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Lab Manual

Physics 2

LabPaq: PK-2

A Lab Manual of 11 Experiments for Independent Study

Published by Hands-On Labs, Inc.

Physics 2: Lab Manual of Experiments for the Independent Study of Physics

Designed to accompany Physics LabPaq PK-2 081611

LabPaq® is a registered trademark of Hands-On Labs, Inc. (HOL). The LabPaq referenced in this manual is produced by Hands-On Labs, Inc. which holds and reserves all copyrights on the intellectual properties associated with the LabPaq’s unique design, assembly, and learning experiences. The laboratory manual included with a LabPaq is intended for the sole use by that LabPaq’s original purchaser and may not be reused without a LabPaq or by others without the specific written consent of HOL. No portion of any LabPaq manual’s materials may be reproduced, transmitted or distributed to others in any manner, nor may they be downloaded to any public or privately shared systems or servers without the express written consent of HOL. No changes may be made in any LabPaq materials without the express written consent of HOL. HOL has invested years of research and development into these materials, reserves all rights related to them, and retains the right to impose substantial penalties for any misuse.

Published by: Hands-On Labs, Inc.

3880 S. Windermere St. Englewood, CO 80110 Phone: 303-679-6252 Toll-free: 1-866-206-0773 Fax: 270-738-0979

www.LabPaq.com

E-mail: [email protected]

Printed and bound in the United States of America.

ISBN: 978-1-866151-40-6

The experiments in this manual have been and may be conducted in a regular formal laboratory or classroom setting with the user providing their own equipment and supplies. The manual was especially written, however, for the benefit of independent study students who do not have convenient access to such facilities. It allows them to perform physics experiments at home or elsewhere by using LabPaq PK-2, a collection of experimental equipment and supplies specifically packaged by Hands-On Labs, Inc. to accompany this manual.

Use of this manual and authorization to perform any of its experiments are expressly conditioned upon the user reading, understanding, and agreeing to abide by all the safety precautions contained herein. Although the author and publisher have exhaustively researched all sources to ensure the accuracy and completeness of the information contained in this book, we assume no responsibility for errors, inaccuracies, omissions or any other inconsistency herein. Any slight of people, organizations, materials or products is unintentional.

Table of Contents Introduction .................................................................................................................................. 4

Important Information to Help Students Study Science ..................................................... 4 WELCOME TO THE WORLD OF SCIENCE! ................................................................................ 4

Laboratory Equipment and Techniques ........................................................................... 13 Use, Disposal, and Cleaning Instructions for Common Materials ................................... 19

HOW TO WRITE LAB NOTES AND LAB REPORTS .................................................................. 21 Lab Notes .......................................................................................................................... 21 Lab Reports ....................................................................................................................... 23 Laboratory Drawings ......................................................................................................... 27 Visual Presentation of Data .............................................................................................. 28 Computer Graphing Using MS Excel ................................................................................. 32

SAFETY CONCERNS ............................................................................................................... 40 Basic Safety Guidelines .................................................................................................... 41 Material Safety Data Sheets ............................................................................................. 46 Science Lab Safety Reinforcement Agreement ............................................................... 50

EXPERIMENTS 1. Static Electricity or Electrostatics .................................................................................... 53 2. Electric Fields ................................................................................................................... 63 3. Introduction to Electrical Circuits .................................................................................... 74 4. Resistors in Series and Parallel ...................................................................................... 87 5. Semiconductor Temperature Sensor .............................................................................. 96 6. Capacitance in a Circuit ................................................................................................. 102 7. Electric Motor ................................................................................................................. 113 8. Reflection and Refraction .............................................................................................. 119 9. Diffraction Grating ......................................................................................................... 130 10.Polarized Light ............................................................................................................... 141 11.Radioactive Decay ......................................................................................................... 147 APPENDIX Using Statistics .................................................................................................................... 154

Introduction Important Information to Help Students Study Science

Version 09.3.05

WELCOME TO THE WORLD OF SCIENCE! Don't be afraid to take science courses. When you complete them, you will be very proud of yourself and will wonder why you were ever afraid of the “S” word – Science! After their first science course most students say they thoroughly enjoyed it, learned a lot of useful information relevant to their personal lives and careers, and only regret not having studied science sooner. Science is not some mystery subject comprehended only by eggheads. Science is simply a way of learning about our natural world and how it works by testing ideas and making observations. Learning about the characteristics of the natural world, how those characteristics change, and how those characteristics interact with each other make it easier to understand ourselves and our physical environment and to make the multitude of personal and global decisions that affect our lives and our planet. Plus, science credits on an academic transcript are impressive, and your science knowledge may create some unique job opportunities. All sciences revolve around the study of natural phenomena and require hands-on physical laboratory experiences to permit and encourage personal observations, discovery, creativity, and genuine learning. As increasing numbers of students embrace online and independent study courses, laboratory experiences must remain an integral part of science education. This lab manual’s author and publisher are science educators who welcome electronic technology as an effective tool to expand and enhance instruction. However, technology can neither duplicate nor replace learning experiences afforded to students through traditional hands-on laboratory and field activities. This does not mean that some experiments cannot or should not be replaced or reinforced by computer simulations; but any course of science study must also provide sufficient hands-on laboratory and field experiences to:

x Engage students in open-ended, investigative processes by using scientific problem solving.

x Provide application of concepts students have seen in their study materials which

reinforce and clarify scientific principles and concepts.

x Involve multiple senses in three-dimensional rather than two-dimensional learning experiences that are important for greater retention of concepts and for accommodation of different leaning styles.

x Stimulate students to understand the nature of science including its unpredictability

and complexity.

x Provide opportunities to engage in collaborative work and to model scientific attitudes and behavior.

x Develop mastery of techniques and skills needed for potential science, engineering, and technology careers.

x Ensure advanced placement science courses transfer to college credit.

The knowledge gained from science courses with strong laboratory components enables students to understand in practical and concrete ways their own physical makeup, the functioning of the natural world around them, and contemporary scientific and environmental issues. It is only by maintaining hands-on laboratory experiences in our curricula that the brightest and most promising students will be stimulated to learn scientific concepts and avoid being turned-off by lecture- and textbook-only approaches. Physical experimentation may offer some students their only opportunity to experience a science laboratory environment. All students – as potential voters, parents, teachers, leaders, and informed citizens – will benefit from a well-rounded education that includes science laboratory experiences, when it is time for them to make sound decisions affecting the future of their country and the world. 19th century scientist, Ira Remsen (1846-1927) on the subject of Experimentation:

This lab manual can be used by all students, regardless of the laboratory facilities available to them. The experiments are based on the principles of micro- and small-scale science which have been successfully used in campus laboratories for decades. LabPaq’s micro- and small-scale experiments can also be performed at home, in a dorm room, or at a small learning center that lacks a formal laboratory. What are Micro- and Small-scale Experiments? You may be among the growing number of students to take a full-credit, laboratory science course through independent study, due to the development and perfection of micro-scale and small-scale experimentation techniques over the past half century. While experimentation on any scale is foundational to fully understanding science concepts, science courses in the past have required experimentation to be performed in the campus laboratory due to the potential hazards inherent in traditional experimentation. Potential hazards, increasing chemical, specimen, and science equipment costs, and environmental concerns made high schools, colleges, and universities reexamine the traditional laboratory methods used to teach science. Scientists began to scale down the quantities of materials and the size of equipment used in experiments and found reaction results remained unchanged. Over time, more and more traditional science experiments were redesigned to be performed on micro and small scales. Educational institutions eventually recognized that the scientific reaction, not the size of the reaction, facilitates learning. Successive comparative assessments have proven that students’ learning is not impaired by studying small-sized reactions. Many assessments even suggest that science learning is enhanced by small-scale experimentation. The primary pioneer and most prominent contributor to micro- and small-scale experimentation was Dr. Hubert Alyea, a chemistry professor at Princeton University, who began utilizing micro-scale experiments in the 1950s. Dr. Alyea reformatted numerous chemistry experiments and also designed many of the techniques and equipment used in micro- and small-scale science today. In the mid-1990s, Dr. Peter Jeschofnig of Colorado Mountain College pioneered the development of LabPaq’s academically aligned, small-scale experiments that can be performed at home. Hands-On Labs, Inc. has subsequently proven that students can actually perform LabPaq's rigorous science experiments at home and still achieve an equivalent, if not higher, level of learning than their campus-based peers.

The Organization of this Lab Manual Before proceeding with your experiments, please thoroughly read and understand each section of this lab manual, so you understand what is expected of you. Introduction and How to Study Science: These sections include important information about general scientific subject matter and specific information about effectively studying science and conducting science experiments. Read these sections carefully and take them to heart! How to Perform an Experiment and Laboratory Equipment and Techniques: Adhering to the procedures described in these sections will greatly facilitate experimental activities. The laboratory techniques and equipment described primarily apply to full-scale experiments and formal laboratories; however, knowledge of these items is important to a basic understanding of science and is relevant to home-based experimentation. How to Write Lab Notes and Lab Reports: Like all serious scientists, you must record formal notes detailing your activities, observations, and findings for each experiment. These notes will reinforce your learning experiences and science knowledge and provide the basis from which you will prepare Lab Reports for your instructor. This section explains how these documents should be organized and prepared. Safety Concerns: The Basic Safety Guidelines and Safety Reinforcement Agreement are the most important sections of this lab manual and should be reviewed before each experiment. The safety sections are relevant to both laboratory and non-laboratory experimentation. The guidelines describe potential hazards as well as basic safety equipment and safety procedures designed to avoid such hazards. Required Equipment and Supplies: If you are performing these experiments in a non- laboratory setting, you must obtain the LabPaq specifically designed to accompany this lab manual. The LabPaq includes all the basic equipment and supplies needed to complete the experiments, except for minor items usually found in the average home or obtained at local stores. At the beginning of each experiment you will find a materials section listing which items are found in the LabPaq and which items you will need to provide. Review this list carefully before you begin an experiment to ensure you have all required items. Experiments: The experiments included in this lab manual were specifically selected to accompany related course materials for a traditional academic term. These experiments emphasize a hands-on, experimental approach for gaining a sound understanding of scientific principles. The lab manual’s rigorous Lab Report requirements help reinforce and communicate your understanding of each experiment’s related science principles and strengthen your communication skills. This traditional, scientific method approach to learning science reflects the teaching philosophy of the authors, Hands-On Labs, Inc., and science educators around the globe.

HOW TO STUDY SCIENCE It is unfortunate that many people develop a fear of science somewhere early in life. Yes, the natural sciences are not the easiest subjects to learn; but neither are they the hardest. Like in any other academic endeavor, if you responsibly apply yourself, conscientiously study your course materials, and thoughtfully complete your assignments, you will learn the material. Following are some hints for effectively studying science and any other subject, both on or off campus. Plan to Study: You must schedule a specific time and establish a specific place in which to seriously devote yourself to your studies. Think of studying like you would think of a job. Jobs have specific times and places in which to get the work done, and studying should be no different. Just as television, friends, and other distractions are not permitted on a job, they should not be permitted to interfere with your studies. If you want to do something well, you must be serious about it, and you cannot learn when you are distracted. Only after you have finished your studies should you allow time for distractions. Get in the Right Frame of Mind: Think positively about yourself and what you are doing. Put yourself in a positive frame of mind to enjoy what you are about to learn, and then get to work. Organize any materials and equipment you will need in advance so you don't have to interrupt your work later. Read your syllabus and any other instructions and know exactly what your assignment is and what is expected of you. Mentally review what you have already learned. Write down any questions you have, and then review previous materials to answer those questions. Move on, if you haven't found the answer after a reasonable amount of time and effort. The question will germinate inside your mind, and the answer will probably present itself as you continue your studies. If not, discuss the question later with your instructor. Be Active with the Material: Learning is reinforced by relevant activity. When studying, feel free to talk to yourself, scribble notes, draw pictures, pace out a problem, or tap out a formula. The more physically active things you do with your study materials, the better you will learn. Have highlighters, pencils, and note pads handy. Highlight important data, read it out loud, and make notes. If there is a concept you are having problems with, stand up and pace while you think it through. Try to see the action taking place in your mind. Throughout your day, try to recall things you have recently learned, incorporate them into your conversations, and teach them to friends. These activities will help to imprint the related information in your brain and move you from simple knowledge to true understanding of the subject matter.

