergent Solutions Soap bubbles provide an example of how a liquid surface can behave like an elastic membrane. Pure water does not easily form bubbles, but adding detergent to the water will alter its properties significantly. Adding soap or detergent (i.e. a surfactant chemical) to water actually lowers the surface tension. How does a decrease in surface tension encourage bubbles? Consider that wherever a bubble has a weak point, the surface concentration of detergent will be decreasing; therefore, the surface tension will be increasing at that point. In this way, the weak points of a bubble are constantly being re-strengthened. This is why detergent bubbles, with their lower surface tension, are more stable than bubbles of pure water. (Detergent in water also reduces evaporation.) Tasks Complete the following activities. Record your observations and answers for one of these activities in your logbook. 1. Floating Needle Carefully wash and dry a dish. Be very careful that you don’t touch the inside of the dish with your fingers. Half-fill the dish with distilled water and gently place a needle flat on the water’s surface. If you have trouble, try placing the needle using a strip of filter paper or a ‘crane’ made from a paperclip. Carefully examine the floating needle from the side. If you dropped the needle straight into the water, it would sink. Why is it now floating instead? Explain how the water supports the needle. Now gently place a few drops of detergent into the water. What happens to the needle when detergent is added? Why? Exercise 3 – 4 PHYC10006 Physics Laboratory Manual 2. Surface Tension Submarine (Demonstration) The object shown in the following diagram is your ‘submarine’: rectangle of wire mesh blob of plasticene table tennis ball Carefully clean a beaker and fill it nearly to the top with water. Put the ‘submarine’ into the beaker – it should float upright, but part of it should be floating above the surface. Using clean fingers push the submarine gently but firmly under the surface. It should stay under. Examine the water surface close to the wire mesh. Describe what you see. From your observations, explain how the water keeps the submarine submerged after it has been pushed under. 3. Soap Bubbles Tie a thread across a wire loop in various different ways. Here are two possible examples: Dip the whole wire loop (with thread) into a liquid detergent solution. Slowly remove the loop. There should be a film of detergent across the loop. Pierce part of the detergent film with a needle. Explain what happens, how and why. There is a variety of other equipment in the lab that you can use to construct soap bubbles. Remember that the physics principles that apply for other bubbles are the same as for the original bubbles. Check Point #1: Show your demonstrator your observations and answers to the questions for your chosen activity. Discuss the other two activities. [Make sure you understand the other two activities, although you don’t have to write about them in your logbook.] PHYC10006 Physics Laboratory Manual Exercise 3 – 5 An Aside: Molecular Detergent The detergent soap films you have been investigating today work because of the behaviour of the different ends of the detergent’s molecules. One end of each molecule is ‘hydrophilic’ (‘water-loving’) and the other end is ‘hydrophobic’ (‘water-hating’). The hydrophilic end is attracted to water molecules, which is how the detergent can dissolve in water. But the hydrophobic end is repulsed by water molecules, which makes it point ‘away’ from water molecules, forming the surface of the detergent-water film (the bubble): hydrophilic hydrophobic Oils and grease are more attracted to hydrophobic molecules than they are to water, which is how detergent helps to clean dishes – the grease is more attracted to the detergent molecules than to the dishes. The overall attraction between the parts of the molecules holds the detergent film (the skin of the bubble) together. Ultimately, it can stretch until there is only a bi-layer of the detergent molecules (as in the diagram above). Section B — Bernoulli’s Equation Background Consider an incompressible, non-viscous fluid (e.g. an ideal normal liquid) that is flowing steadily through a tube. Bernoulli’s Equation describes this ‘streamline’ flow behaviour at any point: P 1 2 v 2 gh constant Here P is the pressure of the fluid, is the density of the fluid, v is the velocity of the fluid, and h is the height of the fluid; the value of the constant will depend on the particular fluid and tube. Because the fluid is incompressible, the density is constant, but P, v and h will be different at different points in the tube. But because Bernoulli’s Equation gives a constant value for all points in the tube, we can use the equation for the fluid at different points. For example: P 1 P 2 v 2 v 1 h 1 h 2 From the diagram above, we can use Bernoulli’s Equation to write that: P 1 1 2 v 1 2 gh 1 P 2 1 2 v 2 2 gh 2 Exercise 3 – 6 PHYC10006 Physics Laboratory Manual The ‘constant’ in Bernoulli’s Equation, whatever it is, must be the same for both points. The height is usually not an important factor, which means that the crucial relation is between pressure and velocity. Bernoulli’s Equation shows that when fluids slow down, their pressure will increase; when fluids are moving faster, their pressure will be lower. Note that Bernoulli’s Equation is derived from the principle of conservation of energy. If we multiply the entire equation by volume V of the fluid, all the terms become energy terms: PV 1 2 Vv 2 Vgh constant PV 1 2 mv 2 mgh constant The second and third terms are clearly the fluid’s kinetic energy and gravitational energy. Also, note that PV describes the work done by the force of the fluid’s pressure – it is also an energy term. Therefore, Bernoulli’s Equation simply says that when an ideal fluid flows freely, the total energy of the fluid is conserved. Unfortunately, today you will be dealing with air, which is not exactly an ideal fluid. Air can be compressed, and its flow is often turbulent instead of laminar (i.e. ‘smooth and steady’). However, the general Bernoulli principle (i.e. that high speed means low pressure, and vice versa) should still apply. Bernoulli’s Equation — Special Cases When a fluid is not flowing (i.e. v = 0), Bernoulli’s Equation becomes: P gh constant This describes how pressure varies with depth (when a fluid is not flowing) – it is directly proportional to the depth of the fluid (i.e. proportional to the weight of the fluid pushing down from above). Today you will be concerned mainly with flowing fluids. When the height of the fluid is not changing very much, h = 0 is a good approximation, and so Bernoulli’s Equation becomes: P 1 2 v 2 constant The Continuity Equation Aside from Bernoulli’s Equation, there is one other useful equation for considering flowing fluids. If a fluid is incompressible, then the density of the fluid cannot change at any point. The flow must be continuous – the amount of fluid flowing through the tube at any point (per unit time) must be the same at every point. This means that we can write: Av constant Here A is a cross-sectional area of the tube at a particular point, and v is the velocity of the fluid moving through that cross-sectional area. For any two points in the tube, we can know that: A 1 v 1 A 2 v 2 Activities You may choose to do one of the two activities below (Either Table Tennis Ball and Funnel or Balancing a Table Tennis Ball). Record your observations and answers for the activity you choose in your logbook. PHYC10006 Physics Laboratory Manual Exercise 3 – 7 1. Table Tennis Ball and Funnel Hold a table tennis ball in an inverted filter funnel, as shown below: Now, blow into the funnel. While still blowing, take your hand away from holding the ball in place and observe the results. A streamline in a fluid is the path that would be traced by an imaginary massless particle moving with the flow of the fluid – it traces the path of the flow. Streamlines are tangent to the velocity of the flow, and they cannot cross. Draw the streamlines within the funnel for the case where air is blown through, but there is no ball in the funnel. Draw the streamlines within the funnel for the case where air is blown through, but the ball is in place. How does the shape of the funnel affect the streamlines? How does the presence of the ball affect the streamlines? Where is the air moving most quickly? If you listen carefully you should hear a rattling noise, made by the ball repeatedly knocking against the funnel. Explain the cause of this effect. 2. Balancing a Table Tennis Ball Use the air supply to blow air upwards with the tube. While the air is blowing through, place a table tennis ball in the air at the top of the tube. Why isn’t the ball blown out of the air stream? Try pushing the ball sideways out of the stream with a pencil. What can you feel? Tilt the tube slightly to the side, so that the stream of air is not completely vertical. What happens? Exercise 3 – 8 PHYC10006 Physics Laboratory Manual Is it possible to hold the ball stationary with a horizontal stream of air? Explain. Draw a diagram of the streamlines when the ball is in a vertical stream of air. Draw a diagram of the streamlines when the ball is in an air stream that is tilted slightly to the side. In these two diagrams, show all the forces acting on the ball. Use these force diagrams to explain the effects you have observed. (Note: although turbulence is a factor in real-life situations, it is reasonable to ignore turbulence in your explanations.) Check Point #2: Show your demonstrator your observations and answers to the questions in your chosen activity. [Make sure you understand streamlines.] Capillary Rise When most liquids come into contact with a tube that is very narrow, the liquid will rise up into the tube against the pull of gravity. This is caused by forces due to surface tension: the liquid molecules are attracted to the surface of the tube. 0° contact angle The force due to surface tension will be the surface tension multiplied by length. If we assume that the liquid surface makes an angle of 0° with the tube wall – so that the force pulls straight up on the liquid – then the length will be the tube’s inner circumference 2πr. F 2r The gravitational weight of the column of liquid will be mg, where the mass of the liquid is density multiplied by volume: W mg Vg r 2 hg At equilibrium – i.e. when the liquid is not moving – the force pulling the liquid up the tube is balanced by the gravitational weight of the liquid in the tube: F W 2r r 2 hg rhg 2 Therefore we can calculate the surface tension from the radius and height of the capillary tube and the density of the fluid. PHYC10006 Physics Laboratory Manual Exercise 3 – 9 Section C — Measuring Surface Tension This experiment involves the following apparatus setup: Directions: Using a travelling microscope, measure the diameter of your capillary tube. Your demonstrator will show you how to use the travelling microscope. Carefully clean a 100 mL measuring cylinder. Fill it almost completely with distilled water. To rinse out the capillary tube, dip it into the water in the measuring cylinder. Lower the tube until it is almost completely immersed and then take it out again. Repeat this several times. Clamp the tube in place above the measuring cylinder. Attach a steel r0uler to the tube with an elastic band. Lower the tube into the water (rubber tubing first) until the top of the rubber tubing is in line with the surface of the water. Measure the height of the water column (in the tube) above the water surface. Repeat this measurement five or six times, to calculate an average value and a half-range estimate of the uncertainty. (If you do not understand half-range uncertainty, see Appendix A – Errors and Uncertainties Analysis.) Analysis From your data, calculate a value for the surface tension at the water-glass interface. (Assume that the density of distilled water is 1.00 g/cm 3 .) Refer to the Capillary Rise section. Remember to include uncertainty analysis for your calculations. How would your calculated result be different if the contact angle between water and tube was not 0° – for example, actually 30°? Discuss. Check Point #3: Show your demonstrator your results. [Make sure you’ve answered all the questions in the analysis section above.] Conclusion: Write a brief conclusion summarising what you did in today’s lab and your results. Remember to discuss whether your results were what you expected and include any sources of error. Exercise 3 – 10 PHYC10006 Physics Laboratory Manual PHYC10006 Physics Laboratory Manual Exercise 4 – 1 Laboratory Exercise 4 Fun with Charges SAFETY Make sure that you have read the General Safety Notes, in the Introductory section of this manual, before you begin. Do not, under any circumstances attempt to repair any of the equipment. If you suspect equipment to be faulty, turn it off at the power point and talk to your demonstrator. Marks Breakdown: Check point #1 - 2 marks Check point #2 - 2 marks Check point #3 - 2 marks Conclusion - 2 marks Lab Performance - 2 marks Outline of Laboratory Exercise In Section A you will investigate electric charges and the forces between them. In Section B you will investigate static electricity using an electroscope. Pre-Lab Exercise: Read the entire laboratory exercise. Read the appropriate section of your textbook (detailing electric charges) before coming to class. Then complete the exercise below as well as the questions in the Introduction section, before answering the questions for the pre-lab task online (http://fyl.ph.unimelb.edu.au/prelabs) for this experiment. [Your marks for the pre-lab will be based on the answers to the online questions, which are taken from the pre-lab work in the manual.] Access the SimPhysics applet, which you should find at: http://fyl.ph.unimelb.edu.au/webraft/efield/efield.html To launch the applet click the ‘Start SimPhysics’ button. This should produce a graph showing a positive and a negative charge. You can click at any position on the graph to show the direction of the field at that position, marked with an x and an arrow. The direction of the field is also the direction of the force that would be experienced by a positive ‘test charge’ at that position. You can move the x and the charges around on the graph, and you can also create new charges. Using the Particles menu, you can also change the sign of the charges. Play with these features and observe the changes in the electric field at different points. (If you are having trouble getting the java applet to work, try using a different web browser.) Exercise 4 – 2 PHYC10006 Physics Laboratory Manual Use the Particles menu to make both original charges positive. Then answer the following questions: 1. For two different locations of the ‘test charge’ (the x), sketch a diagram of the SimPhysics window showing the positions of all charges and the direction of the field vector. 2. In the SimPhysics window, go to the Vectors menu and select Vector Graph. Sketch the arrows that appear on this graph. You can turn the Vector Graph off again from the same menu. Using the Particles menu, now change the sign of the two charges to make both charges negative. Then answer the following questions: 3. For two different locations of the ‘test charge’ (the x), sketch a diagram of the SimPhysics window showing the positions of all charges and the direction of the field vector. PHYC10006 Physics Laboratory Manual Exercise 4 – 3 4. In the SimPhysics window, go to the Vectors menu and select Vector Graph. Sketch the arrows that appear on this graph. Introduction Most of what we know about electricity has been discovered only over the past two hundred years. But there is one aspect of electricity that people have known for much longer: static electricity. For centuries, people have been annoyed by the zap of static electricity. You may have felt a shock when touching metal after walking across a carpet; you may have noticed your clothes stuck together after they were tumbled in a clothes dryer. These are both common examples of static electricity. Like any other kind of electricity, static electricity arises from the interaction of electric charges. There are two different kinds (‘signs’) of electric charge, positive and negative. Charges with the same sign repel each other, while charges with opposing signs are attracted to each other. Whether repulsive or attractive, the magnitude of the force that each charge experiences is given by: F k q 1 q 2 r 2 Here q 1 and q 2 are the two charges, r is the distance between the two charges, and the constant k =9.0 x 10 9 N m 2 C -2 . The direction of the force is along a straight line, r, between the two charges. As well as this electric force, we also talk about the electric field produced by a charge. The electric field E at a point in space is the force exerted on a positive charge at that point, divided by that charge. This is a way of describing all the possible forces that could be exerted by a single charge – the field is the force ‘per charge’: E F q k q 1 q 2 r 2 q 2 k q 1 r 2 Here q 1 is the charge producing the field E, while q 2 is the charge that experiences (‘feels’) that field. This q 2 always cancels out (as in the equation above), because any particular field will only depend on the charge that is ‘creating’ it, not on anything else. Where two charges are close together, their two fields will overlap. The total field at a particular point in space will be the two individual fields at that point, added together. (Similarly, a charge placed at this particular point will feel a total force, which is the two electric forces from the two charges added together.) Exercise 4 – 4 PHYC10006 Physics Laboratory Manual To visualise the field of a charge, we can draw a series of lines and arrows indicating the direction and magnitude of the field at various points. By convention: The arrows on these field lines trace the direction that a positive charge would travel in the field: away from positive charges and towards negative charges. Because F =qE, the direction of the field is the same as the direction of the force (on a positive charge, that