Do the Work and Think about What You Are Doing: Sure, there are times when you might get away with taking a shortcut in your studies, but in doing so you will probably shortchange yourself. The things we really learn are the things we discover ourselves, which is why we don't learn as much from simple lectures, passive videos, or someone simply telling us the answers to our questions. Discovery learning – figuring things out for ourselves – is the most effective and long-lasting form of learning. When you have an assignment, don't just go through the motions. Enjoy your work, think about what you are doing, be curious, ask yourself questions, examine your results, and consider the implications of your findings. These critical thinking techniques will improve and enrich your learning process. When you complete your assignments independently and thoroughly, you will be genuinely knowledgeable and can be very proud of yourself. How to Study Independently There is no denying that learning through any method of independent study is very different from learning through classes held in traditional classrooms. It takes a great deal of personal motivation and discipline to succeed in a course of independent study where there are no instructors or fellow students to give you structure and feedback. These problems are not insurmountable, and meeting the challenges of independent study can provide tremendous personal satisfaction. The key to successful independent study is having a personal study plan and the personal discipline to stick to that plan. Properly Use Your Learning Tools: The basic tools for web courses and other distance learning methods are often similar, consisting of computer software, videos, textbooks, and study guides. Check with your course instructor to make sure you acquire all the materials you will need. You can obtain these items from campus bookstores, libraries, or the Internet. Related course lectures and videos may even be broadcast on your local public and educational television channels. If you choose to do your laboratory experimentation independently, you will need the special equipment and supplies described in this lab manual and contained in its companion LabPaq. For each study session, first work through the appropriate sections of your course materials, because these serve as a substitute for classroom lectures and demonstrations. Take notes as you would in a regular classroom. Actively work with any computer and text materials, carefully review your study guide, and complete all related assignments. If you do not feel confident about the material covered, repeat the previous steps until you do. It is wise to always review your previous work before proceeding to a new section to reinforce what you’ve previously learned and prepare you to better absorb new information. Actual experimenting is among the last things done in a laboratory session.

Plan to Study: A normal science course with a laboratory component may require you to spend as many as 15 hours a week studying and completing your assignments. To really learn new material requires at least three hours of study time each week for each hour of course credit taken. This applies as equally to independent study as it does to regular classroom courses. On a school campus science students are usually in class for three hours and in the laboratory for two to three hours each week. Then, they still need at least nine hours to read their text and complete their assignments. Knowing approximately how much time is required will help you formulate a study plan at the beginning of the course. Schedule Your Time Wisely: The more often you interact with study materials and call them to mind, the more likely you are to reinforce and retain the information. It is much better to study in several short blocks of time rather than in one long, mind-numbing session. Accordingly, you should schedule several study periods throughout the week or during each day. Please do not try to do all of your study work on the weekends! You will burn yourself out, you won't learn as much, and you will probably end up feeling miserable about yourself and science too. Wise scheduling can prevent such unpleasantness and frustration. Choose the Right Place for Your Home Laboratory: The best place to perform at-home experiments will be determined by the nature of the individual experiments. However, this place is usually an uncluttered room where a door can be closed to keep out children and pets; a window or door can be opened for fresh air ventilation and fume exhaust; there is a source of running water for fire suppression and cleanup; and there is a counter or tabletop work surface. A kitchen usually meets all these requirements. Sometimes the bathroom works too, but it can be cramped and subject to interruptions. Review each experiment before starting any work to help you select the most appropriate work area. Because some of the equipment and supplies in your LabPaq may pose dangers to small children and animals, always keep safety in mind when selecting a work area, and always choose an area where you cannot be disturbed by children or pets. Use a Lab Partner: While the experiments in the LabPaq can be performed independently, it is often fun and useful to have a lab partner to discuss ideas with, help take measurements, and reinforce your learning process. Whether your partner is a parent, spouse, sibling, or friend, you will have to explain what you are doing, and in the process of teaching another, you will better teach yourself. Always review your experiments several days ahead of time so you have time to line up a partner if needed. Perform Internet Research: Students in today’s electronic information age are often unaware of how fortunate they are to have so much information available at the click of a mouse. Consider that researchers of the past had to physically go to libraries, search through card catalogs for possible sources of information, and wait weeks to receive books and journals that may not contain the information they needed. Then they had to begin their search all over again! Now you can find information in a matter of minutes.

Since most courses today include online components, it is assumed that you have reasonable computer skills. If you make ample use of those skills and include online research as part of your study routine, you can greatly enhance your depth of learning as well as improve your grades. Keep a web browser open as you review your course materials and laboratory assignments. When you encounter words and concepts that you have difficulty fully understanding, perform a quick web search and review as many sites as needed until the definition or concept is clear in your mind. Web searches are especially valuable in science. For example, if you have difficulty with a concept, you can usually perform an image search that will help visually clarify the object of interest. Perform a text search to find descriptions and information from leading scientists at famous institutions all over the world. For unfamiliar terms, enter the word “define” plus the unfamiliar term into your search engine and a myriad of differently phrased definitions will be available to help you. This lab manual lists numerous respected websites that you may find useful, and you will undoubtedly find many more on your own. Rely only on trusted government and educational institutions as sources for valid research data. Be especially skeptical of and double-check information garnered from personal blogs and wiki sites like wikipedia.org, where anyone, regardless of their expertise or integrity, can post and edit information. As students all over the world are finding, the worldwide web is a treasure trove of information, but not all of it is valid! Finally, while website links in this lab manual were valid at the time of printing, many good websites become unavailable or change URLs. If this happens, simply go to one of the other sites listed or perform a web search for more current sites. HOW TO PERFORM AN EXPERIMENT Although each experiment is different, the process of preparing, performing, and recording an experiment is essentially the same. Read the Entire Experiment before You Start: Knowing what you are going to do before you do it will help you organize your work and be more effective and efficient. Review Basic Safety: Before beginning work on any experiment, reread the lab manual’s safety sections, try to foresee any potential hazards, and take appropriate steps to prevent safety problems. Organize Your Work Space, Equipment, and Materials: It is hard to organize your thoughts in a disorganized environment. Assemble all required equipment and supplies before you begin working.

Outline Your Lab Notes: Outline the information needed for your Lab Notes and set up any required data tables before the experiment, to make it easier to enter observations and results as they occur. LabPaq CDs normally include a Report Assistant containing .rtf files of each experiment’s questions and data tables. These files can be copied and pasted into your Lab Notes to facilitate your compilation of data and text information. Perform the Experiment According to Instructions: Follow all directions precisely in sequential order. This is not the time to be creative. Do not attempt to improvise your own procedures! Think About What You Are Doing: Stop and give yourself time to reflect on what has happened in your experiment. What changes occurred? Why? What do they mean? How do they relate to the real world of science? This step can be the most fun and often creates "light bulb" experiences of understanding. Clean Up: Always clean your laboratory space and laboratory equipment immediately after use. Wipe down all work surfaces that may have been exposed to chemicals or dissection specimens. Blot any unused chemicals with a paper towel or flush them down the sink with generous amounts of water. Wrap dissection specimens in newspaper and plastic and place them in a sealed garbage can. Discard used pipets and other waste in your normal trash. Return cleaned equipment and supplies to their LabPaq box and store the box out of reach of children and pets. Complete Your Work: Complete your Lab Notes, answer the required questions, and prepare your Lab Report. If you have properly followed all the above steps, the conclusion will be easy.

Why Experimental Measurements Are Important:

We measure things to know something about them, to describe objects, and to understand phenomena. Experimental measurement is the cornerstone of the scientific method; thus, no theory or model of nature is tenable unless the results it predicts are measurable and in accordance with the experiment.

Your primary tasks in a science laboratory course are to create experimentally measured values, compare your results to accepted theoretical or measured values, and gain a full understanding of scientific concepts. This is true for experiments done both inside and outside of a formal laboratory. Each experiment is predicated upon a theory of scientific principle and represents a test of that theory through experimentation, observation, measurements, and analysis.

Laboratory Equipment and Techniques While many of these techniques and equipment are most applicable to specific science disciplines in formal laboratory facilities, knowledge of these items is often required for the study of other science disciplines and when working in a home laboratory. Dispensing Chemicals: To avoid contamination when pouring liquid chemicals from a reagent (ree-ey-juhnt) bottle with a glass stopper, hold the stopper in your fingers while carefully pouring the liquid into the desired container. When pouring from a screw-cap bottle, set the cap down on its top so that it does not become contaminated or contaminate anything. Be certain to put the correct cap on the bottle after use. Never pour excess chemicals back into a reagent bottle, because this may contaminate the reagents. If any liquid spills or drips from the bottle, clean it up immediately. To obtain samples of a powdered or crystalline solid from a container, it is best to pour the approximate amount of solid into a clean, dry beaker or onto a small piece of clean, creased paper for easy transport. Pour powders and crystals by tilting the container, gently shaking and rotating the solids up to the container lip, and allowing the solids to slowly fall out. If you pour too much solid, do not put any solid back in the container. Also, never put wooden splints, spatulas, or paper into a container of solids to avoid contamination. Dropping Chemicals: In micro-scale science, you use only small drops of chemicals, and it is extremely important that the drops are uniform in size and carefully observed. To ensure uniformity of drop size, use scissors to cut off the tip of the pipet perpendicular to the pipet body; cutting at an angle will distort drop sizes. Turn the pipet upside down so the dispensing chamber behind the dropper is full of liquid. Then hold the dropper in front of your eyes so you can carefully observe and count the number of drops dispensed as you slowly squeeze the pipet.

You can see the incorrect (left) and correct (right) way to dispense drops. The pipet should be held in a vertical position at eye level to ensure drops are uniform in size and the correct drops are dispensed.

Heating Chemicals: Heat solid and liquid chemicals with great care to prevent explosions and accidents.

Liquids in Beakers: To heat liquids in beakers or flasks, ensure that these containers are well supported above the heat source. Generally, the beaker or flask is placed on wire gauze supported by an iron support attached to a stand. The heat source is placed under the beaker or flask. Liquids in Test Tubes: When heating liquids in test tubes, always use a test tube holder. Evenly heat the test tube contents by carefully moving the test tube back and forth in the flame. Heat the test tube near the top of the liquid first; heating the test tube from the bottom may cause the liquid to boil and eject from the tube.

Heating Sources for Small-scale Techniques: For micro- and small-scale science experimentation, the most commonly used heat sources are alcohol burners, candles, and burner fuel. Alcohol burners can be a problem because their flame is almost invisible, and they cannot be refilled while hot. Candles, while effective for heating small quantities of materials, tend to leave a sooty, carbon residue on the heated container that obstructs observations. Sterno and similar alcohol based fuels are very volatile and cannot be safely shipped; however, the Glycol-based fuel used in LabPaqs is safe to ship. Chafing dish (i.e., burner fuel) is actually the best of these alternatives because it has a visible flame, is easily extinguished, and does not leave excessive flame residue. Regardless of the type of burner used, never leave an ignited heat source unattended. Mass Measurement Equipment: Note that weighing scales are often called balances since weights are calculated using balance beams. Triple and quadruple beam balances are the most common measuring equipment found in laboratories. However, with today's precision technology, digital top-loading balances are becoming increasingly popular.