is – it’s the opposite direction for negative charges). Because of this, every single field line begins on a positive charge and ends on a negative charge. Field lines are drawn so that in areas where the electric field is stronger (i.e. closer to a charge), the field lines are closer together. Field lines are a kind of metaphor – the lines themselves do not ‘actually’ exist, but they are a good way for us to imagine the behaviour of the field (which does exist). You may have seen field lines demonstrated in your lectures using caraway seeds in electrically-charged oil: Charges and Friction You may have noticed that when certain objects are rubbed together, they can become charged with static electricity. This can be understood according to the following principles: All objects have electrons on their surface. A neutral (i.e. not charged) object has exactly the same number of protons (positive charges) and electrons (negative charges). The positive and negative charges cancel each other out. Cloth, plastic, or any other usual object will naturally be neutral (unless something is done to charge it). Different materials have different affinities for electrons. This refers to how likely they are to want to attract extra electrons (high affinity) or to lose the electrons that they already have (low affinity). When a high-affinity material is rubbed against a low-affinity material, electrons will move from the low-affinity surface to the high-affinity surface. The balance between protons and electrons will be altered, and so the objects will become charged. PHYC10006 Physics Laboratory Manual Exercise 4 – 5 Electron affinities are recorded in a Triboelectric Series table: POSITIVE Low Affinity for Electrons (from most +ve to least) NEUTRAL NEGATIVE High Affinity for Electrons (from least –ve to most) Human Skin Paper Lucite Leather Cotton Amber Rabbit Fur Steel Sealing Wax Glass Wood Acrylic Quartz Polystyrene Mica Rubber Balloon Human Hair Acetate, Rayon Nylon Synthetic Rubber Wool Polyester Lead Plastic Wrap Cat Fur Polyethylene (e.g. sticky tape) Silk Polypropylene (e.g. the lid of a box of Tic-Tacs) Aluminium Vinyl (PVC) If you rubbed polystyrene against leather, which object would end up positively charged? You have some cat fur, some polyester and some vinyl. You want to charge a piece of polyethylene to one kind of charge (i.e. positive or negative) and also a piece of acetate to the opposite kind of charge (i.e. negative or positive). What objects do you rub together, and why? In this lab exercise you will have a clear plastic strip (acetate) and a white plastic strip (polyethylene). You will rub both strips with polyester – in what ways (positive or negative) will the two plastic strips become charged? Exercise 4 – 6 PHYC10006 Physics Laboratory Manual Section A Electric Field Lines In this part of the lab you will explore software simulations of electric charges and fields. There are two different simulations to explore: the SimPhysics applet (you should already be familiar with this – see the Pre-Lab Exercise) and the Elf program. You should spend a few minutes playing with both of these programs. Explore the menu items and familiarise yourself with everything that the programs can do. SimPhysics This applet can be accessed at http://fyl.ph.unimelb.edu.au/webraft/efield/efield.html. As described in the Pre-Lab Exercise, this program uses an arrow to indicate the electric force at a point due to the charges on screen. Charges can be moved around, have their sign changed, and be added or deleted. The Vector Graph menu option displays a grid of force arrows across the entire window. Elf This program can be accessed via the shortcut on your computer’s desktop. Like SimPhysics, it displays electric force, but it shows the individual components as well as the total force. Unlike SimPhysics, it can also display field lines and equipotentials. (Equipotentials are the lines along which the electric potential – i.e. the potential energy per charge, or voltage – is equal.) After you have thoroughly clicked around both of these programs, use the software to sketch your own diagrams, in your logbook, of the following four arrangements of charge. Each diagram should include all charges involved, electric field lines, equipotential lines, and several appropriate force arrows (showing both direction and magnitude). Where more than one charge is involved, show how the individual electric forces add to create the total force. 1. One positive charge 2. One negative charge 3. Two positive charges 4. A dipole (i.e. one positive charge and one negative charge together, of equal magnitude) For this dipole, where is the field strongest? How does this relate to the field lines? (Answer all questions in your logbook.) Sketch in closer detail a region of the dipole field that contains two different equipotential lines. Sketch the field lines and equipotential lines in this region, and label the equipotentials with the value of their potential. Finally, sketch a path from a point on one equipotential line to a point on the other. What would happen as a positively charged particle moved along the path you have sketched (from one equipotential line to another)? Could the electric field cause this motion, or would an external force (a ‘push’) be required? Explain. What kind of energy transformation would occur for a positive charge moving from one equipotential line to another – Kinetic Energy into Electric Potential Energy, or vice versa? What about for a negative charge? For a charge of +1 C, what would be the magnitude of this energy change? In terms of energy and energy transformations, what does it mean that all the points on an equipotential line have the same potential? (Think about the definition of ‘potential’.) Check Point #1: Show your demonstrator your observations and answers to the questions above. [Make sure you understand the difference between field lines and equipotentials.] PHYC10006 Physics Laboratory Manual Exercise 4 – 7 Section B In this experiment you will have two strips of plastic: clear (acetate) and opaque (polythene). To charge these plastic strips, the best technique is to begin by holding a strip at the end marked with a dot. Then, holding a piece of cloth between the thumb and forefinger of your other hand, start near the dot end (where you are holding the strip with your first hand) and firmly press the cloth onto the strip as you pull it down the length of the strip. Repeat this several times, effectively rubbing the cloth down the plastic strip, and the end without the dot should become charged. Electrostatics On your desk is a stand, with a holder suspended from the stand by a piece of cotton. Directions: Charge the piece of acetate (clear plastic) as described above. Place the acetate in the holder so that it can rotate freely. Charge a second piece of acetate (clear plastic, again). Bring the charged ends of the two pieces of charged acetate close together. Do not let them touch! When the two pieces of acetate are close together, what do you observe? Now charge a piece of polythene (opaque plastic). Bring the charged end close to the charged end of the acetate in the holder. What do you observe now? Replace the acetate in the holder with a piece of charged polythene. Bring a piece of charged acetate close to the charged polythene in the holder. Then bring a second piece of charged polythene close to the polythene in the holder. What do you observe? In your logbook report, you should summarise your observations in a table similar to the one below. For each case indicate whether you observed attraction, repulsion or no effect. In Holder: Test material: Clear Acetate Test Material: Opaque Polythene Clear Acetate Opaque Polythene Now take the holder off the stand and replace it with an aluminium ball (‘red charge’) suspended by a string. Directions: (Be sure to answer all the questions below) Hold the aluminium ball between your thumb and forefinger. This is to ensure that the string is uncharged. Charge a piece of clear acetate and bring its charged end close to the aluminium ball. (Don’t let them touch!) What do you observe? Now let the aluminium ball touch the piece of charged acetate. What do you observe now? How does this differ from before? Repeat the entire procedure just described, but this time using a piece of opaque polythene instead of clear acetate. What happens now? Check Point #2: Show your demonstrator your observations and discuss your findings. [Make sure you understand what’s happening with charges in this experiment.] Exercise 4 – 8 PHYC10006 Physics Laboratory Manual The Electroscope The electroscope is made of an insulating case with a metal cap outside and a copper plate inside. A gold leaf is attached to the copper plate inside, but positioned so that it can move away from the plate. When a charged object is brought close to the electroscope, the gold leaf will move in response to the electric force – this is how the detector basically works. To determine the sign of some charged object, the electroscope itself must be charged first. But if the electroscope’s metal cap is simply rubbed with some charged object, this will not charge up the electroscope very well – rubbing will have only a small effect on the cap’s charge. Question: Why does rubbing the metal cap with a charged plastic strip transfer only a small amount of charge? To charge the electroscope, it is better to charge by induction. This is shown in the following diagrams: In other words: bring a charged rod close to the electroscope cap, touch the cap with your hand (this provides the ‘Earth’ connection through your body), remove your hand, and then remove the rod. Note that the charge induced on the electroscope in this way will always be opposite to the charge on the object used for the induction (i.e. the rod). The following diagram shows in more detail the motion of charged particles during induction, and the effect that this has on the motion of the gold leaf: Of course, you should remember that there will actually always be both positive and negative charges on the rod and on the electroscope. However, most of these charges will effectively cancel each other out – we can ignore them. What is shown in the diagrams above are the excess charges. These are not cancelled out, because they have no nearby opposite-charge counterparts. Procedure Charge the electroscope twice by induction, as described above. Use a piece of charged clear acetate as your induction rod for Electroscope 1, and use a piece of charged opaque polythene as your induction rod for Electroscope 2. PHYC10006 Physics Laboratory Manual Exercise 4 – 9 Record your predictions for what you think will happen when you do the following: Bring a charged clear acetate strip close to Electroscope 1 Bring a charged opaque polythene strip close to Electroscope 1 Bring your bare hand close to Electroscope 1 Bring a charged clear acetate strip close to Electroscope 2 Bring a charged opaque polythene strip close to Electroscope 2 Bring your bare hand close to Electroscope 2 Explain your reasoning. Are your predictions consistent with your model of what is happening? Now actually do these tests as described in the six points above, and record your observations. Do your observations of the six points match your predictions? If not, why not? Discuss. WARNING: At all times be careful that the object being tested is not brought too close to the electroscope, or the following glitch may occur with the gold leaf inside the electroscope: lower +ve charges Neg charged electroscope +ve charged object well above cap more +ve charges still more +ve charges still lower - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + - - - - - - - - - - - - - - + + lower +ve charges Neg charged electroscope +ve charged object well above cap more +ve charges still more +ve charges still lower - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + - - - - - - - - - - - - - - + + In other words, the electroscope charge may be accidentally reversed! If in doubt, discharge your electroscope and start again. Check Point #3: Show your demonstrator your predictions and observations. [Make sure you’ve answered all the questions above.] Conclusion: Write a brief conclusion summarising what you did in today’s lab and your results. Remember to discuss whether your results were what you expected and include any sources of error. Exercise 4 – 10 PHYC10006 Physics Laboratory Manual PHYC10006 Physics Laboratory Manual Exercise 5 – 1 Laboratory Exercise 5 Electrical Circuits SAFETY Make sure that you have read the General Safety Notes, in the Introductory section of this manual, before you begin. Do not, under any circumstances attempt to repair any of the equipment. If you suspect equipment to be faulty, turn it off at the power point and talk to your demonstrator. BATTERIES: LOOK CLOSER If any of the batteries in the laboratory appear to be damaged or leaking, do not touch them – they contain strongly corrosive chemicals and will burn you. Notify your demonstrator immediately. Marks Breakdown: - Check point #1 - 1 mark - Check point #2 - 1 mark - Check point #3 - 2 marks - Check point #4 - 2 marks - Conclusion - 2 marks - Lab Performance - 2 marks Outline of Laboratory Exercise This laboratory exercise is designed to be a basic introduction to building and understanding electrical circuits. In the Section A you will explore basic electrical concepts, investigating a set of simple circuits involving light globes. You will predict and measure voltage in these circuits. In the Section B you will predict and measure current in circuits involving light bulbs Pre-Lab Exercise: Read the entire laboratory exercise. Read the appropriate section of your textbook (detailing Ohm’s Law and electric circuits) before coming to class. Be sure that you understand the concepts of ‘voltage’, ‘current’, ‘resistance’ and ‘electrical power’. Then complete the question below and the exercises in the Introduction section, before answering the questions for the pre-lab task online (http://fyl.ph.unimelb.edu.au/prelabs) for this experiment. [Your marks for the pre- lab will be based on the answers to the online questions, which are taken from the pre-lab work in the manual.] Exercise 5 – 2 PHYC10006 Physics Laboratory Manual Introduction Although electricity is an essential part of the modern world, it is not well understood by the general public. Many people believe that the words ‘electricity’, ‘voltage’, ‘electric power’ and ‘electric current’ all mean the same thing – you may not even be sure about this yourself. Electricity also plays a crucial role in cell biology. For example, the way that charge leaks across the membrane of a cell can be modelled as a capacitor applying voltage across a resistor: + – + + + + + + + – – – – – – + – – plasma membrane cytoplasm R Cm A basic understanding of electricity is also essential to understanding how to protect yourself from electric shock. This laboratory exercise examines these basic electrical concepts, emphasising current as the ‘rate of flow of charge’ and voltage as the energy difference that causes the charge to flow. The potential difference (or ‘voltage drop’) between two points in a circuit is the difference in electrical potential energy, per charge, between the two points. It is this voltage difference – the difference in potential energy per charge – which makes the charge flow. This is how voltage produces current. NOTE: The terms voltage, potential and potential difference are all different words for the same thing. Voltage is sometimes called potential because it is short for ‘potential energy per charge’. But be careful – ‘potential energy per charge’ is not exactly the same thing as ‘potential energy’! Make sure you understand what is going on. Remember: voltage =potential energy per charge. Voltage makes the current flow. If you think of electrical current like water flowing down a hill, the voltage represents the steepness of the hill. Circuit Diagrams Electrical circuits are generally represented using circuit diagram symbols. Each type of electrical component has its own standard symbol, for example: switch light globe resistor A ammeter V voltmeter battery + - PHYC10006 Physics Laboratory Manual Exercise 5 – 3 Below is a picture of a circuit, and its corresponding circuit diagram: A B 6.0 V C D It is important to realise that the circuit diagram does not necessarily show the physical location of each component. Instead it shows the connection pathways: the ways in which the components are connected to each other. For example: of the following three diagrams, the first two are identical but the third is different. Make sure that you understand how and why this is so. B D A C A B C D A B C D Which of the following circuit diagrams are equivalent (i.e. which pairs of diagrams represent the same circuit)? A B C D A B C D A B C D A B C D Voltage Light globes are simple but very useful devices for exploring simple electrical circuits. The filament in an incandescent light globe glows as electrical current passes through it, transforming the electrical energy carried by charge into light and heat. The brightness of a light globe is an indication of the rate of this transformation of energy – i.e. the power being ‘used’ by the globe. Exercise 5 – 4 PHYC10006 Physics Laboratory Manual charges have lower potential energy charges have higher potential energy globe emits energy as electromagnetic radiation drift of charge Consider that the power dissipated (used) by the globe must be equal to the charge per second passing through the globe, multiplied by the energy dissipated per unit charge. By definition: Current =charge per second passing through the globe Voltage =change in electrical potential energy per unit charge I (current) + V (voltage) light globe battery - Therefore: Electrical Power =Voltage x Current P =VI You might like to think of this as similar to flowing water used to turn a water wheel. In this process, the gravitational potential energy of the water is converted into kinetic energy of the water wheel. water has higher potential energy water has lower potential energy water wheel gains kinetic energy water flow A battery would be similar to a pump to push the water back to the top Similarly, a light globe converts the electrical potential energy of the electrical current into light and heat. Voltage is the measure of the difference in electrical potential energy per charge between two different points in the circuit. The unit of voltage is the Volt (V), which is equal to one J oule per Coulomb (J C -1 =energy per charge). PHYC10006 Physics Laboratory Manual Exercise 5 – 5 Why doesn’t it make sense to say that ‘the voltage at point X is 3 volts’? Remember: in most situations, a battery supplies a circuit with constant voltage. The amount of current in the circuit will vary according to the resistance of the circuit components. Wiring Circuits To make it easier to correctly set up complicated circuits, you may find it easiest to wire them up loop- by-loop as shown below. Start at a convenient point (like the positive terminal of the battery) and work your way around the circuit diagram component-by-component until you have completed a loop back to your starting point: + - V + - V If the circuit has more than one loop, complete the next loop next. + - V + - V You might also find it helpful to try to arrange your circuit components on your bench so that the layout looks as close as possible to the actual circuit diagram. Constructing circuits is a skill that will be useful to you later in the semester. Make sure that every person in your group gets practice at wiring up circuits. Section A TAKE NOTE Batteries go flat. Do not leave batteries connected to a circuit for more time than is necessary – only connect batteries briefly, to examine the brightness of the light globes, and then disconnect them (or leave the switches open) when not actually doing this. Exercise 5 – 6 PHYC10006 Physics Laboratory Manual Resistance Construct the following three circuits. Observe the brightness of each globe when the switch is closed. The difference between the second and third circuits is very important. The globes in circuit two are connected in series (in a row), while the globes in circuit three are in parallel (next to each other). Every circuit component has its own resistance, R. This is a measure of how much energy it takes to make current to flow through the component. The voltage drop over a component is proportional both to the resistance and to the amount of current. When components (like light globes) are added in series, the total resistance is the sum of the individual resistances: R T = R 1 + R 2 +...+ R N (Here N is the total number of components in series.) However, when components are added in parallel, the resistances are added inversely. The total resistance is the inverse of the sum of the inverse resistances: 1 R T = 1 R 1 + 1 R 2 +...+ 1 R N ¬ R T = 1 R 1 + 1 R 2 +...+ 1 R N | \ | . | ÷1 Note: this means that when components are added in parallel, the total resistance actually reduces! The more components there are in parallel, the more pathways there are for the current to flow. This means less total resistance overall. Of the three circuits shown above, which will drain the energy of a battery most quickly? Explain (in your logbook). Voltmeters Construct the following circuit: PHYC10006 Physics Laboratory Manual Exercise 5 – 7 With the switch closed, measure the voltage across the battery (hold the red lead of the voltmeter against the positive terminal of the battery, and the black lead against the negative terminal). Note that the voltmeter has more than one voltage range. When measuring an unknown voltage, always try with the largest range first and work down. (The needle deflection on the dial should increase as you switch to the lower ranges – if it doesn’t, something is going wrong.) With the voltmeter joined to the circuit like this, the circuit diagram should actually be: V With switches closed, measure voltages for the following circuit configurations. V V V How are these voltage measurements related to each other? (Answer in your logbook.) Now construct the two circuits shown below. Measure the voltages at each marked voltmeter position and record your measurements on the circuit diagrams in your logbook. V V V V V V V Compare your voltage measurements of these circuits. Do your results make sense, considering the energy transformations taking place in the circuit? Explain. What can you say about the voltages across different components connected in series (like the three light globes in a row, above)? Construct the following circuit. Use a voltmeter to measure and record the voltages V AB , V CD , V AC etc (where e.g. V AB is the potential difference between point A and point B). Exercise 5 – 8 PHYC10006 Physics Laboratory Manual V AC = V BD = V AB = V CD = V DF = V CE = V EF = F E D C A B Looking at the circuit, what energy transformations are taking place across the different points? Try to explain the voltages you have measured in terms of these energy transformations. In general, what effect will a battery, a light globe or a section of wire have on electrical potential energy? Compare your measurement for V AB (the voltage across the battery in the circuit above), with your original measurement for voltage across a battery (at the beginning of this Voltmeters section, above). What effect does a particular circuit have on the voltage supplied by a battery? Consider circuits with components in series compared to circuits with components in parallel (you have already measured voltages for both of these). In terms of the energy transformations involved, explain the difference between voltage over series components and voltage over parallel components. Check Point #1: Show your demonstrator your measurements, diagrams and answers to the questions above. [Make sure your diagrams are neat and legible!] Section B — Current Apart from a voltmeter, another useful device for studying circuits is an ammeter. Ammeters measure current which is the amount of charge passing through a point per second. The unit for this is the Ampere (A), often abbreviated to amp, which is equal to Coulomb per second (C s -1 ). Construct the three circuits below and record the ammeter readings for each. You should be able to trace the red terminal of the ammeter back around the circuit to the positive terminal of the battery. (If your ammeter is connected the wrong way around, the needle will move backwards.) A A A Note that just like voltmeters; ammeters have more than one measurement range – be sure that you use the most appropriate range for your final measurement. Discuss and explain your measurements. Considering the definition of current, do your measurements make sense? PHYC10006 Physics Laboratory Manual Exercise 5 – 9 Now construct the circuits below. Measure the currents with ammeters in place as shown. A Circuit A A Circuit B A Circuit C Analysis — Answer all the following questions in your logbook. Consider the three circuits you have just examined. Is the total current from the battery (i.e. the total charge per second emerging from the battery) affected by the components of the circuit? How does the total current change when globes are added in series (i.e. comparing circuit B to circuit A)? How does the total current change when globes are added in parallel (i.e. comparing circuit B to circuit C)? How does the effect of components in series versus components in parallel differ for the circuit voltage compared to the circuit current? Compare your ammeter results to your voltmeter results from the Section A. Recall the discussion of resistance in Section A. Resistance is the factor that determines how much current flows for a given source of voltage. How is the total resistance of the circuit affected by adding globes in series (i.e. comparing circuit B to circuit A)? How is the total resistance of the circuit affected by adding globes in parallel (i.e. comparing circuit B to circuit C)? Try to explain how this works. If you are having difficulty understanding resistances in parallel, talk to your demonstrator. Check Point #2: Show your demonstrator your answers to the questions above. [Don’t forget to draw all the circuits you construct in your logbook.] Currents in Parallel Now measure the current in each separate parallel arm of Circuit C (above). Are your results consistent with your understanding of how current works? Explain. The following circuit will be set up with four ammeters in place at once, so that all four current measurements may be made simultaneously. A A A A Exercise 5 – 10 PHYC10006 Physics Laboratory Manual From these measurements, try to explain the relationship between currents in different parts of the circuit. Were any of the measured currents similar to measurements made in previous circuits? How would you explain this similarity? Check Point #3: Discuss your findings with your demonstrator. [Make sure you can explain the relationship between current in different parts of a circuit.] Understanding Circuits Consider the following circuit: D G E B C F A H I Using your understanding of electrical circuits, predict the various voltages and currents for this circuit as listed in the table below. (You should include a table like this in your logbook.) You should also predict how bright each light globe will be (compared to the brightness you observed in the standard circuits A, B, C above). After you have made your predictions, measure the actual voltages and currents of the real circuit to check your predictions. Predicted Value Measured Value Predicted Value Measured Value V AB I A V CD I C V DE I F V CE I H V FG I I Were any of your predictions wrong? If so, make sure that you understand why and explain your mistake in your report. What electrical conditions are required for two light globes to produce the same brightness? Check Point #4: Show your demonstrator your table. Discuss your predictions if they were wrong. [Make sure you’ve also answered the questions above.] Conclusion: Write a brief conclusion summarising what you did in today’s lab and your results. Remember to discuss whether your results were what you expected and include any sources of error. PHYC10006 Physics Laboratory Manual Exercise 6 – 1 Laboratory Exercise 6 Capacitors SAFETY Make sure that you have read the General Safety Notes, in the Introductory section of this manual, before you begin. Do not, under any circumstances attempt to repair any of the equipment. If you suspect equipment to be faulty, turn it off at the power point and talk to your demonstrator. CAPACITORS: ONE WAY ONLY! The capacitors you will use in this exercise are electrolytic capacitors, so it is essential that they are wired in circuits the correct way around. If connected incorrectly, they may become irreparably damaged or even explode. Connect the black ‘–‘ end to the earth side of the circuit, as shown in the circuit diagrams below. Double-check all connections before turning on the power. If in doubt, talk to your demonstrator. BATTERIES: LOOK CLOSER If any of the batteries in the laboratory appear to be damaged or leaking, do not touch them – they contain strongly corrosive chemicals and will burn you. Notify your demonstrator immediately. Marks Breakdown: Check point #1 - 2 marks Check point #2 - 1 mark Check point #3 - 1 mark Check point #4 - 2 marks Conclusion - 2 marks Lab Performance - 2 marks Outline of Laboratory Exercise In Section A you will familiarise yourself with the Cathode Ray Oscilloscope (CRO) apparatus, examining basic capacitor behaviour and investigating the energy stored in a charged capacitor. In Section B you will examine the charging-discharging behaviour of a capacitor and how this relates to the capacitor’s time constant. Pre-Lab Exercise: Read the entire laboratory exercise. Read the appropriate section of your textbook (detailing capacitors and capacitance) before coming to class. Then complete the question below before answering the questions for the pre-lab task online (http://fyl.ph.unimelb.edu.au/prelabs) for this experiment. [Your marks for the pre-lab will be based on the answers to the online questions, which are taken from the pre-lab work in the manual.] Exercise 6 – 2 PHYC10006 Physics Laboratory Manual Reading a CRO Read the entire laboratory exercise carefully before answering the following questions. Pay close attention to the section below on Cathode Ray Oscilloscopes (CROs). From the following diagrams of CRO outputs and settings, determine the necessary input voltages. Note that on the diagrams below, 1 scale division = 1 cm. For the signal shown on the rightmost diagram below, also determine the time taken for input voltage to increase from 0 to 10 V. SETTINGS: Timebase: Off 0.1 ms / cm 0.01 ms / cm Y-gain: 2.0 V /cm 1.0 V /cm 5.0 V / cm Input Voltage: Introduction In the Electrical Circuits laboratory exercise, you dealt entirely with direct current (DC) circuits – circuits where the electrical supply is at a constant ‘direct’ voltage (e.g. from a battery). DC circuits are continuous conducting paths of constant voltages, currents and resistances. Most real-life electrical circuits are not DC. Instead, they run on alternating current (AC) – electrical supply with a voltage that continuously varies from positive to negative, alternating like a sine wave. Mains electrical supply (i.e. power points) in Australia is AC power at approximately 240 V (RMS), alternating at a frequency of 50 Hz. (Note: RMS stands for root mean square. Mains voltage is constantly cycling from positive to negative, but the RMS value calculates a meaningful ‘average peak value’ over this cycle.) When a circuit contains voltages that alternate or otherwise vary with time – e.g. circuits that contain components such as capacitors or inductors – then Ohm’s Law alone is not enough. We need to be able to analyse voltages and currents as they are changing. In this exercise you will learn how to use a cathode ray oscilloscope (CRO) to investigate time-varying electrical signals. PHYC10006 Physics Laboratory Manual Exercise 6 – 3 Cathode Ray Oscilloscope (CRO) An electrical circuit is connected to the CRO, which displays a voltage-vs-time graph of its input signal. The glowing ‘dot’ on the CRO display moves vertically according to the voltage of the input – the scale, positioning and timebase (time scale) can all be modified. For example: if the central line is set to measure 0 volts, and the Y-gain (vertical scale) is set to 2 V/cm, then the dot will move up or down on the display a distance of 1 cm for every input voltage difference of 2 volts. If a 6 V battery is attached, the dot will move 3 cm up; if the battery is connected to the input terminals in reverse, then the dot will move 3 cm down. SETTINGS: Timebase: Off Y-gain: 2 V / cm Input Voltage: (nothing) Timebase: Off Y-gain: 2 V / cm Input Voltage: 6 V (DC) Timebase: Off Y-gain: 2 V / cm Input Voltage: 6 V (DC) Reversed The advantage of a CRO compared to a voltmeter is that the CRO can move the dot from left to right at a steady speed, making it easier to visualise a voltage that is changing over time. If the dot is moving quickly enough from left to right, it will appear on screen as a solid line. For example: suppose the dot is set to move horizontally at 1 cm/s and the Y-gain set to 1 V/cm. If the input voltage started at 0 V, rose steadily to 3 V over 2 seconds and then fell back to 0 V another 2 seconds later, we would see the dot trace a diagonal line up from left to right (3 cm up, 2 cm across) and then another diagonal line down from that point (3 cm down, a further 2 cm across). Similarly, a voltage that varies sinusoidally will appear on the CRO as a continuous sine wave. In the examples below, the input voltage is labelled according to its amplitude and frequency. SETTINGS: Timebase: 0.1 ms / cm Y-gain: 2 V / cm Input Voltage: 6 V, 1 kHz Timebase: 0.2 ms / cm Y-gain: 2 V / cm Input Voltage: 6 V, 1 kHz Timebase: 0.05 ms / cm Y-gain: 2 V / cm Input Voltage: 6 V, 1 kHz Exercise 6 – 4 PHYC10006 Physics Laboratory Manual We can measure the frequency of the signal directly from the CRO display. If the distance taken to move through one full cycle on the screen is 10 cm, then we can work backwards from the timebase setting to determine the period of one full cycle. The frequency is the inverse of the period. A diagram of the CRO control panel is shown below. Don’t panic – you will only need to know a few of the controls to understand what is going on. Triggering MODE Channel 2 OR X X Gain POS. Coupling X input Channel 1 OR Y Coupling Y Gain Y input POS. Power Intensity Focus Timebase Horizontal Position The Y-gain and Timebase controls are discussed above. The input electrical signal is connected to the CRO through a coaxial cable connected to the Y input. Section A Capacitors If a constant voltage is applied across a light globe or a basic resistor, then a constant current will flow through the circuit. However, capacitors are not so simple. A capacitor is commonly formed by two parallel surfaces with no conducting path between them – therefore, current cannot flow through a capacitor. Capacitor Parallel plates C Circuitry Symbol for Capacitor PHYC10006 Physics Laboratory Manual Exercise 6 – 5 Capacitors are useful because when voltage is applied, charge accumulates and is stored on the capacitor plates. This ability to store charge is proportional to the voltage applied, according to the capacitor’s capacitance: Q CV Here Q is the charge stored on the plates, C is the capacitance of the capacitor, and V is the voltage on the plates. For a parallel-plate capacitor, the capacitance will be proportional to the surface area of the plates – the more surface area; the more charge can ‘fit’ on the plates. And because electric fields weaken over distance, capacitance is also inversely proportional to the distance between the two plates. Note that charge does not accumulate on the plates instantly. As voltage is applied, current flows to the plates and begins to ‘charge them up’. The rate of this charging becomes slower and slower as the charge on the plates builds up. (Imagine a car park filling up – the more cars have already gone in, the more time it will take each new car to find a free space.) Capacitance and Dielectrics Capacitance is the amount of electric charge that