Triple and Quadruple Beam Scale: These balances typically include a hanging pan and vary in their degree of accuracy. After the scale has been set at zero, the object to be weighed is placed in the hanging pan, and balancing weights are added or subtracted by moving a pointer across a horizontal bar scale. When exact scale is achieved, the pointer indicates the object’s mass. Digital Top Loading Balance: This scale is initially zeroed by pressing the zero button. If your are using weighing paper or a small beaker, first tare the paper or beaker by placing it on the scale and pressing the tare button. This will produce a zero reading, and the weight of the paper or beaker will be excluded from the weighing process. Hanging Spring Scales: Measurements are taken by suspending the item from a scale, often within a container. Spring scales are not easily tared, so the container weight should be separately calculated and subtracted from the combined weight of the item and the container.

The Non-digital Analytical Balance: This instrument is very delicate, and the instructions for its use are quite detailed. Because of its extreme sensitivity, weighing on the analytical scale must be carried out in a closed chamber that is free from drafts. This instrument is seldom used by first-year science students.

Volume Measurement Equipment: To obtain accurate measurements from any glass volume measurement container, such as a beaker or graduated cylinder, you must identify and correctly read a curved surface known as the meniscus. The meniscus of water and water- based solutions concaves downward and is read at the very bottom of its curve. A mercury meniscus is convex and is read at the very top of its curve. There is no meniscus issue associated with plastic containers. Filtration Equipment: Gravity filtration is used to remove solid precipitates or suspended solids from a mixture. It works like a small funnel or spaghetti strainer, except that it is lined with fine, conical filter paper to trap the solids. After pouring a mixture into the filter from a beaker, use a special spatula, called a rubber policeman, to scrape any remaining solids from the beaker wall into the conical filter paper. Then, use a wash bottle to rinse residue from both the beaker and rubber policeman into the filter cone to ensure that all the mixture's particles pass through the filter. Suction filtration uses a vacuum to suck a mixture through a filter. It is much faster than but not always as efficient as gravity filtration. The required vacuum is usually created by the aspirator of a laboratory water faucet. Bunsen Burner: This old, tried-and-true heat source relies on the combustion of natural or bottled gas. To achieve the best flame, you must properly adjust the burner's gas inlet valve and air vent. Open the valves only halfway before lighting the burner. The safest way to light the burner is to bring a lighted match to the flame opening from the side, not the top. When the burner is lit, close the air vent and adjust the gas inlet valve until the flame is approximately 10 cm high. The flame should be luminous and yellow. Next, open the air vent until the flame becomes two concentric cones. The outer cone will be faintly colored and the inner cone will be blue. The hottest part of the flame is at the tip of the blue cone. Graduated Cylinder: Graduated cylinders are available in a wide range of sizes. To read a volume in a graduated cylinder, hold the cylinder at eye level so the contents level and you can directly view the meniscus. Looking at a meniscus from below or above will create parallax and cause a false reading. Always read any scale to the maximum degree possible, including an estimate of the last digit. Buret: Burets are long, graduated tubes usually used in titration. They have a stopcock or valve on the bottom that allows you to dispense liquids in individual drops and accurately measure the quantity dispensed. Use caution when opening the stopcock to ensure that only one drop is dispensed at a time. Pipet: Pipets are small tube-type containers with openings at one end if made of plastic or at both ends if made of glass. They come in a range of volumes and are generally used to transfer specific amounts of liquids from one container to another.

Berel Pipet: These soft and flexible pipets are made of polyethylene plastic and are extensively used in LabPaqs. They have long, narrow tips and are used to deliver chemicals and to collect products. Berel pipets come in different sizes, and their tips can have different diameters and lengths. You can modify them to serve diverse purposes such as chemical scoops, gas generators, or reaction vessels. Volumetric Flask: Volumetric flasks are pear-shaped flasks with long necks used for the preparation of solutions whose concentrations need to be very accurate. Flasks come in a variety of sizes ranging from a few milliliters to several liters, and their volume levels are precisely marked. When the liquid level inside a volumetric flask is such that the meniscus lines up with the calibration mark on the neck, the volume of the liquid is exactly as stated. Unlike volumetric flasks, the markings on beakers, Erlenmeyer flasks, and most other laboratory containers are very good approximates but are not intended to be exact and precise volume measurements. Wash Bottles: These plastic squeeze bottles produce a small stream of water that can be easily dispensed as needed (e.g., washing out residue from a container). The bottles usually contain distilled or deionized water and are typically used to top off the last few milliliters of a vessel and avoid overfilling. In micro- and small-scale experimentation, plastic pipets are used for similar functions. Tissue Culture Well Plates: These microplates are plastic trays containing numerous shallow wells arranged in lettered rows and numbered columns. Similar to test tubes and beakers, you can use the wells to observe reactions, to temporarily store chemicals during experiments, and to hold pipets. The most commonly used plates are 24-well and 96-well. Distilled Water and Deionized Water: Tap water frequently contains ions that may interfere with the substances you are studying. To avoid such interference, use distilled or deionized water any time water is needed for dilution of concentration or the preparation of experimental solutions. Wash used glassware with soap, rinse with tap water, and rinse again with distilled water.

Use, Disposal, and Cleaning Instructions for Common Materials These procedures are not repeated for each experiment, because it is assumed students will always refer to them before beginning any experiment. Properly cleaning the laboratory after experimentation is a safety measure! Instrument Use

x Small quantities of chemicals are usually packaged in thin stem pipets. The drop size dispensed from small dropper bottles is different from that of the pipets. Most experiments require pipet-sized drops. It may be necessary to squeeze a few drops of chemical from a dropper bottle into a well plate, and then use a clean, empty pipet to suck up and drop the chemical.

x Once dispensed, do not return chemicals to their dropper bottles as this could cause

contamination. To avoid over-dispensing, squeeze out only a few drops of chemicals into a well plate at a time. Squeeze out more as needed.

x To use burner fuel, unscrew the cap, light the wick, and place the can under a burner

stand. Extinguish the fuel by gently placing the cap over the flame to deprive it of oxygen. Leave the cap sitting loosely on top of the wick when you are not using the fuel in order to avoid unnecessary evaporation and ensure an ample supply of fuel for all experiments. Allow the fuel to cool completely before tightly screwing on the cap for storage. If you screw the cap on while the fuel is still hot, you may create a vacuum that will make it very difficult to reopen the fuel can in the future.

x To reseal a pipet, heat the tip of a metal knife and press the pipet tip onto the hot

metal while twirling the bulb. Never simply hold a flame to the tip of the stem!

x To minimize contamination, avoid touching the surfaces of clean items that might later come in contact with test chemicals.

Storage and Disposal

x Items in LabPaq auxiliary bags are generally used multiple times or for several different experiments. Always clean and return unused auxiliary items to the bag after completing an experiment.

x Blot up used and leftover chemicals with paper towels and place in a garbage bin or

flush down a drain using copious amounts of water. The quantities of chemicals used in LabPaqs are very small and should not negatively impact the environment or adversely affect private septic systems or public sewer systems.

x Discard non-chemical experimental items with household garbage but first wrap

them in newspaper. Place these items in a securely covered trash container that cannot be accessed by children and animals.

x LabPaqs containing dissection specimens will usually contain specific information

regarding their handling. After completion of any dissecting work, wrap dissection specimens in news or waste paper, seal in a plastic bag, and place in a closed trash bin for normal garbage disposal.

Cleaning Instructions

x To clean a thin-stemmed plastic pipet, squeeze the bulb to draw up and then expel tap water from the bulb several times. Repeat this process with distilled water. Dry the pipet by repeatedly squeezing the bulb while tapping the tip on a clean paper towel. Then use gravity to help dry the pipet by forcefully swinging the pipet into a downward arch while squeezing the bulb. Lay the pipet on a clean paper towel or place it in a test tube stand and allow it to air dry.

x Use a mild liquid dishwashing detergent mixed with warm water to loosen solids or

oils that adhere to experimental glassware, plastics, and equipment and to clean laboratory equipment and the laboratory area after an experiment. Use tap water to rinse washed items well and remove all traces of detergent.

x Use a soft cloth or a test tube brush to loosen and clean residue from the surfaces of

experimental glassware, plastics, and equipment.

x Use a final rinse of distilled water to clean tap water mineral residue from newly washed items, especially beakers, cylinders, test tubes, and pipets.

x Dry test tubes by placing them upside down in the test tube rack. Air dry other items

by placing them on paper towels, aluminum foil, or a clean dishtowel. Important Notice Regarding Chemical Disposal: Due to the minute quantities and diluted and/or neutralized chemicals used in LabPaqs, the disposal methods previously described are well within acceptable levels of disposal guidelines defined for the vast majority of local solid and wastewater regulations. Since regulations occasionally vary in some communities, you are advised to check with your local area waste authorities to confirm these disposal techniques are in compliance with local regulations and/or if you should seek assistance with disposal.

HOW TO WRITE LAB NOTES AND LAB REPORTS Generally two basic records are compiled during and from scientific experimentation. The first record is your Lab Notes which you will record as you perform your experiments. Entries in your lab notebook will be the basis for your second record, the Lab Report. The Lab Report formally summarizes the activities and findings of your experiment and is normally submitted to your instructor for grading.

Lab Notes Scientists keep track of their experimental procedures and results as they work by recording Lab Notes in a journal-type notebook. In laboratories these notebooks are often read by colleagues, such as directors and other scientists working on a project. In some cases scientific notebooks have become evidence in court cases. Consequently, Lab Notes must be intelligible to others and include sufficient information so that the work performed can be replicated and there can be no doubt about the honesty and reliability of the data and the researcher. Notebooks appropriate for data recording are bound and have numbered pages that cannot be removed. Entries include all of your observations, actions, calculations, and conclusions related to each experiment. Never write data on pieces of scratch paper to transfer later, but always enter the data directly into the notebook. When you record erroneous data, neatly draw a light, diagonal line through the error, and write a brief explanation as to why you voided the data. Also record information you learn from an error. Mistakes can often be more useful than successes, and knowledge gained from them is valuable to future experimentation. As in campus-based science laboratories, independent study students are expected to keep a complete scientific notebook of their work which may or may not be periodically reviewed by the instructor. Paperbound 5x7 notebooks of graph paper work well as lab notebooks. Since it is not practical to send notebooks back and forth between instructors and students for each experiment, independent study students usually prepare formal Lab Reports and submit them along with their regular assignments to the instructor via email or fax. Lab Notes of experimental observations can be kept in many ways. Regardless of the procedure followed, the key question for deciding what kind of notes to keep is: Do I have a clear enough record that if I pick up my lab notebook or read my Lab Report in a few months, I can still explain to myself or others exactly what I did? Lab Notes generally include these components:

Title: Match the title to the title stated in the lab manual.

Purpose: Write a brief statement about what the experiment is designed to determine or demonstrate.

Procedure: Briefly summarize what you did to perform this experiment and what equipment you used. Do not simply copy the procedure statement from the lab manual.

Data Tables: Always prepare tables before experimenting, so they will be ready to receive data as it is accumulated. Tables are an excellent way to organize your observational data, and where applicable, the Procedure section advises a table format for data recording.

Observations: Record what you observed, smelled, heard, or otherwise measured? Generally, observations are most easily recorded in table form.

Questions: Thoughtfully answer the questions asked throughout and at the end of experiments. The questions are designed to help you think critically about the experiment you just performed.