can be stored on the capacitor plates per volt of potential difference between the capacitor plates. A variable capacitor is a useful device for investigating capacitance: it can vary the size of the capacitor plates, distance between the plates, and the material between the plates. Dielectrics are insulating materials that do not conduct charge. However, the materials contain dipoles that are free to rotate, and which will align themselves with the electric field. When the dipoles line up together, they will create their own electric field, and this will alter the behaviour of the capacitor as a whole. Dielectrics are placed in capacitors for multiple reasons. They can allow higher voltages to be applied between the plates, increasing the capacitance and decreasing the necessary size of the capacitor. Because they are insulators, dielectrics can coat the conducting plates of the capacitor so that the plates are in close contact without creating a short circuit – this also allows the size of the capacitor to be decreased. At a high enough voltage (3 x 10 6 V m -1 ), an electric field will ionise the air itself (this is how lightning is made); insulating the capacitor with a dielectric instead of air prevents this. All these reasons are useful, but the most important reason for a dielectric is to increase the capacitance. When the dipoles align in the electric field between the plates, they create their own electric field in the opposite direction to the existing field. Because electric fields add together, the total electric field between the plates is therefore reduced. The relationship between electric field strength E, voltage V and distance d is as follows: V Ed Therefore as the field E is reduced while d is constant, the voltage between the plates is also reduced. And since Q = CV (see above), if Q remains constant while V is reduced then the effective capacitance C is increased. Energy stored in a capacitor As a side-effect of storing charge, capacitors can also be used as a way to store a fixed amount of energy. This is their practical application in many modern electronic devices. In this lab you will attempt to confirm that the energy stored in a charged capacitor is: U 1 2 CV 2 Here U is the energy stored, C is the capacitance and V is the charging voltage. Exercise 6 – 6 PHYC10006 Physics Laboratory Manual The circuit shown below will be wired up as demonstrations. You may operate the circuits yourself, however ask your demonstrator before you investigate the circuit. + - + First of all, be sure the power supply is set to 5 V. Charge the capacitor by closing the first switch for approximately 10 seconds. Then open the switch and allow the capacitor to discharge through the light globe by holding down the second switch in the circuit. Measure the length of time that the globe glowed, and note how bright the globe appears at the start of the discharge (i.e. the peak brightness). The brightness and duration of the light globe’s glow should be an indication of how much energy was stored in the capacitor. When considering the brightness of globes in other situations, refer to this original brightness (and the length of time that it glowed for) as a reference point. For what length of time did this reference globe glow? (Record this in your logbook.) This measurement was for a single globe at 5 V. According to the theoretical formula above, we expect that the energy stored by the capacitor should be dependent on the charging voltage as well as the capacitance. Ask your demonstrator to connect another capacitor in parallel to the first capacitor. Draw this new circuit in your logbook. Using the same procedure as before, charge the capacitors before letting them discharge through the light globe. How does the brightness and duration of glow compare to the original circuit? What does this imply about the energy stored by the capacitors in this circuit, compared to the energy stored in the original circuit? Assuming that the energy stored in the circuit is related to voltage and total capacitance according to U = ½ CV 2 , how do you think that adding the capacitor in parallel has altered the total capacitance? What do think happens to the total capacitance when multiple capacitors are added in parallel? Explain. Now ask your demonstrator to remove the capacitor placed in parallel, and instead connect it in series with the original capacitor (i.e. the circuit now contains two capacitors, in series). Draw a circuit diagram. Charge and discharge the capacitors again, as before. How does the brightness and duration of this ‘series’ glow compare to the original circuit and to the parallel circuit? What does this imply about the energy stored by the capacitors in this series circuit, compared to the energy stored in the other circuits? Assuming that the energy stored in the circuit is related to voltage and total capacitance according to U = ½ CV 2 , how do you think that adding the capacitor in series has altered the total capacitance? What do think happens to the total capacitance when multiple capacitors are added in series? Explain. The circuit below is also set up as a demonstration. This time the power supply is set to 10 V. + - + + Charge and discharge the capacitors as before. How do the glows of these four globes compare to the glows of the previous circuits (in both brightness and duration)? PHYC10006 Physics Laboratory Manual Exercise 6 – 7 This last circuit uses the capacitors to power four globes instead of only one. If the brightness is the same as before, but the glow lasts for a longer time, then it seems that more energy was stored in the capacitor. If the brightness and duration of glow are both the same as a previous globe, but there are 4 globes instead of 1, then the energy in the capacitor is 4 times as much as previous. Since we doubled the voltage and received apparently four times as much energy, it seems that the energy stored in a capacitor may in fact be proportional to V 2 (because two squared = four). Check Point #1: Discuss your findings with your demonstrator, including your answers to the questions above. [Make sure all members of your group fully understand capacitance.] Section B Charging and Discharging a Capacitor If a capacitor is connected to a DC voltage, the plates will charge up until they reach their capacity (according to Q = CV), and then the current will stop flowing. But if we connect a capacitor to an alternating voltage, the voltage will be switching its direction back and forth. If the time the capacitor takes to charge is similar to the time it takes for the voltage to switch back and forth, then the plates will repeatedly charge and discharge – the charge (current) flowing backwards and forwards in time with the alternating voltage source. Construct a circuit consisting of a resistor and a capacitor to the CRO as shown below, and use an alternating voltage (square wave) signal generator for the power supply. This type of circuit is often called an RC circuit (R for resistor, C for capacitor). Construct the following circuit. Use the resistor colour code chart (see the Appendix) to identify the correct resistor. Signal Generator CRO 1 k 0.27 µF When setting up this circuit, remember to connect the black ‘–‘ end of the capacitor to the correct (‘earth’) terminal of the signal generator, as shown. It is also important that there is no circuit element between the earth connections of the signal generator and the CRO. Set the signal generator to supply a 6 V peak-to-peak square wave at a frequency of 200 Hz. You should confirm this signal by temporarily leaving the resistor and capacitor out of the circuit, so that the CRO will display the ‘original’ signal supplied to the circuit. Check with your demonstrator that your CRO is set up correctly. NOTE: Your CRO is not broken! It is very easy to wrongly configure the CRO settings, so that you cannot see the correct signal. It is extremely rare for a CRO to be actually broken or defective – double-check that all settings and connections are correct before you give up. Once the ‘original’ square wave signal is confirmed by the CRO, reconnect the resistor and capacitor to the circuit. The CRO should be connected to either side of the capacitor, so that it will display the voltage difference between the two capacitor plates. You should be able to see the ‘curves’ of changing voltage as the plates repeatedly charge and discharge – you may need to fine-tune the Exercise 6 – 8 PHYC10006 Physics Laboratory Manual frequency of the signal generator for it to match the capacitor’s charging-discharging rate. Adjust the Y-gain of the CRO to display the charging-discharging curves as large as possible on the CRO screen. Sketch the charging-discharging voltage curves displayed on the CRO, making careful note of the voltage and time scales and other CRO settings. Your demonstrator will show you how to set the CRO coupling switch temporarily to ‘Ground’, to check the ‘zero volts’ position on the display. Question: What happens if you vary the frequency and magnitude of the signal generator (the power supply)? Explain how this affects the amplitude and period of the capacitor’s charging- discharging curve on the CRO. Check Point #2: Show your demonstrator your sketched curves and your answers to the above questions. [Make sure you now know how to operate a CRO.] The Time Constant of a Capacitor It can be shown that while a capacitor is discharging, the voltage across the capacitor plates changes according to this equation of exponential decay: V V max e t RC Here V = voltage, V max is the maximum voltage, t = time, R = the resistance in the circuit and C = the capacitance in the circuit. Note that the negative sign indicates that the voltage is decreasing. The product of R and C is called the time constant, : RC This is a useful constant value of the circuit. Whenever the time elapsed reaches this ‘time constant’ value (i.e. t = ), we know that the voltage will have decreased to a natural logarithmic proportion of 1/e (i.e. approximately one-third) of the maximum: V V max e RC V max e RC RC V max e 1 1 3 V max By looking at a voltage-vs-time graph of the discharge curve, we can therefore estimate the value of RC by looking at the time taken for voltage to drop by two-thirds. V max ~V max /3 0 t = RC t V PHYC10006 Physics Laboratory Manual Exercise 6 – 9 Using this method of graphical approximation, measure the time constant for your circuit according to the curve displayed on your CRO. Analysis From your measured value of the time constant and the known resistance of your circuit, use the time constant formula to calculate the expected capacitance of your circuit’s capacitor. Note that the total circuit resistance includes the circuit resistor itself (1 kΩ) and the internal resistance of the signal generator (which is approximately 600 Ω). Remember to calculate ± uncertainty values for your results. Assume that the uncertainty in the total circuit resistance is 10%. (If unsure about uncertainty analysis, see Appendix A.) Does the calculated value for capacitance match the manufacturer’s value (written on the capacitor), within uncertainties? If not, why not? Check Point #3: Show your demonstrator your value for the time constant. [Make sure you include uncertainties and answer the other questions above.] Changing Resistance Repeat the measurement of the time constant as above, but this time replace the 1 kΩ resistor in the circuit with a 10 kΩ resistor. To clearly display the new discharge curve, you will need to alter the CRO settings. Sketch the new charging-discharging curves in your report. Remember to note the Y-gain and timebase scales. How are these curves different from the curves for the 1 kΩ circuit? Why are they different in these ways? (Talk to your demonstrator if unsure.) Changing Capacitance If the capacitance C were increased by a factor of 10, how would you expect the discharging characteristics to change? What if C were decreased by a factor of 10? Explain your answers. Check Point #4: Show your demonstrator your answers to the questions above. [Make sure you’ve also sketched the appropriate graphs and labelled them correctly.] Conclusion: Write a brief conclusion summarising what you did in today’s lab and your results. Remember to discuss whether your results were what you expected and include any sources of error. Exercise 6 – 10 PHYC10006 Physics Laboratory Manual PHYC10006 Physics Laboratory Manual Exercise 7 – 1 Laboratory Exercise 7 Magnetic Interactions SAFETY Make sure that you have read the General Safety Notes, in the Introductory section of this manual, before you begin. Do not, under any circumstances attempt to repair any of the equipment. If you suspect equipment to be faulty, turn it off at the power point and talk to your demonstrator. WARNING – HOT The wire and coil used in the experiment will both become very hot. Be sure that you do not touch the wire or the coil. Marks Breakdown: Check point #1 - 1 mark Check point #2 - 1 mark Check point #3 - 2 marks Check point #4 - 2 marks Conclusion - 2 marks Lab Performance - 2 marks Outline of Laboratory Exercise In Section A you will investigate the behaviour of magnetic fields, the magnetic force on moving electrons, electromagnets, and examples of magnetic induction. In Section B you will investigate Faraday’s Law of Induction and Lenz’s Law, and see how the principle of electromagnetic induction may be used to ‘steal’ electricity. Pre-Lab Exercise: Read the entire laboratory exercise. Read the appropriate section of your textbook (detailing electromagnetism) before coming to class. Then complete the exercises in the Introduction section and Section A, before answering the questions for the pre-lab task online (http://fyl.ph.unimelb.edu.au/prelabs) for this experiment. [Your marks for the pre-lab will be based on the answers to the online questions, which are taken from the pre-lab work in the manual.] Exercise 7 – 2 PHYC10006 Physics Laboratory Manual Introduction In magnetism, North and South are the names given to the two opposite magnetic qualities. North and South magnetic poles are attracted to each other by magnetic forces, while two North poles (or two South poles) will repel each other. This is essentially the same as the way that positive and negative electric charges attract and repel each other due to electric fields and forces. (As you will learn, this is because electricity and magnetism are fundamentally related.) However, although positive and negative charges are independent objects, magnetic poles are always found together as a linked pair of North and South, called a magnet. The planet Earth is a giant magnet. Because of this, magnetic objects like compasses will tend to align themselves with the Earth’s magnetic field: Note that because of this, the Earth’s South magnetic pole is actually close to the geographic North Pole (in the Arctic, where Santa Claus lives), and similarly the North magnetic pole is near the geographic South Pole (in Antarctica). Compass Needles in Magnetic Fields The diagrams below each illustrate a magnet in a magnetic field at the instant that the magnetic field is ‘turned on’ (i.e. before the magnet has had any time to ‘feel’ the forces due to the field). The left side of the magnet is North and the right side is South. Uniform Field Non-Uniform Field Suppose the magnets are compass needles, free to rotate around their centre but otherwise fixed and unable to move translationally. PHYC10006 Physics Laboratory Manual Exercise 7 – 3 1. Predict the motion of the magnet in the uniform field as a result of the forces shown. 2. Predict the motion of the magnet in the non-uniform field as a result of the forces shown. 3. Now suppose the magnets are not compass needles, but instead iron filings – i.e. very small magnets that are free to move (assume no friction). Describe the motion of the magnets in each of the two fields. Magnets are affected by external magnetic forces, as well as producing their own magnetic field. Electric charges will also experience magnetic forces, but only when a charge is moving. Static electric charges are not affected by magnetic force. The force on a moving charge can be described according to the vector product: F q v B Here F is the force experienced by the charge, q is the charge, v is the velocity of the moving charge and B is the strength of the magnetic field. Because electric current is simply moving charge, electric current feels magnetic force. As a result, a wire carrying electric current will seem to be affected by magnetic force, due to the force felt by the moving charges that it carries. This force can be described according to the vector product: F i L B Here F is the force on the wire, i is the current through the wire, L is the length of wire and B is the strength of the magnetic field. (This force equation is equivalent to the F =qvB equation above.) When the magnetic field is perpendicular to the length of wire, this vector product becomes a simple multiplication. IMPORTANT: the key fact to remember from this is the difference between fields and forces. While electric field lines are in the same direction as electric force – easy to remember – the magnetic field lines are not the same direction as magnetic force! The direction of magnetic force is perpendicular to the field, according to the vector product equations above. This can be confusing. To remember the direction of forces due to vector products, you may find the Right Hand Rules helpful: The Right Hand Rule (for Forces) (Also known as the Right Hand Slap Rule.) Because of the vector product, the force experienced by a moving positive charge (or current) will be in a direction perpendicular to both the other two vectors (i.e. the magnetic field and the velocity of the charge). You can form the shape of these vectors using your right hand: Exercise 7 – 4 PHYC10006 Physics Laboratory Manual The direction of force is pointing up, out of your right palm. This rule also works if the velocity vector (the thumb) is the direction of the current. The Right Hand Grip Rule (for Fields) The Right Hand Grip Rule describes the magnetic field that is produced by a moving charge (or by current flowing along a wire). Remember: while electric field lines are straight lines going out from electric charges, magnetic field lines are perpendicular to the motion of the charge. This means that the magnetic field lines are circles which loop around the axis of moving charge. If your right thumb is the direction of the current (or moving charge), the magnetic field lines produced by that current will be loops. The loops curl around in the same direction as your fingers. Section A Magnetic Field Lines You will be provided with two magnets and a small compass. The compass has a magnetic needle that is free to rotate: placing the compass at some point near the other magnets, the direction of its needle will indicate the direction of the total magnetic field at that point. Before you begin, check that your compass is working properly. With all magnets kept away from the compass, the needle should point North. However, small compasses sometimes get their poles reversed – it may instead point South. If there seems to be a problem, see your demonstrator. When you have calibrated your compass needle, use it to determine which ends of your magnets are North and which are South. Next, you should have a grid similar to the one overleaf: PHYC10006 Physics Laboratory Manual Exercise 7 – 5 N S N S With the magnets arranged on the grid as shown, the magnetic field to the right of the magnets (where the grid is) should be a symmetrical mirror image of the field to the left of the magnets. Use your compass needle to determine the direction of the magnetic field at each grid point, and sketch that direction on the grid. (This is not supposed to be a precise measurement, so don’t spend too much time on this.) A compass needle cannot measure the magnitude of the magnetic field, but by finding its direction at many points we can map the direction of the field. When you have mapped the field across the whole grid, sketch the magnetic field lines. By convention, field lines go from North to South (i.e. the same direction as the compass needle). When you are done, stick your grid into your logbook. Magnetic Fields Produced by Electric Current Magnets are not the only objects that create magnetic fields – for instance, electrical current produces a magnetic field. In a laboratory environment there may be many different sources of magnetic field. The net magnetic field at any point will be the vector sum of all the magnetic fields present at that point: i.e. the Earth’s global magnetic field in addition to any local fields (from electrical devices, nearby magnetic materials, etc). Using your compass, find the direction of the net magnetic field at your bench. Does your compass point North (i.e. the ‘real’ magnetic / geographic North of the Earth)? Explain. Check Point #1: Show your demonstrator your grid with magnetic field lines you’re your answers to the other questions above. [Make sure you discuss the sources of magnetic field at your bench.] Demonstration 1: Force on a Current Carrying Conductor in a Magnetic Field Use the right-hand slap rule to predict the direction of the force on the straight portion of the conductor AB (shown in the diagram below), carrying a current I as shown. I B N S A I I Exercise 7 – 6 PHYC10006 Physics Laboratory Manual Draw the diagram in your logbook to show your prediction. Switch on the current and check your prediction. Reverse the direction of the current I and observe the deflection of length AB. Write down your observation in your logbook. Demonstration 2: Electrons Moving in a Magnetic Field There is a single discharge tube apparatus (see below) in the laboratory. Your demonstrator will organise a demonstration of this. Make sure that you have already read the questions below and that you are prepared to get the necessary information from this demonstration. You should answer the first question before the demonstration and the second question after the demonstration. SAFETY WARNING On the discharge tube, do not touch the ends of the wire from the voltage source! If you do, you will receive a very painful (although probably not fatal) electric shock. The discharge tube consists of two oppositely-charged electrodes at either end of an evacuated discharge tube: fluorescent screen evacuated discharge tube e's + - Electrons are accelerated by the potential difference (voltage) between the two electrodes, travelling to the right in the diagram above. The paths of the electrons are made visible by the fluorescent screen. Use the Right Hand Rule (see above) to predict the direction that the electrons will be deflected when the N-pole of a magnet is brought towards the tube from the front (on the diagram above, towards the page). When the power to the induction coil is turned on and the discharge tube activates, you will be able to check your prediction. You should also see what happens when the S-pole is brought towards the tube instead of the N-pole. In both cases, how does the electron beam deflect? How do the results compare to your predictions? If your predictions were wrong, explain how and why. Check Point #2: Show your demonstrator your predictions above and discuss your observations. [Make sure you understand what is happening in the demonstration.] Section B — Induced Voltages and Currents Moving charges will produce a local magnetic field, but the reverse is also true – a changing magnetic field will similarly induce charges to move (i.e. produce current). Consider a magnet moving into a coil of wire: PHYC10006 Physics Laboratory Manual Exercise 7 – 7 N S µA A spiral coil of wire with many closely-spaced turns – called a solenoid – is connected to a micro- ammeter as shown in the diagram above. As the magnet moves into the coil, any induced current will be measured by the micro-ammeter. Experiment 1 Observe the micro-ammeter as you push the magnet into the coil, North end first (as shown above). What happens? Try moving the magnet at different speeds into and out of the coil, and turning the magnet around South-first instead of North-first. Describe what happens. Check Point #3: Write your observations in your logbook and discuss them with your demonstrator. [Make sure you understand what is happening.] It may be helpful to imagine that the magnet is ‘inducing’ a source of voltage, like a battery. This ‘battery’ (source of potential difference) induces a current to flow, which we measure through the micro-ammeter: µA + - through micro-ammeter current flows from +to - The sign (i.e. direction) of the voltage induced will depend on the direction of the induced current in the coil. This direction (or ‘polarity’) will depend on the motion and orientation of the changing magnetic field (i.e. your moving magnet). Magnetic Flux A common way to think about changing magnetic fields is to think about magnetic flux. Flux is a measure of the number of field lines passing through a region of space: more field lines means that the field is denser closer to a pole and therefore more powerful. Field lines are technically not ‘real’, so flux is not exactly ‘real’ either, but the concepts are useful because they are good metaphors for something that is definitely real – the strength of the magnetic field itself. Exercise 7 – 8 PHYC10006 Physics Laboratory Manual Because of this, we can define magnetic flux as the product of the magnetic field and the area through which we are defining the flux: B A BAcos Here is the magnetic flux, B is the magnetic field, and A is the vector describing the area of the flux. The flux through an area A is the dot product of the area itself and the magnetic field passing through the area. When a magnet’s North pole is pushed into a region of space like the solenoid, you should be able to imagine that the field lines in that region will increase (and therefore, so will the magnetic flux). The rate of change in flux is proportional to the induced voltage and current. Inductors From your observations, you should be able to understand that coils of wire – like the solenoid you have been using today – are able to induce current from changing magnetic fields (and vice versa, to induce magnetic fields from moving charges). Because of this ability, coils of wire (or devices with similar properties) are often called inductors. There are two equivalent ways to explain your observations of induction in this Experiment. Explaining Magnetic Induction — Lenz’s Law The changing magnetic field (due to the moving magnet) creates an induced voltage, which produces a current in the solenoid (because voltage makes current flow). This current produces its own magnetic field. The induced current flows in a direction such that its own magnetic field opposes the change in magnetic field that was due to the moving magnet. This is illustrated below for a single loop of the solenoid coil: A loop of the coil before the magnet approaches. As the magnet approaches, its field lines pass through the coil. The magnet's approach causes a change in magnetic flux (increased field) to the right. The magnetic field due to induction must oppose this change of flux, so it is opposite – i.e. to the left. For the induced current to have created this flux to the left, the current must flow in loop as shown (recall Right Hand Grip Rule). This is Lenz’s Law: that the flux created due to magnetic induction will always be opposite to the changing flux that induced it in the first place. Explaining Magnetic Induction — Energy Conservation When you induce a current by moving the magnet into the coil, you are supplying energy to the coil – the energy needed to make the current flow. The only way for you to supply energy to the coil is to do work against a force – i.e. a force that opposes you moving the magnet. This opposing force can only come from a magnetic field in the wire, which can only be produced by current flowing through the wire. If you know the direction of the force that you are working against, you can figure out the direction of the field that must be producing that force. And when you know the direction of that field, PHYC10006 Physics Laboratory Manual Exercise 7 – 9 you can deduce the current flow that must have produced that field. This reasoning is illustrated below, again for a single loop of the solenoid coil: As you may be able to see, this is actually just another way to describe Lenz’s Law – the two explanations are equivalent. If you don’t understand either explanation, talk to your demonstrator. Experiment 2 Do the explanations above correctly predict the current flow that you observed in your solenoid? Explain. Push the magnet back into the solenoid, N-pole first. Now remove the magnet again. Observe the behaviour of the micro-ammeter – what is happening? Push the magnet into the solenoid, S-pole first. Observe the behaviour of the micro-ammeter – what is happening? Now remove the (S-pole first) magnet and observe the behaviour of the micro-ammeter – what is happening? Of the four basic possibilities – N-pole first in, N-pole first out again, S-pole first in, S-pole first out again – which are equivalent, and why? Faraday’s Law of Induction Faraday’s Law of Induction says that the voltage induced in a closed loop of wire is directly proportional to the rate of change of magnetic flux through the loop: d dt Here is the induced voltage and is the magnetic flux (as defined above). The minus sign indicates that the direction of induced voltage is opposite to the change in flux, as described by Lenz’s Law. From Faraday’s Law, we can draw the following conclusions: A flux that doesn’t change over time – e.g. stationary magnet – creates zero induced voltage. A small change in flux over some time produces a small induced voltage. A bigger change in flux over the same time produces a bigger induced voltage. A small change in flux over less time will produce a bigger induced voltage. Force to the left As the magnet approaches, there must be a force opposing the approach. N This repulsive force must be caused by a similar magnetic pole – i.e. in the case, North. I According to the right hand grip rule, the current to produce this must flow as shown above. Exercise 7 – 10 PHYC10006 Physics Laboratory Manual With this in mind, Faraday’s Law should explain your observations of the strength of the induced voltage in relation to the changing speed of the magnet through the coil. If not, talk to your demonstrator. Faraday’s Law — Analysis Move the magnet through the coil again – first slowly, and then more quickly. How do the signals change? Does Faraday’s Law explain this? Explain how. Check Point #4: Discuss your observations with your demonstrator and show them your answers to the above questions. [Make sure you’ve answered all the questions in Experiment 2.] Conclusion: Write a brief conclusion summarising what you did in today’s lab and your results. Remember to discuss whether your results were what you expected and include any sources of error. PHYC10006 Physics Laboratory Manual Exercise 8 – 1 Laboratory Exercise 8 Properties of Radiation SAFETY Make sure that you have read the General Safety Notes, in the Introductory section of this manual, before you begin. Do not, under any circumstances attempt to repair any of the equipment. If you suspect equipment to be faulty, turn it off at the power point and talk to your demonstrator. It is a general rule that you must not eat or drink in the laboratories. This is extremely important when dealing with radioactive materials. The substances you will be handling today are not especially dangerous under normal conditions – but if they enter your body they can be extremely harmful, even fatal. If you are thirsty, use the water fountain at the eastern end of the laboratories. To minimise your exposure to radiation, always be sure to: • Keep the radioactive source as far away from you as possible. • Minimise the time that you are exposed to the source. • Shield the radioactive source (using the lead blocks provided) whenever possible. • Wash your hands after handling the source and at the end of the lab session. The lead shielding blocks are also toxic. Wash your hands after handling them to prevent lead poisoning. The radiation detectors used in the laboratory are powered by a high voltage power supply. If any leads or components appear damaged, talk to your demonstrator immediately. RADIOACTIVE MATERIALS In this exercise you will be dealing with samples of radioactive material. When you receive a source of radioactivity from your demonstrator, you must sign for it on the radioactive sources record. When you return the radioactive source to your demonstrator at the end, you must sign AGAIN on the radioactive sources record. You MUST return all radioactive materials and sign the record for this before you leave. Marks Breakdown: - Check point #1 - 3 marks - Check point #2 - 3 marks - Conclusion - 2 marks - Lab Performance - 2 marks Exercise 8 – 2 PHYC10006 Physics Laboratory Manual Outline of Laboratory Exercise In Section A you will investigate two types of smoke detectors and how they work. You will also examine the effects of increasing distance from a radioactive source. In Section B you will examine the quantitative effects of radiation shielding. The insights you gain will hopefully help you to understand the effectiveness of radiation protection strategies – the ways in which a combination of shielding and distance can reduce radiation exposure. Pre-Lab Exercise: Read the entire laboratory exercise. You must pay particular attention to the relevant Safety Notes for this exercise, as well as the discussion of Radioactivity in the Introduction (below). Then complete the exercises below, in the Introduction section and Section A, before answering the questions for the pre-lab task online (http://fyl.ph.unimelb.edu.au/prelabs) for this experiment. [Your marks for the pre-lab will be based on the answers to the online questions, which are taken from the pre-lab work in the manual.] Pre-Lab Exercise You will need to read the entire laboratory exercise before you can answer this question. Consider the case of Sarah the molecular biologist. Sarah works with radioactive isotopes from behind a Perspex screen, 2 metres away from the source of radiation. She has a mass of 50 kg and an effective surface area of 0.7 m 2 facing the radiation, and she spends approximately 10 hours a week, 45 weeks a year, working with radiation in this way. Calculate Sarah’s annual radiation dose (in Sieverts) if the source of radiation is a sample of Cobalt-60 producing gamma radiation with an energy of 1.2 MeV = 1.92 x 10 -13 J per photon, at a rate of 40 mega-Becquerels (MBq). Does Sarah exceed the maximum safe dosage of 20 milli-Sieverts (mSv) per year? Note: 1 Becquerel (Bq) = 1 photon of radiation produced per second; 1 Sievert (Sv) = an absorbed dose of radiation energy of 1 J kg -1 . PHYC10006 Physics Laboratory Manual Exercise 8 – 3 If Sarah worked in exactly the same way but was 50 cm from the source instead of 2 m, would she exceed the maximum safe dosage? Introduction — Radioactivity The term radioactivity refers to any process in which atoms of a particular element spontaneously change into atoms of a different element. Sometimes this happens when an unstable nucleus ejects part of itself as an alpha particle (which is actually two protons and two neutrons bonded together – i.e. a Helium nucleus). Alpha particles are the most damaging form of radiation, but they do not penetrate shielding easily – they will usually be stopped by any material as dense as piece of paper. Alpha decay is relatively uncommon. More often, elemental change happens because the nucleons (neutrons and protons) inside the nucleus change – either a proton turns into a neutron, or vice versa. This type of change is accompanied by the emission of a charged particle (called a beta particle) and/or other radiation from the atom’s nucleus. Beta particles and gamma rays are generally less damaging but more penetrative than alpha particles – they require more dense shielding materials. (A beta particle is actually either an electron or an anti-electron. Anti-electrons are called positrons.) When a nucleus decays, the ‘daughter’ nucleus (i.e. the nucleus after it has changed) is often in an excited state. This is