Conclusions: What did you learn from the experiment? Base your conclusions on your observations during the experiment. Write your conclusions in your best, formal English, using complete sentences, full paragraphs, and correct spelling.

Some general rules for keeping a lab notebook are:

1. Leave the first two to four pages blank so you can add a Table of Contents later. Entries in the Table of Contents should include the experiment number, name, and page number.

2. Neatly write your records without being fussy. 3. Do not provide a complete Lab Report in your lab notebook. Instead, record what you

did, how you did it, and what your results were. Your records need to be substantial enough that any knowledgeable person familiar with the subject of your experiment can read the entries, understand exactly what you did, and repeat your experiment if necessary.

4. Organize all numerical readings and measurements in appropriate data tables. Refer

to the sample Lab Report in this lab manual. 5. Always identify the units (e.g., centimeters, kilograms, or seconds) for each set of

data you record. 6. Always identify the equipment you are using so you can refer to it later if you need to

recheck your work. 7. Capture the important steps and observations of your experiments using digital

photos in which you are pictured. Photos within your Lab Report document both what you observed and that you actually performed the experiment.

8. Record more rather than less data. Even details that may seem to have little bearing on your experiment (e.g., time and temperature variances when the data were taken) may turn out to have great bearing on your future results analysis.

9. Make a note if you suspect that a particular data set may not be reliable. 10. Never erase data. If you think an entry in your notes is in error, draw a single line

through it and note the correction, but don’t erase or scratch it out completely. You may later find that the information is significant after all.

Errors: Although experimental results may be in considerable error, there is never a wrong result in an experiment. Whatever happens in nature, including the laboratory, cannot be wrong. If you made your observations and measurements carefully, your results will be correct. Errors may have nothing to do with your investigation, or they may be mixed up with so many other unexpected events that your report is not useful. Even errors and mistakes have merit and often lead to our greatest learning experiences. Errors provide important results to consider; thus, you must think carefully about the interpretation of all your results, including your errors. Experiment Completion: The cardinal rule in a laboratory is to fully carry out all phases of your experiments instead of “dry-labbing” or taking shortcuts. The Greek scientist, Archytas, summed this up very well in 380 B.C.:

Lab Reports This lab manual covers the overall format that formal Lab Reports generally follow. Remember, the Lab Report should be self-contained, so anyone, including someone without a science background or lab manual, can read it, understand what was done, and understand what was learned. Data and calculation tables have been provided for many of the experiments in this lab manual, and you are encouraged to use them. Computer spreadsheet programs such as Microsoft® Excel® and websites like nces.ed.gov/nceskids/Graphing/Classic/line.asp can also greatly facilitate the preparation of data tables and graphs. Visit www.ncsu.edu/labwriter/ for additional information on preparing Lab Reports.

Lab Reports are expected to be word processed and to look organized and professional. They should be free of grammar, syntax, and spelling errors and be a respectable presentation of your work. Avoid writing in the first person as much as possible. Lab Reports should generally contain and clearly distinguish the sections discussed in detail below. The presentation and organization skills you’ll develop by producing science Lab Reports is beneficial to all potential career fields. Lab Report Format: Title Page This is the first page of the Lab Report and consists of:

a. Experiment number and/or title b. Your name c. Names of lab partner(s) d. Date and time experiment was performed e. Location if work was performed in the field f. Course number

Section 1: Abstract, Experiment, and Observation Abstract: Even though the abstract appears at the beginning of the Lab Report, you will write it last. An abstract is a very concise description of the experiment’s objectives, results, and conclusions and should be no longer than a paragraph. Experiment and Observation: In chronological order, carefully and concisely describe what was done, what was observed, and what, if any, problems were encountered. Describe what field and laboratory techniques and equipment you used to collect and analyze the data on which the conclusions are based. Insert photos and graphic illustrations in this section; graphics should be in .jpg or .gif format to minimize electronic file size. Show all your work for any calculations performed. Title every graph and clearly label the axes. Data point connections should be “best-fit curves,” which are smooth, straight or curved lines that best represent the data, instead of dot-to-dot data point connections.

Include all data tables, photos, graphs, lists, sketches, etc. in an organized fashion. Include relevant symbols and units with data. Generally one or two sentences explaining how data was obtained is appropriate for each data table.

Note any anomalies observed or difficulties encountered in collecting data as these may affect the final results. Include information about any errors you observed and what you learned from them. Be deliberate in recording your experimental procedures in detail. Your comments may also include any preliminary ideas you have for explaining the data or trends you see emerging.

Section 2: Analysis – Calculations, Graphs, and Error Analysis Generally, the questions at the end of each experiment will act as a guide when preparing your results and conclusions. The analysis is written in paragraph form and no more than one or two pages long. As you write, consider the following:

a. What is the connection between the experimental measurements taken and the final results and conclusions? How do your results relate to the real world?

b. What were the results of observations and calculations? c. What trends were noticed? d. What is the theory or model behind the experiment? e. Do the experimental results substantiate or refute the theory? Why? Be sure to refer

specifically to the results you obtained. f. Were the results consistent with your original predictions of outcomes or were you

forced to revise your thinking?

g. Did errors (e.g., environmental changes or unplanned friction) occur? If so, how did these errors affect the experiment?

h. Did any errors occur due to the equipment used (e.g., skewed estimates due to a lack

of sufficient measurement gradients on a beaker)?

i. What recommendations might improve the procedures and results? Error Analysis: In a single paragraph, comment on the accuracy and precision of the apparatuses used, include a discussion of the experimental errors, and include an estimate of the errors in your final result. Remember, errors are not mistakes. Errors arise because the apparatus and/or the environment inevitably fail to match the ideal circumstances assumed when deriving a theory or equation. The two principal sources of error are:

Physical phenomena: Elements in the environment may be similar to the phenomena being measured and may affect the measured quantity. Examples include stray magnetic or electric fields or unaccounted for friction. Limitations of the observer, analysis, and/or instruments: Examples include parallax error when reading a meter tape, the coarse scale of a graph, and the sensitivity of the instruments.

Human errors and mistakes that are not acceptable scientific errors include: calculator misuse (e.g., pushing the wrong button, misreading the display); misuse of equipment; faulty equipment; incorrectly assembled circuits or apparatuses.

Section 3: Discussion, Results, and Conclusions Discussion: Carefully organize your discussion to include consideration of the experiment’s results, interpretation of the results, and uncertainty in the results. This section is written in paragraph form and is generally no more than one to two pages in length. Occasionally it will be more appropriate to organize various aspects of the discussion differently. While not all of the following questions will apply to every experiment, consider them when writing your Lab Report. Results:

a. What is the connection among your observations, measurements, and final results? b. What were the independent or dependent variables in the experiment? c. What were the results of your calculations? d. What trends were noticeable? e. How did the independent variables affect the dependent variables? For example, did

an increase in a given independent variable result in an increase or decrease in the associated dependent variable?

Interpretation of Results:

a. What is the theory or model behind the experiment you performed? b. Do your experimental results substantiate or agree with the theory? Why or why not?

Be sure to refer specifically to your experimental results. c. Were these results consistent with your original beliefs or were you forced to

reevaluate your prior conceptions? Uncertainty in results:

a. How much did your results deviate from expected values? b. Are the deviations due to error or uncertainty in the experimental method? Can you

think of ways to decrease the amount of uncertainty? c. Are the deviations due to idealizations inherent in the theory? What factors has the

theory neglected to consider?

d. In either case, consider whether your results display systematic or random deviations.

Lab Notes and Lab Reports undoubtedly sound complex and overwhelming at first, but don’t worry. They will make more sense to you when you begin performing the experiments and writing reports. After writing your first few Lab Reports, the reports will become second nature to you. Refer to the sample Lab Report in this manual.

Laboratory Drawings Laboratory work often requires you to illustrate findings in representational drawings. Clear, well organized drawings are an excellent way to convey observations and are often more easily understood than long textual descriptions. The adage “a picture is worth a thousand words” really is true when referring to Lab Notes. Give yourself ample drawing space and leave a white margin around the actual illustration so it is clearly visible. Also leave a broad margin along one side of your drawing to insert object labels. Use a ruler to draw straight lines for the labels and connecting lines to the corresponding objects. The image below provides an example of how laboratory drawings should look when they are included in a formal Lab Report. Students often believe they can’t draw; however, with a little practice, anyone can illustrate laboratory observations. A trick many artists use is to form a mental grid over the scene and draw within the grid. For example, quickly make a free hand drawing of the diagram below. Now, mentally divide the diagram into quarters and try drawing the diagram again. In all likelihood, the second, grid-based drawing yielded a better result.

SOURCE OF DRAWING Your Name Such as MUNG BEAN Date of Drawing TITLE OF DRAWING Such as CELL STRUCTURE

Visual Presentation of Data Like pictures, good graphs and tables can quickly and clearly communicate information visually; hence, graphs and tables are often used to represent or depict collected data. Graphs and tables should be constructed to stand alone – all the information required to understand a graph or table should be included. Tables A table presents data clearly and logically. Independent data is listed in the left column and all dependent data is listed to the right. While there will be only one independent variable, there can be more than one dependent variable. The decision to present data in a table rather than a graph is often arbitrary; however, a table may be more appropriate when the data set is too small to warrant a graph or is large, complex, and not easily illustrated. Often, data tables display raw data, and a graph provides visualization of the data. Graphs A graph is composed of two basic elements: the graph itself and the graph legend. The legend provides the descriptive information needed to fully understand the graph. In the graph at right, the legend shows that the red line represents Red Delicious apples, the brown line represents Gala apples, and the green line represents Wine Sap apples. Without the legend it would be difficult to interpret this graph. When inserting a graph, choose “Scatter” as the type of graph. Trend line or Line of best fit: To more clearly show the trend between two sets of data, ”lines of best fit” or ”trend lines” are added to data. This enables us to determine the general trend of the data or to better use the data for predictive purposes. Excel or a similar spreadsheet program can easily add a trend line to the data. Use Excel to make a scatter plot of the data and then add a trend line. In most cases the line may not

Plant Height versus Fertilizer Solution X-Axis Y-Axis Fertilizer % solution

Plant Height in cm

0 25 10 34 20 44 30 76 40 79 50 65 60 40

pass through very many of the plotted points. Instead, the idea is to get a line that has equal numbers of points on either side. Most people start by viewing the data to see which trend line fits the data the best (i.e. which kind of trend line comes closest to the points). For most (but not all) of the data a linear trend line will provide a good fit. Trendlines are most useful to predict data that is not measured. In interpolation, the trend line is used to construct new data points within the range of a discrete set of known data points. Similarly, a trend line can be used to extrapolate data that are outside of the measured data set. This is illustrated in Figures 1 through 4.

Sample data set:

Time, t (seconds)

Distance, x (cm)

0.1 3.8 0.3 6.1 0.5 7.95 0.8 11

Figure 1: Sample data

Figure 2: Scatter graph of sample data

Figure 3: Scatter graph with a trendline and the equation of the line.

As an example of interpolation, if we want to know the cm-displacement at a time of 0.6 s on the Figure 4 Interpolation of data point, we add a vertical line from 0.6 s to the trendline, and then a horizontal line to the distance. This will reads an approximately distance of 9 cm. More accurately, the slope equation of the line may be used to calculate this value: y=10.182 x + 2.885; y = 10.182*0.6+2.885 = 8.99 cm To extrapolate, we would extend the trendline beyond the collected data and repeat the above process. We could also use the slope equation of the line. For example, using the equation to extrapolate the distance at 1 sec. : y = 10.182*1.0+2.885 = 13.1 cm Graph Setup: Consider a simple plot of the Plant Height versus Plant Fertilizer Concentration as shown in one of the data tables above. This is a plot of points on a set of X and Y coordinates. The X-axis or abscissa runs horizontally; the Y-axis or ordinate runs vertically. By convention, the X-axis is used for the independent variable – a manipulated variable in an experiment whose presence determines the change in the dependent variable. The Y-axis is used for the dependent variable – the variable affected by another variable or by a certain event. In this example, the amount of fertilizer is the independent variable and goes on the X-axis. The plant height, since it may change depending on changes in fertilizer amount, goes on the Y-axis. One way to determine which data goes on the X-axis versus the Y-axis

Figure 4: Interpolation of a data point

is to think about what affects what. Does fertilizer affect plant height or does plant height affect fertilizer. Only one of these options should make sense. Plant height will not change the fertilizer, but the fertilizer will affect the plant height. The variable that causes the change is independent, and the variable that changes is dependent. If the data deals with more than one dependent variable, it would be represented with three lines and a key or legend would identify which line represents which data set. In all graphs, each axis is labeled, and the units of measurement are specified. When a graph is presented in a Lab Report, the variables, the scale, and the range of the measurements should be clear. Refer to the table below when setting up a line graph.

How to Construct a Line Graph Step Explanation 1 Identify the

variables. x Independent variable: Controlled by the experimenter.

- Goes on the X-axis – the abscissa. - Located on the left side of a data chart.

x Dependent variable: Changes with the independent variable. - Goes on the Y-axis – the ordinate. - Located on the right side of a data table

2 Determine the range.

x Subtract the lowest data value from the highest. - Calculate each variable separately.

3 Determine the scale.

x Choose a scale that best fits each variable’s range (e.g., increments of one, two, five, etc.). - Choose a scale that spreads the graph over most

of the available space. 4 Number and label

each axis. x The axes tell what the graph’s data lines represent.

- Always include units of measure (e.g., days, time, meters, etc.).

5 Plot the data points. x Plot each data value on the graph with a dot. - Add the numerical data next to the dot, if there is

room and you avoid cluttering the graph. 6 Draw the graph. x Draw a straight or curved line that best fits the data

points. - Most graphs are shown as smooth lines, not dot-

by-dot connections. 7 Title the graph. x The title should clearly tell what the graph is

depicting. x Provide a legend to identify different lines, if the

graph has more than one set of data.

Computer Graphing Using MS Excel These instructions apply to the 2003 version of Excel. If you have a newer version, perform an Internet search for current instructions. This set of general instructions will be used to plot the following data:

Time, t (seconds) Distance, x (cm) 0 0 .1 9.8 .2 30.2 .3 59.9 .4 99.2 .5 148.9

When graphing x-y data, you must first determine which variable will be the X-variable and which will be the Y-variable. If you are unsure, review the previous Visual Presentation of Data section. Create a File

1. Open a blank Excel spreadsheet. 2. Save the file under an appropriate name, such as Exercise 1-Time vs

Distance.

Create Data Table

1. Enter the X-data points in the first column (A). 2. Enter the Y-data points in the second column (B).

Note: It is often useful to enter zero as the first data value, but not always. Nonetheless, it is a good habit to start.

3. Highlight all the data values by placing the curser in the first cell to be highlighted (A1) and either:

x Clicking and holding the left mouse button while pulling the mouse and

curser down and to the right so the cells are highlighted and then releasing the button.

x Holding the <Shift> key on the keyboard and using the direction arrows to move the cursor over the desired area until all cells are highlighted.

Create Graph

4. Click the Chart Wizard icon on the toolbar or select Chart from the Insert menu.

Step 1: Chart Type

5. Select XY (Scatter) from the Standard Types tab. 6. Select your preferred Chart sub-type. Although

you can choose graphs with data points, graphs with smooth lines are preferable.

7. Click Next >.

Step 2: Chart Source Data Carefully review this information to ensure the graph has the correct values for the vertical and the horizontal axes.

8. Select the Columns option button on the Data Range tab.

The range should read =Sheet1!$A$2:$B$7 This means the data:

x Comes from Sheet 1 of the workbook. x Comes from cells A2 through B7. x Has been organized by data columns

instead of data rows.

9. Under the Series tab, the values for the X- and Y-axes are as follows:

X Values: =Sheet1!$A$2:$A$7 Y Values: =Sheet1!$B$2:$B$7 This means:

1. The data comes from Sheet 1 of the workbook.

2. The X-value data comes from cells A2 through A7.

3. The Y-value data comes from cells B2 through B7.

Note: If the data is reversed, replace the incorrect column letters and numbers with the correct ones.

10. To maintain the appropriate reference, rename the series of data points from the default, Series1, by entering another name in the Name field. Data is commonly used.

11. Click Next >.

Step 3: Chart Options

12. Chart Options allows you to assign titles and labels to your graph as well as determine the appearance of gridlines and legends. Make your selections.

13. Click Next >.

Step 4: Chart Location

14. Choose the location where your graph will be created. x As new sheet: Opens a new page on which the graph will appear. x As object in: Places the graph in the current spreadsheet.

If you’re unsure, select As object in so the data and graph will appear on the same page.

15. Click Finish to complete the graph.

Using Excel® To Calculate the Slope of the Line 1. Put your cursor on the line in your graph and right-click.

An option menu will drop down; select “Add Trendline.”

2. Left-click on “Add Trendline.” The window to the right will appear with icons for the types of trend lines possible.

3. For most data you will usually want a “Linear” trendline.

However, from your math classes you should recognize that the curve in your final graph (previous page) resembles a parabola which represents a quadratic or 2nd order polynomial equation. Thus, among the trendline options you will click on the polynomial option.

4. Note that a trendline has now been added to your graph as seen in the top graph of the

double graph at right. If you accidentally clicked on linear trendline, the trendline would look like the bottom graph. You can see that the linear trendline does not fit as well polynomial one.

5. Now, put your cursor on the trendline itself and right-click; then left-click on the “Format Trendline” option that appears.

6. In the box that then appears, select the “Options” tab in the Format Trendline box. Then check:

a. "Set intercept = 0", and b. “Display equation on chart”.

7. Click OK and the new graph below appears with the

equation for the trendline shown on it in the form y=mx+ b. You should recognize that m = slope. (Caveat: Only click on “select intercept = 0” when the line goes through zero.)

SHORTCUT: You can select the type and formatting of a trendline in one step. From Step 3 after selecting the polynomial option, go straight to the Options tab where you can immediately check “Set intercept = 0 “and “Display equation on chart”. Click OK and you are done. Delete your graph and start over to practice and feel comfortable with all the above graphing steps and this shortcut.

Using Excel® for Calculations Many times in physics and scientific or engineering work, one must repeat the same basic calculations using different sets of numbers. As an example consider trying to find the average speed between the distances in our earlier table. The first calculation would look like … Vavg = ¨x = 9.8 cm – 0.0 cm = 98 cm/s ¨t 0.1 – 0.0 s

The second calculation would be Vavg = ¨x = 30.2 cm – 9.8 cm = 204 cm/s ¨t 0.2 – 0.1 s There are only five calculations to compute here and doing all five on a calculator is not a lot of work. However, if there were 100 or 1000 such calculations, it would be extremely laborious! Fortunately Excel® can do these calculations easily and quickly with formulas plus copy and paste functions. Let’s try it with the above data. First, enter the time and distance data into Excel®. Start by inputting the zero values in “cells” A1 and B1 and then enter the rest of the data in the A and B “columns.” (Hint: you may wish to begin inputting your data in “row” 5 or so in the future in order to leave space above the data to later include a spreadsheet title or other information.) Observe that the first non-zero data is in row 2 and in cells A2 and B2. In addition, our time data [t] is in column A and our distance data [x] is in column B. Next, think about how you might construct a formula for our problem. If ¨x, the change in distance can be computed as B2-B1, and ¨t, the change in time can be computed as A2-A1, then we could use this formula for the change in distance over the change in time: = (B2-B1)/(A2-A1) This formula is a math statement that says the difference of the values in boxes B3 and B2 should be divided by the difference of the values in boxes A3 and A2. In order to record in column C the average speed between the distances for all of the sets of data, you must first input the formula above into cell C2 and then copy and paste it into the remaining cells. To do this: 1. Place your curser in the cell C2 2. Insert an equal sign [=] to alert Excel® this will be a formula rather than data.

Time (seconds) Distance (cm) 0 0 .1 9.8 .2 30.2 .3 59.9 .4 99.2 .5 148.9

3. Type your = (B2-B1)/(A2-A1) formula using no extra spaces between numbers and operative signs and hit enter. Observe that your formula appears in the fx box above the columns as it is entered. Refer to this box to make sure your formula is typed correctly.

4. If your formula was correctly input Excel® will do the calculation for you and a value of 98 should appear in C2.

You can now use the same formula for each of the successive sets of values and simplify the process by using the copy and paste functions. When you copy a formula from one Excel® cell and then paste it in another cell, Excel® automatically adjusts the formula to correspond to the cursors’ new position. To copy and paste data from a cell, move your cursor to that cell and either use:

¾ Your mouse: right click to display options and click copy or paste ¾ Edit command at the top of your screen: select the copy or paste option and left

click the mouse or hit enter on the keyboard.

¾ Keyboard commands: use Control + C for copy and Control + V for paste 5. Move your cursor to cell C2 and “copy” its contents in one of the ways described above.

When the cell appears to vibrate, its contents can be copied into other cells. Now move the cursor to 3C and “paste” it in one of the ways described above. To stop the source cell vibrations and end the possibility of copying its data further, hit enter or escape. Note that the formula for cell C3 now correctly reads =(B3-B2)/(A3-A2) and corresponds to the data in row 3.

6. To transfer the formula into multiple cells at the same time, copy the formula in cell C2, highlight cells C3 through C6, and paste. Note that the formula adjusts itself for each row of data and Excel® will properly calculate the average velocity for each of the additional sets of data; the answers are now shown in column C.

Reinforcing Exercise: For the set of data values located on the next page, find the average acceleration between each of the speeds using Excel®.

Time (sec) Speed (cm/s) 0.0906 138 0.1361 184 0.1714 219 0.201 249 0.2267 275 0.2281 274 0.2511 299 0.262 310 0.2916 340 0.3075 355 0.3187 364 0.3371 386 0.3417 390 0.3642 408 0.3723 422 0.3872 435 0.3994 441 0.4224 471 0.452 499

SAFETY CONCERNS You, as a responsible science student and researcher, are solely responsible for safely storing and using your LabPaq materials and for conducting your experiments in a safe and responsible manner. Items in your LabPaq can be especially dangerous to children and pets, so the LabPaq should always be kept safely stored out of their reach. The LabPaq may contain acids or other chemicals that can cause burns if mishandled plus serious illness and or death if consumed. Many LabPaq items are made of glass and/or have sharp edges that pose potential risks for cuts and scratches. While LabPaq thermometers do not contain mercury, they might still break and cause injury. LabPaqs contain small items and materials that could cause choking, injury, or death if misused. Experimentation may require you to climb, push, pull, spin, and whirl. While these activities are not necessarily dangerous, they can pose hazards, and you should always undertake these activities cautiously and with consideration for your surroundings. If you need to climb to take measurements, make sure any stool, chair, or ladder you use is sturdy and take ample precautions to prevent falls. It is wise to have a partner help keep you stable when you must climb. Be especially aware of experimental equipment that you must put in motion, and act cautiously to ensure that items cannot go astray and cause injury to people or property. If you or anyone accidentally consumes or otherwise comes into contact with a substance that could be toxic or cannot be easily washed away, immediately call:

The National Poison Control Center: 1-800-222-1222

Your eyesight is precious and should be protected against chemical spills or splashes as well as flying objects and debris. Always wear safety goggles when working with chemicals of any kind and when working with non-chemical objects that could possibly fly into your eyes. Since chemicals, dirt, and germs are often involved in laboratory experiments, you should never eat or smoke in your laboratory area. Protect your body by keeping your hair tied back from your face and by wearing old clothing that fully covers your arms and legs.