analogous to atomic excitation, when electrons are raised into unstable higher- energy states – but when a nucleus is excited, it is not electrons but instead the nucleons which are in higher-energy states. To release the excess energy, the protons and neutrons emit gamma rays: high- energy photons of electromagnetic radiation. Gamma rays from nucleons are usually at much higher energies (~MeV) than photons from electrons (e.g. X-rays) – the energy difference between an excited state and a ground state is much larger for nucleons than for electrons. The radioactive source you will be using in today’s exercise is a sample of Cobalt-60. This transforms via beta decay (ß - ) into an excited nucleus of Nickel-60, which then emits a gamma ray (¸) with an energy of 1.2 MeV as it de-excites. In nuclear physics terms, this reaction is represented as follows: ¸ v | + + + + ÷ ÷ Ni * Ni Co 60 60 60 Your source is covered by a thin metal shield, which will absorb everything but the gamma rays. This means that your source should appear to be producing 1.2 MeV gamma rays only. Exercise 8 – 4 PHYC10006 Physics Laboratory Manual Geiger Counters In the following laboratory exercise you will be using a Geiger counter to detect radiation. A Geiger counter consists of a cylindrical case containing a mixture of gases, with a wire running along its axis. The wire is insulated from the case and held at a positive electrical potential (voltage) relative to the case, using a DC power supply. Gas Mixture + ion flow - ion flow Interaction Site Gas is ionised, enabling current flow Anode (+) Cathode (-) Insulator Incident Radiation Filament wire When radiation enters the counter, it ionises some of the gas molecules in its path. The negative ions or free electrons created by this ionisation are attracted to the counter’s anode (via the wire), while positive ions are attracted to the counter’s cathode (via the case). They are accelerated by the electric field difference between cathode and anode (due to the voltage from the power supply). As the charges accelerate they collide with other gas molecules, thereby causing more ionisation, and more free charges, and even more ionisation. This process of charge multiplication occurs many times. Ultimately, a substantial negative charge will be deposited on the anode. The current flow that results between cathode and anode is employed to produce the Geiger counter’s ‘clicking’ sound. In general: radiation entering the Geiger counter is used to produce electrical current, which provides the power to electronically detect that the radiation exists (and ‘click’ to inform you of it). Background Radiation You should notice that the radiation counter will detect continual radiation even when the radioactive source is not nearby. This is background radiation – the constant small amount of radiation that exists everywhere around us, all the time. Ordinary concrete and bricks contain traces of radioactive material (e.g. Thorium, Potassium), and we are also bombarded by many cosmic rays from outer space. When measuring the radioactivity of a particular source, it is obviously necessary to first measure the average background radiation, and then subtract this background from your measured data. The Randomness of Radioactive Decay Radioactive materials decay one nucleus at a time. Each nucleus decays at random, and independently of the other atoms around it. Because of this randomness, if we count the number of decays over a certain length of time and then repeat our measurement, we don’t expect to get the exact same number of decays each time. However, the probability that a nucleus will decay is not completely random – it is determined by the structure of the nucleus. Since all the nuclei have the same structure, every nucleus has the same probability of decay. The variation to expect in the number of decays over a given time interval can be predicted using the statistics of probability. If we count the number of decays per minute over and over again, statistical analysis leads us to expect that the different numbers measured will cluster around a central average value N 0 (the mean): PHYC10006 Physics Laboratory Manual Exercise 8 – 5 frequency with which a given number occurs number of decays per time N 0 This mean value N 0 is the number that best represents the average rate of decay. But if we make only one measurement, how close to N 0 do we expect our measurement to be? Statistical analysis shows that for a normal distribution of randomness, 68.3% of measurements will be within ± one standard deviation of the mean, 95.4% of measurements will be within ± two standard deviations, and 99.97% will be within ± three standard deviations. For the kind of randomness exhibited by radioactive decay (which is called a Poisson distribution), it turns out that the standard deviation is equal to the square root of the mean: N0 . Because we know that radioactive decay follows this statistical pattern, we can use this standard deviation value as our statistical ± uncertainty value (see also Appendix A). So if we make a single measurement which gives us a number N, then we can be 68.3% sure that the actual mean value is within the range: N ± N We cannot know the mean from a single measurement, but this statistical analysis lets us know how close our measurement must be to the mean, within a definite range of uncertainty. This is useful. To take account of the background radiation, we must find N as a result of the total number of counts N t minus our number of background counts N b . Instead of taking the square root of N, we must then take the square root of our total measurements. Considering background radiation, our result is: N t ÷ N b ( ) ± N t + N b Note that although we are subtracting the two measurements (total and background) to get N, we can’t subtract our two uncertainties – it doesn’t make sense for our total uncertainty to get smaller! Therefore, when calculating uncertainties we add them together instead. (See Appendix A – Errors and Uncertainties Analysis if you’re confused by this.) Statistical Uncertainty — Example Suppose you measure a total number of counts (i.e. from the radioactive source in addition to background radiation) of N t = 1200. You also measure background counts for the same length of time as N b = 400. Therefore: N = N t – N b = 1200 – 400 = 800 And the uncertainty is: √(N t + N b ) = √( 1200 + 400) = √1600 = 40 So our final data result is written: N = 800 ± 40 This means that we have a statistical 68.3% probability that the ‘actual’ mean value is a number between 760 and 840. Note that this uncertainty has nothing to do with uncertainties in our apparatus, or any kind of other experimental error – the uncertainty here is entirely due to the statistical randomness of radioactive decay. Exercise 8 – 6 PHYC10006 Physics Laboratory Manual REMEMBER: you must calculate statistical uncertainty values for all your measurements. Suppose you are measuring the radiation from a radioactive source. After a period of 30 seconds, your detector has reached 1241 counts. What is the statistical uncertainty (± value) in this measurement (i.e. the average number of counts per 30 seconds)? Suppose that your detector is measuring radiation at a mean rate of 50 counts per minute. For how many minutes would you let the detector run, in order for the final total number of counts to have an uncertainty of 3% (i.e. an estimated standard deviation equal to 3% of the estimated mean)? Section A Smoke Detectors Smoke detectors are the most important fire safety device in any building. Being far more sensitive to smoke than human beings, they are an essential fire early-warning device and have saved countless lives. There are two main types of smoke detector commonly found in the home: Ionisation and Photoelectric. Both of these types work by emitting and detecting radiation. Your demonstrator will demonstrate the workings of an Ionisation-type detector. Ionisation Ionisation occurs when a molecule is stripped of its outer electrons. Radiation can cause ionisation. In an ionisation-type smoke detector, a radioactive source is used to ionise molecules in the air. PHYC10006 Physics Laboratory Manual Exercise 8 – 7 Radiation source is in centre of chamber Air enters here The radiation travels radially outwards, interacting with the air in between the centre of the chamber and the outer metal casing. Power from the smoke detector’s internal battery is used to accelerate the electrons (from the ionised air molecules) towards the positive plate, where they are registered as current. Meanwhile the ionised air molecules (stripped of their outer electrons) are now positively charged, so they are accelerated in the opposite direction (towards a negative plate), where the electrical circuit is completed. Negative Plate Positive Plate Radiation Source Ionised air When smoke enters the chamber, the smoke particles neutralise the ionised air molecules and stop them from being attracted to the negative plate. This means that current will no longer flow through the circuit. It is this interruption to the current that triggers the smoke detector alarm. Smoke detectors are usually encased in plastic, but their internal radiation needs to be shielded from the outside. What type of radiation (alpha, beta, or gamma) do you think ionisation-type smoke detectors should use? Why? (Read the background in Part 2: Radioactivity and Distance if you’re unsure.) For safety, the radioactivity of smoke detectors should be as little as possible. However, it is also important that the amount of radioactive material in the detector does not reduce to zero over the smoke detector’s lifespan – the half-life (time taken for radioactivity to reduce by half) cannot be too Exercise 8 – 8 PHYC10006 Physics Laboratory Manual short. From the following table, which radioactive source do you think would be most suitable for use in a smoke detector? Why? Source Radiation produced Half-life Americium-239 Alpha 11.9 hours Americium-241 Alpha 432.2 years Uranium-255 Alpha 95 milliseconds Uranium-235 Alpha, Gamma 703,800,000 years Radioactivity and Distance It is well known that strong radiation can be harmful to biological organisms – for example, it can cause cancer. People who work in places where they may be exposed to radiation regularly (e.g. radiologists, dentists, biologists) need to be able to limit their exposure to radiation below a safe upper limit. This safe upper limit is currently believed to be 20 milli-Sieverts (mSv) per year – about 10 times greater than natural background radiation. In this experiment your source of radioactivity will be a sample of Cobalt-60. As discussed in the Introduction, this is primarily a source of 1.2 MeV gamma rays. These gamma rays will generally interact with matter in one of two ways: - Photoelectric Effect: The gamma-ray photon collides with a tightly-bound electron and its energy is completely absorbed. The probability of this happening depends on the number of electrons in the photon’s path; the probability also increases in proportion to the fourth power of the atomic number (Z 4 ) of the atoms involved. - Compton Scattering: The gamma-ray photon collides with a free or loosely-bound electron and its energy and momentum are partially transferred to the electron. The scattered photon ‘bounces off’ with less energy than it had before. The probability of this happening depends on the number of electrons in the photon’s path. You will be investigating how the intensity of radiation varies with distance from the source. Inverse Square Law The intensity of electromagnetic radiation (i.e. including gamma rays) is defined as the power (energy per time) that strikes a unit area (i.e. one square metre). In general, a source of radiation will emit its energy evenly in all directions. This means that if you imagine a sphere with the radiation source at its centre, the amount of energy passing through the entire sphere must be the same at any given radius. This is because the total energy is always conserved. PHYC10006 Physics Laboratory Manual Exercise 8 – 9 As you get further from the centre, the sphere of radiation around the source becomes larger. As a sphere gets larger, its surface area increases, but the total energy must remain the same. The radiation becomes more ‘spread-out’ – the intensity (i.e. power per area) must decrease as the surface area increases. Since the surface area of a sphere is 4πr 2 , the proportionality of power-to-surface-area also tells us the relation between intensity and distance: I · 1 r 2 Here I is intensity and r is the distance from the source. As you get further from the source, the intensity becomes less and less (according to the square of the distance). It is this ‘inverse square’ proportionality of the radiation intensity that you will be investigating. Testing the Inverse Square Relationship Your demonstrator will show you how to use your Geiger counter. SAFETY NOTE Do not change the high voltage setting on your radiation detector. Be sure to use both hands when adjusting the position of the Geiger tube. Record and calculate your data in Excel. Directions: - Measure the background radiation for 30 seconds. (Ensure that the radioactive source is fully shielded and well away from the detector.) You may wish to do this several times in order to find an average result. - Place the source 2 cm in front of the detector and record the radiation counts for the same length of time (30 seconds). How will you measure the distance from source to detector? - Take measurements of the radiation counts (for 30 seconds) with the source placed at increasing distances: 4 cm, 8 cm, 16 cm and 32 cm from the detector. According to the inverse square law (see above), the relation between distance and intensity of radiation should be: 1 Intensity (counts) versus Distance. It is this relation that must be investigated. Using Excel, graph your data according to this relation. (Remember to subtract the background radiation first.) Do you expect to see an inverse square relationship? Why? Exercise 8 – 10 PHYC10006 Physics Laboratory Manual In Excel, use another column to calculate the ± uncertainties in your data (as described in the Randomness of Radioactive Decay section, above). Use these ± uncertainties as error bars for your data points (see Appendix B or ask your demonstrator if you aren’t sure how to do this). Answer the following questions in your logbook: - How big are your error bars compared to your actual data (i.e. how big is √N compared to N), as percentages? - How could you reduce the (percentage) uncertainty in your measurements? Is it better to measure for a shorter or longer period of time? - On your graph, can you draw a straight line through the data points (within the error bars)? If you could, what would this imply? - Use Excel to create a best fit trendline through your data points. Does the best fit trendline pass through the origin? If not, what does the value of its axis intercept mean? - How important is the background measurement to your data? How does the graph change if the background data is not subtracted from the total counts? Check Point #1: Show your demonstrator your plot and your answers to the questions above. [Make sure your final printed plot includes error bars and a trendline.] Section B — Radiation Shielding When radiation passes through matter, its intensity is reduced – this is called attenuation, and it is the basis of radiation shielding. Different materials absorb radiation differently. (For example, bones absorb X-rays more thoroughly than flesh, which is why bones cast ‘shadows’ in X-ray photographs.) You will investigate the change in radiation intensity that occurs when increasing amounts of a shielding material (lead) are placed between a radioactive source and the detector. As before, you will be using the radiation detector and the Co-60 source. We expect the number of photons absorbed by a small thickness dx of material, at a depth x inside the total material, to be proportional to the number of photons that can penetrate to the depth x as well as to the thickness of the layer dx: number of photons, N 0 number of photons, N x absorber thickness, x dx If the number of photons at point x is N x , then the absorption of a number of photons dN should be proportional to these quantities: dN = ÷ì N x dx PHYC10006 Physics Laboratory Manual Exercise 8 – 11 Here the proportionality constant ì is called the linear attenuation coefficient. This constant will vary according to the nature of the radiation involved and according to the properties of the shielding material. In general, the constant will be larger for more dense materials – higher for lead than for aluminium, and higher for bone than for muscle or fat. From the above relation, we can see that: dN N = ÷ìdx Integrating this equation, we can find the relation: 1 N N 0 N x } dN = ÷ ìdx 0 x } ln N x N 0 | \ | . | = ÷ìx N x = N 0 e ÷ìx This equation implies that the relation between x and the log of N will be linear, with a gradient of –ì. N x N x = N 0 e - x ln (N) x ln (N x ) = ln (N 0 ) - x d 1/2 is half-thickness d 1/2 d 1/2 Question: How would you use these graphs to find the value of ì? (Answer this in your logbook.) Data Measurement You will need to record the background radiation, total radiation, and thickness of shielding. In your analysis, remember to subtract the background radiation from the total measured counts. You must also calculate the uncertainty in your measurements. Remember that the uncertainty in the number of counts N is √(N total +N background ) – see the discussion on Statistical Uncertainty, above. However, you will not be graphing N, but instead the logarithm of N – so you will also need to calculate the uncertainty in the log of N. (See Analysis, below, for an explanation of logarithmic uncertainties.) The easiest way to analyse your results is to set up an Excel spreadsheet with columns recording all important data: the thickness of shielding, the total counts, the actual counts (i.e. total minus background), the uncertainty in actual counts, the log of actual counts, and the uncertainty in the log of actual counts. You will be provided with lead shielding