You also need to protect your home furnishings from damage during your experimentation. Cover your work surface with plastic or paper towels when appropriate to prevent ruining furniture and to aid in cleanup. The best safety tools you have are your own mind and intellectual ability to think and plan. After previewing each experiment, carefully think about what safety precautions you need to take to experiment safely, and then take them! Since it is impossible to control students’ use of this lab manual and related LabPaqs or students’ work environments, the author(s) of this lab manual, the instructors and institutions that adopt it, and Hands-On Labs, Inc. – the publisher of the lab manual and the producer of LabPaqs – authorize the use of these educational products only on the express condition that the purchasers and users accept full and complete responsibility for all and any liability related to their use of same. Additional terms authorizing the use of a LabPaq are contained in its Purchase Agreement available at www.LabPaq.com.

Basic Safety Guidelines This section contains vital information that you must thoroughly read and completely understand before beginning to perform experiments. Science experimentation is fun but involves potential hazards which you must acknowledge to avoid. To safely conduct science experiments, you must learn and follow basic safety procedures. While there may be fewer safety hazards for physics and geology experimentation than chemistry and biology, safety risks exist in all science experimentation and should be taken very seriously. Thus, the following safety procedures review is relevant to all students regardless of their field of study While this lab manual tries to include all relevant safety issues, not every potential danger can be foreseen, as each experiment involves different safety considerations. You must always act responsibly, learn to recognize potential dangers, and always take appropriate precautions. Regardless of whether you will be working in a campus or home laboratory setting, it is extremely important that you know how to anticipate and avoid possible hazards and to be safety conscious at all times.

Basic Safety Procedures Science experimentation often involves using toxic chemicals, flammable substances, breakable items, and other potentially dangerous materials and equipment. All of these things can cause injury and even death if not properly handled. These basic safety procedures apply when working in a campus or home laboratory. x Because eyesight is precious and eyes are vulnerable to chemical spills and splashes,

shattered rocks and glass, and floating and flying objects: - Always wear eye protecting safety goggles when experimenting.

x Because toxic chemicals and foreign matter may enter the body through digestion:

- Never drink or eat in laboratory areas. - Always wash your hands before leaving the laboratory. - Always clean the laboratory area after experimentation.

x Because toxic substances may enter the body through the skin and lungs:

- Ensure the laboratory always has adequate ventilation. - Never directly inhale chemicals. - Wear long-sleeved shirts, pants, and enclosed shoes when in the laboratory. - Wear gloves and aprons when appropriate.

x Because hair, clothing, and jewelry can create hazards, cause spills, and catch fire while

experimenting: - Always tie or pin back long hair. - Always wear snug fitting and preferably old clothing. - Never wear dangling jewelry or objects.

x Because a laboratory area contains various fire hazards:

- Smoking is always forbidden in laboratory areas. x Because chemical experimentation involves numerous potential hazards:

- Know how to locate and use basic safety equipment. - Never leave a burning flame or reaction unattended. - Specifically follow all safety instructions. - Never perform any unauthorized experiments. - Always properly store equipment and supplies.

x Because science equipment and supplies often include breakable glass and sharp items

posing potential risks for cuts and scratches; and small items and dangerous chemicals potentially causing death or injury if consumed:

- Carefully handle all science equipment and supplies. - Keep science equipment and supplies stored out of the reach of pets and small

children. - Ensure pets and small children will not enter the lab area while experimenting.

x Because science experimentation may require students to climb, push, pull, spin, and whirl:

- Undertake these activities cautiously and with consideration for the people, property, and objects that could be impacted.

- Ensure stools, chairs, or ladders used to climb are sturdy and take ample precautions to prevent falls.

x Because your best safety tools are your own mind and intellectual ability:

- Always preview each experiment, carefully think about what safety precautions need to be taken to experiment safely, and then take them.

Basic Safety Equipment: You can find the following pieces of basic safety equipment in all campus laboratories. Informal and home laboratories may not have all of these items, but you can usually make simple substitutions. You should know the exact location and proper use of these items.

Eyewash Station: All laboratories should have safety equipment to wash chemicals from the eyes. A formal eyewash station looks like a water fountain with two faucets directed up at spaces to match the space between the eyes. In case of an accident, the victim's head is placed between the faucets while the eyelids are held open, so the faucets can flush water into the eye sockets and wash away the chemicals. In an informal laboratory, you can substitute a hand-held shower wand for an eyewash station. After the eyes are thoroughly washed, consult a physician promptly.

Fire Blanket: A fire blanket is a tightly woven fabric used to smother and extinguish a fire. It can cover a fire area or be wrapped around a victim who has caught on fire.

Fire Extinguisher: There are several types of fire extinguishers, but at least one should be available in all laboratories. You should familiarize yourself with and know how to use the particular fire extinguisher in your laboratory. At a minimum, home laboratories should have a bucket of water and a large container of sand or dirt to smother fires.

First-Aid Kit: This kit of basic first-aid supplies is used for the emergency treatment of injuries and should be standard in both formal and informal laboratories. It should always be well stocked and easily accessible.

Fume Hood: A fume hood is a hooded area containing an exhaust fan that expels noxious fumes from the laboratory. Experiments that might produce dangerous or unpleasant vapors are conducted under this hood. In an informal laboratory such experiments should be conducted only with ample ventilation and near open windows or doors. If a kitchen is used for a home laboratory, the exhaust fan above the stove substitutes nicely for a fume hood.

Safety Shower: This shower is used in formal laboratories to put out fires or douse people who have caught on fire or suffered a large chemical spill. A hand-held shower wand is the best substitute for a safety shower in a home laboratory.

Safety Goggles: There is no substitute for this important piece of safety equipment! Spills and splashes do occur, and eyes can very easily be damaged if they come in contact with laboratory chemicals, shattered glass, swinging objects, or flying rock chips. While normal eyeglasses provide some protection, objects can still enter the eyes from the side. Safety goggles cup around all sides of the eyes to provide the most protection and can be worn over normal eyeglasses when necessary.

Spill Containment Kit: This kit consists of absorbent material that can be ringed around a spilled chemical to keep the spill contained until it can be neutralized. The kit may simply be a container full of sand or other absorbent material such as cat litter.

Potential Laboratory Hazards: Recognizing and respecting potential hazards is the first step toward preventing accidents. Please appreciate the grave dangers the following laboratory hazards represent. Work to avoid these dangers and consider how to respond properly in the event of an accident. Acid Splatter: When water is added to concentrated acid, the solution becomes very hot and may splatter acid. Splattering is less likely to occur if you add acid slowly to the water. Remember this AAA rule: Always Add Acid to water, never add water to acid. Chemical Ingestion: Virtually all chemicals found in a laboratory are potentially toxic. To avoid ingesting dangerous chemicals, never taste, eat, or drink anything while in the laboratory. All laboratories, and especially those in home kitchens, should always be thoroughly cleaned after experimentation to avoid this hazard. In the event of any chemical ingestion, immediately consult a physician. Chemical Spills: Flesh burns may result if acids, bases, or other caustic chemicals are spilled and come in contact with skin. Flush the exposed skin with a gentle flow of water for several minutes at a sink or safety shower. Neutralize acid spills with sodium bicarbonate – simple baking soda. If eye contact is involved, use the eyewash station or its substitute. Use the spill containment kit until the spill is neutralized. To better protect the body from chemical spills, wear long-sleeved shirts, full-length pants, and enclosed shoes when in the laboratory. Fires: The open flame of a Bunsen burner or any heating source, combined with inattention, may result in a loose sleeve, loose hair, or some unnoticed item catching fire. Except for water, most solvents, including toluene, alcohols, acetones, ethers, and acetates, are highly flammable and should never be used near an open flame. As a general rule, never leave an open flame or reaction unattended. In case of fire, use a fire extinguisher, fire blanket, and/or safety shower. Fume Inhalation: To avoid inhaling dangerous fumes, partially fill your lungs with air and, while standing slightly back from the fumes, use your hand to waft the odors gently toward your nose. Lightly sniff the fumes in a controlled fashion. Never inhale fumes directly! Treat inhalation problems with fresh air, and consult a physician if the problem appears serious. Glass Tubing Hazards: Never force a piece of glass tubing into a stopper hole. The glass may snap, and the jagged edges can cause serious cuts. Before inserting glass tubing into a rubber or cork stopper hole, be sure the hole is the proper size. Lubricate the end of the glass tubing with glycerol or soap, and then, while grasping the tubing with a heavy glove or towel, gently but firmly twist it into the hole. Treat any cuts with appropriate first aid.

Heated Test Tube Splatter: Splattering and eruptions can occur when solutions are heated in a test tube. You should never point a heated test tube towards anyone. To minimize this danger, direct the flame toward the top rather than the bottom of the test tube. Gently agitate the tube over the flame to heat the contents evenly.

Horseplay: A laboratory full of potentially dangerous chemicals and equipment is a place for serious work, not for horseplay! Fooling around in the laboratory is an invitation for an accident. Shattered Glassware: Graduated cylinders, volumetric flasks, and certain other pieces of glassware are not designed to be heated. If heated, glassware is likely to shatter and cause injuries. Always ensure you are using heatproof glass before applying it to a heat source. Take special caution when working with any type of laboratory glassware CAUTION for Women: If you are pregnant or could be pregnant, you should seek advice from your personal physician before doing any type of science experimentation.

Material Safety Data Sheets An important skill in the safe use of chemicals is the ability to read a Material Safety Data Sheet (MSDS). An MSDS is designed to provide chemical, physical, health, and safety information on chemical reagents and supplies. It provides information about how to handle, store, transport, use and dispose of chemicals in a safe manner. An MSDS also provides workers and emergency personnel with the proper procedures for handling and working with chemical substances. While there is no standard format for an MSDS, any MSDS provides basic information about physical data, toxicity, health effects, first-aid procedures, chemical reactivity, safe storage, safe disposal, required protective equipment, and spill cleanup procedures. An MSDS is required to be readily available at any business where any type of chemical is used. Even daycare centers and grocery stores need MSDSs for their cleaning supplies. It is important to know how to read and understand an MSDS. An MSDS is generally organized into the following sections:

Section 1: Product Identification Chemical name and trade names Section 2: Hazardous Ingredients Components and percentages Section 3: Physical Data Boiling point, density, solubility in water, appearance, color, etc. Section 4: Fire and Explosion Data Flash point, extinguisher media, special fire fighting procedures, and unusual fire and explosion hazards Section 5: Health Hazard Data Exposure limits, effects of overexposure, emergency and first-aid procedures

Section 6: Reactivity Data Stability, conditions to avoid, incompatible materials, etc. Section 7: Spill or Leak Procedures Steps to take to control and clean up spills and leaks and waste disposal methods Section 8: Control Measures Respiratory protection, ventilation, protection for eyes or skin, or other needed protective equipment

Section 9: Special Precautions How to handle and store, steps to take in a spill, disposal methods, and other precautions

The MSDS is a tool available to employers and workers for making decisions about chemicals. The least hazardous chemical should be selected for use whenever possible, and procedures for storing, using, and disposing of chemicals should be written and communicated to workers. View MSDS information at www.hazard.com/msds/index.php. You can also find a link to MSDS information at www.LabPaq.com. If there is ever a problem or question about the proper handling of any chemical, seek information from one of these sources.

Safety Quiz Refer to the illustration on the following page when answering the questions.

1. List three (3) unsafe activities in the illustration and explain why each is unsafe.

2. List three (3) correct procedures depicted in the illustration.

3. What should Tarik do after the accident?

4. What should Lindsey have done to avoid an accident?

5. Compare Ming and David's laboratory techniques. Who is following the rules?

6. What are three (3) things shown in the laboratory that should not be there?

7. Compare Joe and Tyler's laboratory techniques. Who is working the correct way?

8. What will happen to Ray and Chris when the instructor catches them?

9. List three (3) items in the illustration that are there for the safety of the students.

10. What is Consuela doing wrong?

Science Lab Safety Reinforcement Agreement Any type of science experimentation involves potential hazards, and unforeseen risks may exist. The need to prevent injuries and accidents cannot be overemphasized! Use of this lab manual and any LabPaqs are expressly conditioned upon your agreement to follow all safety precautions and accept full responsibility for your actions. Study the safety section of this lab manual until you can honestly state the following: � Before beginning an experiment I will first read all directions and then assemble and

organize all required equipment and supplies. � I will select a work area that is inaccessible to children and pets while experiments are

in progress. I will not leave experiments unattended, and I will not leave my work area while a chemical equipment is set up unless the room is locked.

� To avoid the potential for accidents, I will clear my home laboratory workspace of all

non-laboratory items before setting up equipment and supplies for my experiments. � I will never attempt an experiment until I fully understand it. If in doubt about any part

of an experiment, I will first speak with my instructor before proceeding. � I will wear safety goggles when working with chemicals or items that can get in my

eyes � I know that except for water, most solvents, such as toluene, alcohols, acetone,

ethers, and ethyl acetate are highly flammable and should never be used near an open flame.

� I know that the heat created when water is added to concentrated acids is sufficient

to cause spattering. When preparing dilute acid solutions, I will always add the acid to the water – rather than the water to the acid – while slowly stirring the mixture.

� I know it is wise to wear rubber gloves and goggles when handling acids and other

dangerous chemicals; I should neutralize acid spills with sodium bicarbonate; and I should wash acid spilled on skin or clothes immediately with plenty of cold water.

� I know that many chemicals produce toxic fumes, and cautious procedures should be

used when smelling any chemical. When I wish to smell a chemical, I will never hold it directly under my nose, but will use my hand to waft vapors toward my nose.

� I will always handle glassware with respect and promptly replace any defective

glassware. Even a small crack can cause glass to break, especially when heated. To avoid cuts and injuries, I will immediately dispose of any broken glassware.

� I will avoid burns by testing glass and metal objects for heat before handling. I know that the preferred first aid for burns is to immediately hold the burned area under cold water for several minutes.

� I know that serious accidents can occur when wrong chemicals are used in an

experiment. I will always read labels before removing chemicals from their containers. � I will avoid the possibility of contamination and accidents by never returning an

unused chemical to its original container. To avoid waste I will try to pour only the approximate amount of chemicals required.

� I know to immediately flush any chemical spill on the skin with cold water and consult

a doctor if required. � To protect myself from potential hazards, I will wear long pants, a long-sleeved shirt,

and enclosed shoes when performing experiments. I will tie up any loose hair, clothing, or other materials as well.

� I will never eat, drink, or smoke while performing experiments.

� After completing all experiments I will clean my work area, wash my hands, and store

the laboratory equipment in a safe place inaccessible to children and pets. � I will always conscientiously work in a reasonable and prudent manner to optimize my

safety and the safety of others whenever and wherever I am involved with any type of science equipment or experimentation.

It is impossible to control students’ use of this lab manual and related LabPaqs or students’ work environments. The author(s) of this lab manual, the instructors and institutions that adopt it, and Hands-On Labs, Inc. – the publisher of the lab manual and producer of LabPaqs – authorize the use of these educational products only on the express condition that the purchasers and users accept full and complete responsibility for all and any liability related to their use of same. Please review this document several times until you are certain you understand it and will fully abide by its terms. Then sign and date the agreement were indicated. I am a responsible adult who has read, understands, and agrees to fully abide by all safety precautions prescribed in this lab manual for laboratory work and for the use of a LabPaq. Accordingly, I recognize the inherent hazards associated with science experimentation; I will always experiment in a safe and prudent manner; and I unconditionally accept full and complete responsibility for any and all liability related to my purchase and/or use of a science LabPaq or any other science products or materials provided by Hands-On Labs, Inc. (HOL). ____________________________________________________ ____________ Student’s Name (print) and Signature Date

EXPERIMENTS

Static Electricity or Electrostatics

Experiment Summary:

Students will have the opportunity to explore the concepts of static electricity, discover how many types of electrical charges exist, and observe how they

interact with each other. They will learn how static electricity is generated and how materials are ranked through the triboelectric series. Students will

conduct various experiments to explore static electricity. �

�

Peter Jeschofnig, Ph.D. Version 09.1.01

Review the safety materials and wear goggles when working with chemicals. Read the entire exercise before you begin. Take time to organize the materials you will need and set

aside a safe work space in which to complete the exercise.

Objectives

x To explore the concepts of static electricity and to discover how many types of electrical charges exist and how they interact with each other.

Materials

Materials From: Qty Item Description: Student Provides 1 Scrap of white paper 1 Transparent tape From LabPaq 1 Aluminum Foil - 6"x 6" 2 Cup, Styrofoam, 8 oz 1 Dark paper - 1/2 Sheet 1 Ruler, Metric Fabrics Bag 1 Fabric Swatch-5 pieces-PK 1 Rabbit fur, swatch - 4"x2" Misc. Supplies Bag 2 Balloons 1 Pepper Packets 1 Salt Packets 1 Thread for PK-2/S 1M per kit

Discussion and Review

We all experience static electricity in our everyday lives. Perhaps we feel a shock when we touch a doorknob after walking across a wool rug. Or perhaps we see the static cling of plastic food wrap as it hugs a bowl or feel the buzz of static electricity when we run our fingers across a television or computer screen. Most of our encounters with static electricity are surprising but not harmful; however, we sometimes hear stories about it destroying computer chips and starting fires. When we tumble clothes in a dryer without a fabric softener, different articles of clothing such as a sweaters, socks, and underwear stick to each other. Why? This occurs because one item gained negative charges from another item that became positively charged by giving up electrons. The charges gained are strong enough to produce an attractive force that keeps the clothes stuck together. In this situation we say that the items have become "electrified" or electrically “charged”. It is often difficult for students to remember that an atom becomes positively charged when it gives up an electron. This seems counter intuitive for when we lose something, it is usually a negative event. Here’s a corny joke to help you remember this concept. Two atoms are walking down the street and one exclaims, “Oh my, I think I’ve lost an electron!” The other asks, “Are you sure? “ The first replies, “Yes, I’m positive!” When you walk or vigorously rub your shoes across a wool rug, your body becomes electrified. The charge that builds up on your body will be removed when you touch another object such as a door handle, light switch, or even a person. Sometimes it will produce a noticeable spark and a little unpleasant shock. Lightning is a dramatic display of how built- up charges are removed. Charges between clouds and the ground build up and become very high. The release of these massive charges is more than just a spark; it is a bolt of lightning that can do a lot of damage!

Two types of electric charges exist in nature: A positive charge like the charge of a proton, and a negative charge like the charge of an electron. Charged objects have an imbalance of protons and electrons. There is a connection between the type of charge on an object and the type of interaction it has with other objects. The interactions possible are attraction, repulsion, and none. Charges of the same type repel each other, while charges of different types attract each other. This basic law is simply stated: Like charges repel. Unlike charges attract. Charges are produced in three basic ways:

x Friction: People have long known that rubbing items together or tearing them apart quickly could produce a charge; this is called charging by friction.

x Induction: An induced charge is created when an electrically charged item near a

conductor causes a redistribution of charges on the conductor.

x Contact: A third way to charge conductors - which are usually metals - is by contact where the charge spreads around all the conductors in contact.

Triboelectric Series: When we rub two different materials together, which one becomes positively charged and which becomes negatively charged? Scientists have ranked materials in order of their ability to hold or give up electrons. This ranking is called the triboelectric series. A list of some common materials is shown here. Under ideal conditions, if two materials are rubbed together, the one higher on the list should give up electrons and become positively charged. You can experiment with things on this list for yourself. In a systematic series of simple experiments, one can determine the existence of charges and the forces produced due to them. You may have noticed that transparent tape like Scotch® tape frequently sticks to your hand when you pull a strip off a roll. This is static electricity at work, and we will use this property of tape to study the electrostatic phenomena. General comments about this lab:

x In this lab, "rub" means to rub vigorously, not to "pet." Vigorous rubbing is required to transfer sufficient amounts of electric charge from one object to another.

x Some objects may have different charges in different areas. Be sure to test the area

you actually rubbed. When you rub one end of a ruler, test that end, not the other!

x At several points in the lab, you will use two strips of sticky tape, called "top" and "bottom" tape, which will generally have opposite charge. The charges of the top and/or bottom tape can become reversed; think about how this can happen. It is wise to check the tape charges occasionally to be sure a reversal has not occurred.

x One caveat is that electrostatic experiments are hard to perform on humid days when

there is too much moisture in the air. Excess moisture produces a leakage for the static electricity charges. Schedule your lab work accordingly.

x This lab is one in which results are sometimes inconsistent. It is best to try each step

at least twice and not write down a result or observation until it is repeated and you are certain of what you observed. Take your time, you’ll find this is a fun lab!

TRIBOELECTRIC�SERIES� Your Hand

Glass Your Hair

Nylon Wool Fur Silk

Paper Cotton

Hard Rubber Polyester

Polyvinylchloride Plastic

Exercise 1

PROCEDURE: Caution: The levels of static electricity used in this lab will not hurt an individual but they may be high enough to impact or ruin calculators, computers, and other electronic equipment with solid state components. Accordingly, do not conduct these experiments next to such electronic equipment. Part I:

1. From white scrap paper cut or tear at least 10 very small pieces of approximately 1-cm squares. Scatter these on a piece of dark colored paper that rests on top of a work table or desk. Then sprinkle a small amount of salt and pepper on the colored paper; several shakes should work fine. Align a plastic ruler parallel to the desktop, just barely above the colored paper and slowly move the ruler back and forth. Observe what happens and record your observations.

2. Next, “charge” the ruler. To do this, wrap a piece of fabric around two sides of the

ruler. Hold the material and ruler firmly between your thumb and fingers in one hand and with the other hand vigorously rub the ruler back and forth for about 5 seconds. Then slowly move the charged ruler over the paper, salt, and pepper. Observe what happens and record your observations.

3. Repeat Step 2 after charging the ruler with each of the different types of material.

Record your observations.

4. Predict what will happen if you substitute tiny bits of aluminum foil and Styrofoam® for the salt and pepper. Test your predictions with small bits of Styrofoam® pinched from the rim of a cup and mini pieces of aluminum foil snipped from the edge of an aluminum foil sheet. Keep the colored paper and the small pieces of white scrap paper for later use in this exercise.

Questions:

A. What happened when you brought the rubbed ruler close to the paper, salt, and pepper?

1. Were all three substances affected equally?

2. What explanations can you offer for why this happened?

B. What combinations of cloth and ruler seemed to produce the greatest effects?

Part II: Set up by again scattering very small scraps of white paper on a dark colored piece of paper that rests on top of a work table or desk.

1. Tear a ~15-cm strip of transparent tape from a roll and stick it firmly to the top of your work table with about 2 cm hanging loosely over the table’s edge.

a. Use a finger to rub the tape against the tabletop so it is well stuck and charged. b. Pull up on the tape’s loose end and carefully lift the tape away from the table top.

c. Touching only the ends of the tape with your fingers, align the tape parallel to the

table surface with the sticky side up. Slowly move the non-sticky side of the tape just barely above the tiny scraps of paper. Record your observations.