blocks of thickness 0.5, 1.0, 2.0 and 4.0 cm. Vary the thickness from 0.0 to 4.0 cm, in 0.5 cm steps, measuring the radiation intensity (i.e. number of counts) at each thickness. The recommended measurement time is 30 seconds. Exercise 8 – 12 PHYC10006 Physics Laboratory Manual Source Geiger tube Absorbers It is also important to keep the radioactive source at the same distance from the detector for all measurements – ensure that you leave enough space at the start to be able to fit 4.0 cm of shielding between source and detector. Analysis Graph your data as the log (N) versus x. It can be shown that the uncertainty in the log of N is related to ∆N (i.e. the uncertainty in N itself – recall that the triangle ‘∆’ (also known as Delta) means ‘the uncertainty in’) as follows: d ln N ( ) dN = 1 N ÷A ln N ( ) = AN N This is how you will calculate the size of the error bars on your graph. For a further explanation of this, see Appendix A – Errors and Uncertainties Analysis. Questions: (be sure to answer these in your logbook) - From your graph, what is the linear attenuation coefficient (ì) of lead for 1.2 MeV gamma rays? - The uncertainty attached to ì is a measure of your confidence in the accuracy of the gradient of the best fit trendline for your graph. According to the error bars on your data points, what are the maximum and minimum gradients for your graph? - Assuming that the maximum and minimum gradients are reasonable uncertainties for your data, express your result for the linear attenuation coefficient as ì = ___ ± __ - What is the physical significance of an absorber of thickness 1/ì? This length 1/ì is called the ‘attenuation length’. - Your calculated attenuation length is based on gamma rays of 1.2 MeV in lead. Estimate the attenuation length of 30 keV X-rays in lead (such as might be used by a dentist to examine your teeth). Assume that attenuation length is proportional to the energy squared (i.e. 1/ì ~ E 2 ). - Dentists wear lead aprons to shield themselves from X-rays. These aprons contain granules of lead 0.5 mm thick. Calculate the attenuation of 30 keV X-rays through an apron like this. Is the dentist safe? - Calculate the attenuation for 1.2 MeV gamma rays through a 0.5 mm thick lead apron. Would this apron be useful for Sarah the molecular biologist (from the problem in the Pre-Lab)? - How can you safely shield yourself from the harmful effects of radiation? Discuss. Check Point #2: Show your demonstrator your plot and your answers to the questions above. [Make sure your final printed plot includes error bars and a trendline.] Conclusion: Write a brief conclusion summarising what you did in today’s lab and your results. Remember to discuss whether your results were what you expected and include any sources of error. PHYC10006 Physics Laboratory Manual A-1 Appendix A Uncertainties & Error Analysis Introduction – What Is Uncertainty? ‘Error Analysis’ and the concept of ‘uncertainties’ are often confusing at first. This because the words ‘error’ and ‘uncertainty’ have a technical meaning in science which is quite different to their meaning in everyday conversation. (The word ‘theory’ suffers from this sort of problem, too.) When we talk about ‘errors’ or ‘uncertainties’ or ‘confidence limits’ in physics (the terms are used fairly interchangeably), we are not talking about mistakes. Experimental results can be mistakes because equipment is used incorrectly, or is faulty, or because the analysis is based on incorrect assumptions; but even perfect equipment can never be perfectly accurate and precise, and this is where the concept of ‘uncertainty’ comes in. Every time we produce a number in experimental physics – whether by measuring something directly with a measuring device, or by calculating a result from our measurements using a formula – the number produced has an uncertainty about it. In physics, all numerical results have an uncertainty like this, which is recorded as a ‘plus or minus’ error value. This plus-or-minus uncertainty states the upper and lower limits of our result: e.g. 3.0 ± 0.1 has an upper limit of 3.1 and lower limit of 2.9. This uncertainty range shows where we confidently expect the ‘actual’ answer to be, based on our experimental results. In a practical sense, all results have ‘uncertainty’ because our measuring devices cannot be perfect; but uncertainties are also unavoidable on a more fundamental level (due to Heisenberg’s Uncertainty Principle, for instance, which you may learn about in later physics study). Unless you are counting something discrete and obvious (like ‘number of people in my group’), there is always an uncertainty in the measuring process. Because of this, every numerical result must always be stated together with its uncertainty. It’s not enough to say that the answer is ‘3’; you always need to say it is ‘3 ± something’. There is an obvious difference between ‘3.00 ± 0.01’ compared to ‘3.0 ± 2.7’. If we don’t record the plus-or-minus uncertainty value, this difference in meaning vanishes. If we don’t know our uncertainties, our results can’t be compared with other results; and if we can’t compare our results to other results, then our results are meaningless. Error Analysis is our set of tools for dealing with experimental uncertainties. The aim is not to eliminate uncertainties – unfortunately, that’s usually impossible. But by figuring out how best to estimate our uncertainties, we will produce practical and useful real-world results. A Golden Rule Ultimately, your analysis of uncertainties is based on your own estimates and judgment. The methods outlined below are guidelines, not absolute laws; every experimental situation will be unique. The key is always to think carefully about what you are doing, to ensure that your analysis is as reasonable and as sensible as possible. A-2 PHYC10006 Physics Laboratory Manual Uncertainties in Measurements The most basic uncertainties are those due to measurements. Whenever you measure a physical quantity – for instance, measuring distance with a ruler, or counting radioactive particles with a scintillator – that measurement has an uncertainty. This is true even if we assume that the equipment is perfectly accurate and correct. There are different sources of uncertainty detailed below. Sometimes only one sort of uncertainty will be relevant or significant; in other situations, there may be multiple sources of uncertainty to deal with. (If you are unsure which uncertainty is more relevant, you should probably choose the largest one.) Recognising which uncertainties are appropriate in which situations can be confusing at first. When in doubt, talk to your demonstrator. You also need to be familiar with the following symbology: If a quantity is labelled ‘x’, then its uncertainty is labelled ‘∆x’. So when we state a numerical result, we want to state ‘x ± ∆x’. Here, the delta symbol ∆ means ‘the uncertainty in (a quantity)’: so ‘∆x’ means ‘the uncertainty in x’. This can be confusing, because in other contexts ∆ can mean ‘the change in (a quantity)’, instead. You must be careful to remember the difference! In the context of experimental results and uncertainties, ∆ always means ‘the uncertainty in’. ∆x is called the absolute uncertainty of x. Ax x , the uncertainty divided by the actual value, is the proportional uncertainty of x. Also, the proportional uncertainty multiplied by 100 is the percentage uncertainty. Taking a Measurement: The ‘Reading Error’ When we read a number from a measuring device – whether by reading a mark on a ruler, or a needle on a dial, or a display on a digital readout – that number has an uncertainty due to the resolution of the measuring device. By ‘resolution’, we mean ‘the smallest values that the device can display’. For instance, a ruler which is marked in millimetres can only be used to measure distances to the nearest millimetre. Remember that the ‘uncertainty’ of a value is what defines its upper and lower ‘confidence limits’: so if a value can be distinguished to the nearest millimetre, this literally means that the difference between its upper and lower limits (its ‘plus-or-minus’ values) is one millimetre. This is called reading error, because it is an error due to how closely we can read the scale. We have the same sort of uncertainty when we read a dial, or when we read a digital readout which only displays a fixed number of decimal places. This ‘reading error’ uncertainty is generally estimated to be plus-or-minus half the smallest division of measurement. For example, using our millimetre ruler we might measure a piece of string to be 153 mm long. We should state this result as 153 ± 0.5 mm. The uncertainty is 0.5 mm due to the reading error: if the result had been more than 153.5, then it would be read as 154, and if less than 152.5, then it would be read as 152 mm. Therefore, the appropriate range is 153 ± 0.5. PHYC10006 Physics Laboratory Manual A-3 Taking Several Measurements: Error from Averages Sometimes we are measuring something which we know is stable and easily controlled (like the length of a piece of string). These sorts of measurements may only need to be made once, and so the reading error is the only appropriate uncertainty to consider. However, often we are trying to measure a quantity which is difficult to capture. You will sometimes find that you can measure the same physical quantity over and over and get a slightly different answer every time. This is normal! In many situations there will be constant small fluctuations in the experimental conditions, or unavoidable variations in the measuring instruments, or natural fluctuations in the physical quantity itself. This results in a set of measurements which are not all precisely the same. This variability is why we repeat measurements: we want to obtain multiple results, which we can then average (or otherwise analyse) to determine the ‘best’, most accurate central conclusion. The more data we have, the better our conclusions are likely to be. Our final result will usually come from the average of our measurements. What is the uncertainty of an average? The simplest way to estimate the uncertainty is to consider the range of the measured values. The uncertainty can be taken as half the range. Here is an example (where the reading error of the initial measurements is 0.1 mm): Measurements: 153.2 ± 0.1; 153.6 ± 0.1; 152.8 ± 0.1; 153.0 ± 0.1 mm Average: (153.2 + 153.6 + 152.8 + 153.0) / 4 = 153.2 mm Range: 153.6 – 152.8 = 0.8 mm Uncertainty: half range = 0.8 / 2 = 0.4 mm Final Result: 153.2 ± 0.4 mm Because the half-range error is significantly larger than the reading error, it is the more appropriate uncertainty to use. The small reading error is insignificant, compared to the larger error due to averaging several results together. But if the reading error was much larger than the half-range error, it would be more appropriate to use the reading error instead. When in doubt, use the largest uncertainty. The half-range error is the appropriate approach to experimental uncertainties where a few (less than 12 or so) measurements have been made. What if there are a hundred measurements, or even more? If there are lots of measurements, then the half-range error becomes less accurate. This is due to the statistics involved: with more data, the average will become more accurate, but the range of results will also increase. However, we can still use the spread of results around the mean to estimate uncertainty. The way to estimate uncertainties with large sets of data is to use statistical techniques: the standard deviation of a set of data is usually a good estimate of its uncertainty. If it is appropriate to use these techniques, they will be detailed in the relevant laboratory exercise notes. A-4 PHYC10006 Physics Laboratory Manual Uncertainties in Calculations Taking a measurement is usually not the end of the experiment. Often, we want to test a theoretical formula, so we will put our measurements into the formula to calculate some new value. We know what the uncertainties of our measurements are, but what are the uncertainties of our calculation? Whenever you calculate with uncertainties, all of the uncertainties in the equation will combine towards producing the uncertainty of the answer. The ways in which the uncertainties in measurement combine to produce uncertainties in the final answer are determined by a few simple formulas, which are based on what sort of calculation it is. The equations below look like they involve a lot of algebra, so they can be intimidating at first. Don’t panic: it’s simpler than it looks, and you can always ask your demonstrator for assistance. NOTE: these formulas are based on mathematical approximations which are not completely accurate, but they are adequate and appropriate for analysis in first year Physics. If you are curious about the ‘correct’ analysis, see http://en.wikipedia.org/wiki/Error_propagation. Addition and Subtraction When we add two measurements together, their uncertainties add together as well. If we subtract one measurement from another measurement, their uncertainties are not subtracted: their uncertainties are added together instead. When we combine data the uncertainty increases, even if the final answer gets smaller! This is always true: it is an important principle to remember. So if R = a + b + … then ∆R = ∆a + ∆b + … Also, if R = a – b – … then ∆R = ∆a + ∆b + … The uncertainty of a sum is the sum of the absolute uncertainties. Addition and Subtraction — Example We measure a piece of string to be 150 mm long, using a ruler which has a reading error (see Taking a Measurement, above) of 10 mm. We also measure the length of a miniature toy car to be 27 mm long, using a different ruler which has a reading error of 0.5 mm. What is the total length of the car attached to the string? Total Length = Car Length + String Length = 150 + 27 mm = 177 mm What is the uncertainty in the total length? This is an addition, so we add the absolute uncertainties. Total Uncertainty = (Uncertainty in Car Length) + (Uncertainty in String Length) = 0.5 + 10 mm = 10.5 mm We should state our final result as: Length of car attached to string = 177 ± 10.5 mm PHYC10006 Physics Laboratory Manual A-5 Multiplication and Division When we multiply two values together, their absolute uncertainties do not multiply together. But they do not add, either. Instead, it can be shown that we need to add the proportional uncertainties of each component. It turns out that this is also the case for division, because division is the simple inverse of multiplication: remember that the uncertainty always increases, even if the final answer gets smaller. So if R = a x b x … then AR R = Aa a + Ab b + … Also, if R = a / b / … then AR R = Aa a + Ab b + … The proportional uncertainty of a product is the sum of the proportional uncertainties. Remember to multiply your answer by the actual value of R, to go from the proportional uncertainty ∆R/R to the absolute uncertainty ∆R. Multiplication and Division — Example We measure the current in an electrical circuit to be 50 A, using an ammeter which has a reading error of 1 A (see Taking a Measurement, above). The circuit consists of a resistor, which is rated by the manufacturer at 4.0 Ω with a 5% tolerance (this 5% is the manufacturer’s estimate of the uncertainty in the resistance, which is a reasonable uncertainty for us to use: 5% of 4.0 Ω is 0.2 Ω). We use Ohm’s Law (V=IR) to calculate the expected voltage V of the circuit, based on our measurements. A is ‘amperes’ (the unit of current), Ω is ‘ohms’ (the unit of resistance), and V is ‘volts’ (the unit of voltage). Voltage = Current x Resistance = (50 A) x (4.0 Ω) = 200 V What about the uncertainty? This is a multiplication, so the total proportional uncertainty is the sum of the other proportional uncertainties. V stands for Voltage, I for Current and R for Resistance. V = I x R Therefore: AV V = AI I + AR R AV 200 = 1 50 + 0.05 x 4.0 4.0 AV 200 = 0.02 + 0.2 4.0 = 0.02 + 0.05 = 0.07 So 0.07 is the proportional uncertainty. To find the absolute uncertainty: ∆V = 200 x 0.07 = 14 We should state our final result as: Voltage = 200 ± 14 V A-6 PHYC10006 Physics Laboratory Manual Raising To A Power When we square a value, or raise it to any other value, we multiply their proportional uncertainties by the power involved. If the power is negative, ignore the negative sign – remember that uncertainties always increase. (However, beware of fractional powers!) So if R = a 2 then AR R = 2 Aa a Or in general, if R = a n then AR R = n Aa a Combining Equations — Example What happens if an equation has multiple parts – say, addition and multiplication and division all together? In this case, we simply break the equation into parts, and combine the uncertainties together one by one. This can involve some very complicated-looking algebra, but don’t panic! Once you know what’s going on, it’s not nearly as bad as it looks. For example: what is the uncertainty of R from this equation? R = 2 mb c ÷ y The solution is to tackle the equation piece by piece. If we think of the (2mb/c) as a single object, then the equation becomes a simple subtraction. Remember: in a subtraction, we add the absolute uncertainties. R = 2 mb c ÷ y AR = A 2 mb c | \ | . | + Ay Remember that ‘∆’ means ‘the uncertainty in’. Next, we need to determine the uncertainty of what is inside the brackets: (2mb/c). The 2 is a simple factor of multiplication, so it has zero uncertainty; therefore we can move it outside the brackets. A 2 mb c | \ | . | = 2A mb c | \ | . | Next we have (mb/c), a multiplication and a division. Remember: when numbers multiply or divide together, the total proportional uncertainty is the sum of their individual proportional uncertainties. A mb c ( ) mb c ( ) = A(mb) mb + Ac c = Am m + Ab b + Ac c Now we have simplified all the uncertainties down to the values which we would have measured: ∆m, ∆b, ∆c and ∆y. We can combine all the parts together: PHYC10006 Physics Laboratory Manual A-7 AR = A 2 mb c | \ | . | + Ay AR = 2A mb c | \ | . | + Ay AR = 2 mb c | \ | . | Am m + Ab b + Ac c | \ | . | + Ay Remember that we multiply proportional uncertainties by the actual values to get the absolute uncertainty. General Functions The above examples should cover anything you may encounter in first year laboratories. If you’re curious, the uncertainties involved in more complicated calculations (such as logarithms) can be determined using the calculus relation below. For any calculation where R is a mathematical function of values (a, b, c, …), the uncertainty of R based on the experimental uncertainties (∆a, ∆b, ∆c, …) can be determined as follows: AR ~ oR oa Aa + oR ob Ab + oR oc Ac + ... Note that this is still an approximation. For a more thorough treatment of this topic, see http://en.wikipedia.org/wiki/Error_propagation. There are many different methods of estimating uncertainties in different situations; learning how to estimate uncertainties appropriately is a key aspect of experimental science. If you have any questions about uncertainty analysis, talk to your demonstrator or tutor. A-8 PHYC10006 Physics Laboratory Manual Minimising Errors Uncertainty Analysis (see above) deals with the statistical uncertainties due to experimental measurement. However, basic statistical uncertainty analysis assumes that the actual measurements are still ‘correct’. In real life, this is not always the case – equipment can be faulty, procedure can be incorrect, assumptions can be false, etc. It is important to understand the ways in which experimental errors can occur, and to learn to recognise and minimise the consequences. Mistakes There are many ways to make a mistake in an experiment: you might use equipment inappropriately, misread a measurement scale, misunderstand what you are supposed to be doing, etc. Even the best analysis of your results cannot overcome procedural errors like these. It is up to you to avoid making mistakes, and to recognise and solve them when they do occur. If you make a mistake (or you suspect that you might have), you should repeat your measurements to check your results. If you are unsure that you are using your equipment correctly, re-read the directions in the manual; if you are still unsure, talk to your demonstrator. Don’t try to cover up your mistakes! Discuss them in your logbook and detail what was changed to solve the problem. You will not lose marks for catching a mistake and fixing it, but you will lose marks if you try to cover it up or ignore it. Systematic Errors Systematic errors are errors which skew all results in a particular direction. They are characteristic of faults in the use of equipment, or a consistent bias caused by the experimenter (for example, always reading the number ‘1.0’ on a dial as ‘10’ instead). Because they skew all results in the same direction, they can’t be corrected by averaging a large number of repeated readings. There are a few typical sources of systematic error which you can learn to watch out for: - Incorrect setting of a meter’s ‘zero’ position - Defective or wrongly-calibrated equipment - Rounding off numbers in the middle of a calculation (instead of only at the end) - Assumptions which are incorrect or inappropriate for the experimental conditions - Use of theory which is incorrect or inappropriate for the experimental conditions - Use of a measurement device which significantly affects the system being observed All measurement devices affect in some way the experimental conditions which they are measuring, but this is a particularly common problem in electronics. You should take note that ammeters and voltmeters can change the characteristics of a circuit very easily. How To Minimise Error There are various general methods by which you can minimise the error and uncertainty associated with a measurement. The most important thing is simply to think about what you are doing. Don’t just blindly follow directions! You should critically assess your experimental method as you go along. Does what you are doing make sense? If not, why not? PHYC10006 Physics Laboratory Manual A-9 Trial Runs Whenever possible, you should do a brief trial run with your equipment before you take your ‘actual’ measurements. This will allow you to familiarise yourself with the equipment, and it provides an opportunity to discover potential sources of error sooner. If problems do occur, you will save time by altering your procedure before (instead of during) the actual experiment. Equipment Assessment You need to decide whether the equipment to be used is accurate enough for the task at hand. Can you (or should you) calibrate it? Should alternative equipment be used instead? Careful Use of Equipment For example: - Meters with needle indicators should be tapped lightly, to check that the indicator is not sticking - Check that the ‘zero’ settings on instruments are actually registering as ‘zero’ - Arrange apparatus so that it cannot be easily knocked or bumped - Connect electrical circuits and all electronic components securely Consistent Procedure Follow standard procedures carefully. When you change procedure or devise your own techniques, write out your new method in point form and follow it closely. If you are consistent and methodical in your approach, you will minimise the variability that comes from haphazard equipment use. Checks and Cross-checks You shouldn’t just record data: you need to think about what the results mean, and check that your answers make sense. Consider the following: - Can you check your results while you are taking them, to see if they are consistent? - Can you and your partner both take readings, and check each other’s work as you go? - Can you draw a graph as your results come in, to see if they are making sense? - Can you already guess, roughly, what the results should be? Are they doing what you expect? A-10 PHYC10006 Physics Laboratory Manual Appendix B Graphs and How to Use Them Graphs are a very useful way to represent and analyse data. Trends and relationships between variables become clear when the data are graphed in a meaningful way. It is important to learn both how to create useful graphs, and also how to extract useful information from them. Plotting Graphs — Key Points - If you haven’t used Excel (2007) to make a graph from spreadsheet data before, now is the time to practice. To begin, select your numerical data to be graphed and choose the Insert tab, and pick Scatter from the Charts section (of the ribbon). You will then need to select your graph and select the Chart tools, Layout tab. In that ‘ribbon’ you will see how to change your axis titles, graph labels and even axis scales (if needed). - When your graph is complete, remember that you can still alter it. You should right-click on elements of the graph to explore the options available. (See also Excel Trendlines, below.) - If you are unsure of how to do something with your graph, explore the tab sections thoroughly and use Excel’s Help function. Excel can do everything that you need – you only need to learn how (and where). If in doubt, ask a fellow student or your demonstrator. - Don’t let your partner do all the work! Remember, your partner won’t always be there – you need to learn how to do graphs for yourself. - Label both axes with the quantity being plotted, as well as the unit in which it is measured, eg: Length (m), Time (s). You should also label the graph itself. - Most of the time, what is being graphed is the relationship between two things: a. The independent variable. This is the quantity that you control, and that you have chosen the initial values of – e.g. the force that you apply to an object. b. The dependent variable. This is the quantity which varies according to the independent variable – e.g. the acceleration that results from the force you apply. Usually, the dependent variable is the thing that we are actually investigating. In general, you should plot the independent variable on the horizontal axis, and the dependent variable on the vertical axis. If in doubt, you should always arrange your graph so that it displays the relationships between data as clearly as possible. - Choose scales that make your graph simple and clear. Choose axis ranges that spread points evenly across the graph, rather than cramping them all into a corner. (This may mean that you need to exclude the zero point of an axis.) - Plot data points clearly, and include error bars (see below) to display the plus-or-minus uncertainty values of each point. - If possible, plot your graph as you go along. This will help you to check that nothing obvious is going ‘wrong’ with your experiment. It will also allow you to fine-tune your choice of measurement points. PHYC10006 Physics Laboratory Manual A-11 - After plotting your data, draw a single straight line or smooth curve through the plotted points (see below). Do not draw short straight lines from each point to the next! Error Bars — Graphing Uncertainties You must always record the uncertainty values of your results (see Appendix A, above). This includes the values displayed on graphs. Uncertainties are displayed on graphs using error bars, which show the ‘plus-or-minus’ values on either side of a data point. For example a distance measurement ‘x’ equal to 153.2 ± 0.4 mm would be displayed with a central data point of 153.2, an upper error bar at 153.6 and a lower error bar at 152.8: x + ∆x = 153.2 + 0.4 = 153.6 x = 153.2 x – ∆x = 153.2 – 0.4 = 152.8 } +0.4 uncertainty } –0.4 uncertainty By including error bars in horizontal as well as vertical directions, you can represent the uncertainties in both dimensions simultaneously. In this way, the error bars will mark out a region of uncertainty in which we expect the ‘actual’ data point (x,y) to be. x yi– yi yi+ yi yi xi+ xi xi– xi xi y When graphing in Excel, error bars can be added to a graph by double-clicking the graph’s data points and then selecting the Chart Tools, layout tab, then choosing Error bars. Select more options, both, and then used the fixed value to place your y error value. At this point Excel will also insert some default x error bars, if you have an error for x as well, select the horizontal error bar and insert correct value, or delete if you do not want them (sometimes they are so small you cannot see them to select – in which case do not worry about them). We need error bars to be able to see the true relationships between data. For instance, without error bars we might obtain a graph like this: (0,0) x y A-12 PHYC10006 Physics Laboratory Manual It appears as if these points could be joined together to fit a sine wave. However, this may not actually be the case. If the uncertainties for x and y are both small (e.g. ~5%), then the error bars look something like this: (0,0) x y As you can see, a sinusoidal curve fits within these error bars quite well, and so it is reasonable to conclude that this relation is probably a sine wave. However, if the uncertainties are larger (e.g. ~50%), then the error bars look something like this: (0,0) x y In this case, a straight line would fit the data just as well as a curve. It may or may not ‘actually’ be a sine wave relation, but the uncertainties are too large for us to be sure. Straight Lines In experimental work, we often want to look for a linear relationship between two physical quantities. If a graph of x versus y produces a straight line, then we may conclude that the relationship between x and y is linear. This means that the quantities are related according to a linear equation (i.e. an equation of the form y = mx + c). Unfortunately, experimental uncertainties will usually ‘blur’ a linear relationship. Data points will rarely form a perfectly straight line on a graph. In these cases, we need to find the line of best fit. The following graph represents a typical example: PHYC10006 Physics Laboratory Manual A-13 x y line of best fit line of maximum slope line of minimum slope When estimating a line of best fit by eye, we expect that the line should pass inside all (or almost all) of the error bars. You should also sketch the lines of minimum and maximum possible gradient, and these too should pass through all (or most) of the error bars. (If you are calculating the gradient of the line using this ‘graphical’ method, then half of the difference between the minimum and maximum gradients will be your plus-or-minus uncertainty values for the gradient.) Examine your data carefully: there may be one or two points which are obviously very different to the others. If you believe that these differences are anomalies, due to some experimental error, then you may decide to ignore them when constructing your line of best fit. (If you think they are mistakes, also be sure to investigate how and why this happened!) Excel Trendlines Excel can be made to construct lines of best fit for its graphs: select the data points on the graph, and right-click to choose Add Trendline from the pop-up menu. However, be careful: Excel’s trendline methods won’t work for all sets of data. Be sure to double-check that its lines look reasonable and sensible. Least Squares Fit This is generally not necessary at a first-year Physics level. If you are curious, however, the best way to manually calculate the line of best fit is usually to use the ‘least squares fit’ method. This method considers the deviation (vertical distance) of each point from the proposed line of best fit. The line of best fit is chosen to be the line for which the total (deviation) 2 of all points is least. y x line deviat ion point If a point falls exactly on the line, then its deviation squared is of course zero. A-14 PHYC10006 Physics Laboratory Manual Reproducing this method by eye requires practice. In general, the most effective method will be for you to use Excel. Converting Curves to Straight Lines A graph will often look more like a curve than a straight line. Unfortunately, it is difficult to sketch a reliable curve from scattered data points, and it is even more difficult to extract an obvious mathematical relation from a curve. However, if we already have a theoretical relation for our data, we can sometimes use this to convert our curve graph into a straight-line graph. A straight-line graph can be used to extract a linear relationship between the data (see Straight Lines, above). Converting to a Straight Line — Example The period T of circular motion of an object of mass M depends on the centripetal force F causing the circular motion, and the radius r of the motion, according to the following equation: 2 2 4 T Mr F t = When F versus T is graphed, we will expect to see a curve corresponding to the above equation. However, it will probably be difficult to show that any curve on a graph definitely matches the above equation. Within experimental uncertainties, it is often impossible to tell the difference between one type of curve and another type of curve (e.g. between a quadratic curve and an exponential curve). It is much easier to look at a linear graph and decide whether or not a line is straight. We can do this now by rewriting the above equation into a linear form. F = 4t 2 Mr T 2 F = 4t 2 Mr ( ) 1 T 2 | \ | . | + 0 y = (m)(x) + c The equation is now in a linear form (i.e. y = mx + c). By graphing F versus (1/T 2 ) instead of F versus T, we should create a linear graph instead of a curve graph. Instead of looking for a curve to check that the data matches the equation, we can instead look for a straight line. PHYC10006 Physics Laboratory Manual A-15 F 1/T 2 rise run gradient = rise/run = 4 t 2 M r F corresponds to y : both are plotted vertically 1 T 2 corresponds to x : both are plotted horizontally 4t 2 Mr corresponds to m : both are the gradients of the line F axis intercept corresponds to c : in this case, zero By converting to a linear graph, we make it much easier to analyse the theoretical relationship between the data. It also makes it easier to extract the information corresponding to the gradient ‘m’ and the axis intercept ‘c’. Linear relationships are also simpler to extrapolate beyond the measured data. It is easy to see how a straight line will continue across the graph; extrapolating a curve is more difficult. A-16 PHYC10006 Physics Laboratory Manual Appendix C SI Units SI stands for Le Système International d’Unités, which is the French title for the International System of Units. SI is the modern version of the metric system, and it is the system of measurements most widely used in science and commerce around the world today. SI is based around seven base units: the metre m (length), the kilogram kg (mass), the second s (time), the ampere A (electric current), the kelvin K (temperature), the candela cd (luminous intensity), and the mole mol (amount of substance). These are the ‘default’ units for all measurements and physics equations. All other SI units of measurement (e.g., see table below) can be reduced to some combination of these seven base units. Except in very special circumstances, all measurements and results should be made and quoted using SI units. Quantity Name of SI Unit Symbol SI Base Units frequency Hertz Hz 1 Hz = 1 / s force Newton N 1 N = 1 kg m / s 2 energy Joule J 1 J = 1 N m power Watt W 1 W = 1 J / s quantity of electric charge Coulomb C 1 C = 1 A s electrical potential / ‘potential difference’ / ‘electromotive force’ Volt V 1 V = 1 W / A = 1 kg m 2 / A s 3 electric capacitance Farad F 1 F = 1 A s / V = 1 A 2 s 4 / kg m 2 electric resistance Ohm O 1 O = 1 V / A = 1 kg m 2 / A 2 s 3 inductance Henry H 1 H = 1 V s / A = 1 kg m 2 / A 2 s 2 PHYC10006 Physics Laboratory Manual A-17 Appendix D Resistor Colour Codes Resistors are labelled in code according to their resistance. This code is indicated on the resistor by a set of coloured lines, as shown: First Digit Second Digit Multiplier Tolerance The first two colours represent the first two digits of the resistance value. The third colour represents the multiplication factor – the power of ten to multiply the digits by. The final colour represents the manufacturer’s tolerance value (the level of uncertainty in the actual resistance). Colour Number Multiplier Tolerance Black 0 1 Brown 1 10 1 1 % Red 2 10 2 2 % Orange 3 10 3 Yellow 4 10 4 0.50 % Green 5 10 5 0.25 % Blue 6 10 6 0.10 % Violet 7 10 7 0.05 % Grey 8 10 8 White 9 10 9 Gold 10 -1 5 % Silver 10 -2 10 % No colour 20 % For example: a resistor with the colour sequence Red-Green-Orange-Silver would have a resistance of 25,000 Ω ± 10%.