2. Charge the tape as in Step 1.

a. Without touching the tape anywhere but on the ends with your fingertips, gently

pull the strip up and then reaffix it with only 2 cm stuck to the top surface and the rest hanging vertically over the table's edge. The non-sticky side faces outward.

b. Next, charge a similar length of tape and gently remove it with your fingertips.

c. Slowly bring the non-sticky side of the second tape close to the non-sticky side of

the suspended length of tape. The non-sticky sides should face each other.

d. What do you observe when the strips are far apart?

e. What do you observe when the strips are brought close together? Record your observations and why you think this happened.

3. Suspend the second length of tape a few centimeters away from the first.

a. Charge a third piece of tape and gently remove it with your fingertips.

b. Slowly bring the non-sticky side of the third tape close to the non-sticky side of the first suspended length of tape and then the second length of tape.

c. Observe the reactions between this tape and the two suspended tapes. Again record your observations and possible explanation for the reactions.

d. Charge the plastic ruler by rubbing it with a cloth and then bring it close to the

suspended tape strips.

e. Observe how the strips react with the charged ruler. Record your observations and ideas what you think has happened.

4. Discard the previous strips of tape. Charge a new ~15 cm length and suspend it.

o. Stick another ~15-cm strip of tape down on your desktop.

p. Stick a third piece on top of the second and rub them well against the desktop.

q. Peel this pair, still stuck together, away from your desk.

r. Run the non-sticky side of the duo over your lips or a water pipe.

s. Bring the pair close to the suspended strip.

t. Record your observations and opinions about what you observe.

5. Carefully and slowly pull apart the two tape strips from Step 4 above.

a. What happens as you separate these?

b. Hold one tape in each hand and slowly bring the two non-sticky sides close to each other.

c. Next bring the tapes, one at a time, near the suspended strip.

d. Observe and record what happens in each case.

e. Suspend each of the three strips from Step 4 above. Bring a charged ruler close

to each strip. Observe and record what happens in each case.

f. Tear scrap paper into a strip approximately the same width and length of the hanging tape strips. Bring the uncharged paper strip close to each of the hanging tape strips and record your observations.

Questions:

A. Why do you think the charged ruler affected the original suspended strip as it did?

B. What happened when you brought the two separated tapes close to each other?

What explanations can you offer for this?

C. How many types of charge did you work with in this exercise? How do you know?

D. If a third type of charge existed, how would it affect the two oppositely charged strips in this exercise?

E. Why do you think the charged ruler affected the two suspended tapes as it did?

F. How would you explain the attraction or repulsion between each of the suspended tapes and the uncharged paper strip?

G. How would you explain the fact that a charged ruler can attract an uncharged object

like the paper bits, salt and pepper?

Part III:

1. Suspend a Styrofoam® cup with a piece of thread, and rub it vigorously with fur.

2. Rub the second Styrofoam® cup with fur and bring it near the suspended cup. What happens? Describe the behavior of the suspended cup.

3. Recharge the second Styrofoam® cup by rubbing it with the fur. Run the cup lightly

over the back of your arm. What do you observe and/or feel happening?

4. Bring the Styrofoam® cup close to another person's hair. What do you observe? What conclusions can you make regarding charged Styrofoam®?

Part IV:

1. Rub an inflated balloon with the fur and try to stick it to different surfaces. What can you make the balloon stick to? Does it stick better to some surfaces? Why?

2. Rub an inflated balloon against your hair and then try to stick it to the same objects

you used for Step 1. Does rubbing with fur work as well as, better than, or worse than if you rub the balloon against your hair instead?

3. Bring the charged balloon close to the paper scraps from Part II. How does the

rubbed balloon affect the paper bits?

4. After rubbing a balloon with fur, bring the balloon near but NOT touching a very thin stream of water. Record your observations. Does the same thing happen when other charged objects are brought near the water? Try some and record the results. Be careful to NOT get the fur wet!

Part V:

1. Wad a small amount of aluminum foil into a ball about 3 cm in diameter and suspend it from a piece of thread about 30 cm long.

a. Tape the loose end of the thread to a support so that the ball hangs freely at a

reachable height which is at least 15 cm above any surface and 30 cm from any side obstructions.

b. Neutralize the ball by touching it with your finger and then charge a plastic ruler

by rubbing it with fur.

c. Steady the ball, and then bring the charged ruler close to but NOT TOUCHING the

ball. If the ball accidentally touches the ruler, neutralize the ball and try again.

d. Describe what you observed. Why does this happen? Use appropriate diagrams to help you explain.

2. Neutralize and steady the aluminum foil ball.

1. Charge the plastic ruler and again bring it close to but NOT TOUCHING the ball.

Then gently and quickly touch the ball with your finger on the side opposite the ruler.

2. Now bring the charged ruler very close, but still NOT TOUCHING the ball and

observe for a few seconds. What do you observe?

3. What does this observation mean in terms of the charge on the ball and the ruler?

4. Exactly what was the purpose of touching the ball while the ruler was nearby?

5. Draw appropriate diagrams to support your verbal descriptions. You should draw

more than one illustrative diagram for this section. 3. Neutralize the aluminum foil ball. Bring the charged ruler close enough to the ball so

that the ball gently and quickly touches it only once. Describe what you observe just after they touch. Explain why this happens in both words and appropriate diagrams.

Electric Fields

Experiment Summary:

Students will have the opportunity to learn about electric fields and determine the shape of equal potential lines surrounding charged objects.

Students will learn how to use a digital multimeter to measure electric fields created by a battery and map out the fields. �

�

Peter Jeschofnig, Ph.D. Version 09.2.01

Review the safety materials and wear goggles when working with chemicals. Read the entire exercise before you begin. Take time to organize the materials you will need and set

aside a safe work space in which to complete the exercise.

Objectives

x To experimentally investigate the concept of the electric field, and

x To determine the shape of equal potential lines surrounding charged objects.

Materials

Materials From: Label or Box/Bag: Qty Item Description:

Student Provides 1 Color pen or pencil From LabPaq 3 Batteries 1.5V, AA 4 Cables, jumper - banded 2 Graph paper 1 Tray-diss-plastic, clear 1 Multimeter-Digital Miscellaneous Supplies Bag 2 Nut, Metal 1 Washer 1 Salt Packets

Discussion and Review

An electric field’s intensity is defined as the electrical force per unit of charge, or E = F/q. Theoretically, an electric field is determined by using a positive test charge, q, and determining the force acting on it at every point in space. The direction of the field is found by the laws of vectors and the rules that tell you whether a force is attractive or repulsive. Since a free charge moves in an electric field by the action of the electric force, then work (W = Fd = Force times distance) is done by the field in moving charges from one point to another, such as from point A to point B. To move a positive charge from point B to point A against the electric field would require work supplied by an external force. The ratio of the work done, W, to the charge, q, in moving the charge between two points in an electric field is called the potential difference, Vab, between the points. Thus, Vab = W/q. If a charge is moved along a path at right angles so it is perpendicular to the field lines, there is no work done (W = 0) since there is no force component along that path. No work means no potential difference from point to point. Hence, the potential is constant along paths that are perpendicular to field lines. Such paths are called equipotentials. An electric field set up by charges can be "mapped" by determining the equipotential lines - equipotential surfaces in three dimensions - that exist in the region around the charges. Potential difference is easily read by a voltmeter, whereas the measurement of forces would present numerous experimental problems. DIGITAL MULTIMETER OPERATING INSTRUCTIONS: It is important that you read and understand the following instructions plus pay attention to the special cautions noted below or you could damage the multimeter and/or blow a fuse. Replacement fuses can be purchased at electronics stores. Direct any use specific questions to your course instructor. Digital Multimeters (DMM): A digital multimeter, DMM, is used in this and future experiments. It is important to familiarize yourself with the DMM’s operations now so you can take accurate measurements without damaging the meter. Multimeters are so called because they can measure three different qualities of a circuit. These qualities, their symbols, and their basic units of measurement are summarized in the table below: A different model of multimeter may be included in your LabPaqs, so generic DMM operating instruction as well as those specific to the Cen-Tech DMM are included here. Regardless of the DMM model in your LabPaq, you should thoroughly review its accompanying instructions in addition to the ones discussed below.

Symbol: V I and A R Measurement:

Units: Voltage

Volt Current Ampere

Resistance Ohm or �

Lead Wires (Cen-Tech): Lead wires must be connected correctly. The black lead is normally connected to the bottom terminal labeled COM for common which is also called ground. The red lead must be connected to the corresponding terminal for what you want to measure. For voltage, resistance and low DC current, use the middle terminal labeled V�mA. (V=volts, �=resistance in ohms, mA=milli-ampere). For DC current above 200mA, use the top 10ADC terminal. Detailed instructions as to when to use the middle vs. the upper terminal for the red lead are given for each of the specific measurement instructions below. Always read instructions carefully to be certain you plug the leads into the correct terminals for the appropriate quantity of what you want to measure. Basic Operations: The CEN-TECH digital multimeter (DMM) has a circular range dial knob and a separate On-OFF switch. The central dial

must be in the appropriate position for the operation you want to perform. The dial has the following positions starting with DCV and going clockwise:

x DCV - To measure DC voltage: settings 200mV, 2000mV(2V); 20V, 200V, 1000V x ACV To measure AC voltage: settings: 200 & 750V

x 1.5V(4.0mA) & 9V(25mA) - To measure battery charge for 1.5V & 9V batteries only

x DCA – To measure DC current – settings: 200µA, 2000 µA (=2mA); 20mA, and

200mA (= 0.2A) x 10A – To measure DC current greater than 200mA x hFE – To measure transistor values x To measure diode voltage drop x Ƙ - To measure resistance – settings: 200 Ƙ, 2000 Ƙ, 20K Ƙ, 200K Ƙ, 2000K Ƙ

Use of the DMM as a DC Voltmeter: To measure voltage (V) difference, the DMM leads are connected to the ends of the component(s) while the circuit is energized. Connect the positive red lead close to the + end of the battery and the negative black lead to the – end of the battery.

1. Turn the center dial to the appropriate DCV setting. The setting selected must be higher than the quantity of expected volts or the DMM fuse may blow out! For a 1.5V system, set at the 2V setting, for a 9V system set it at the 20V setting, etc. If you do not know the range of your value, start with the highest range and switch down to lower ranges as necessary. This will prevent damage to the meter that might occur if you select a range too low for the voltage you are measuring.

2. Plug the red cable lead into the center V�mA jack. Plug the black cable lead into the

bottom COM jack.

3. Switch the multimeter on via the ON-OFF switch.

4. To measure the voltage, carefully touch the appropriate points in the circuit with the tips of the multimeter’s probes.

5. Read and record the measurement.

6. When testing is complete, turn off the DMM; remove the test leads, and store your

DMM. Use of the DMM as an Ohmmeter: To measure the resistance (R) of a component such as a resistor, the component must be disconnected from the circuit. You will get an incorrect measurement if the component is in the circuit. You may also damage the meter if the component is in the circuit and the circuit is also energized. This is the only DMM reading that requires the circuit to be disconnected. You may measure circuit resistance up to 2000K ohms.

1. Turn the range selector switch to an appropriate � setting higher than the expected ohms. For a 100 Ƙ resistor, set the range switch on the 2000 Ƙ setting, etc.

2. Plug the red cable lead into the center V�mA jack. Plug the black cable lead into the

bottom COM jack.

3. Switch on the multimeter via the On-OFF switch.

4. Touch the test leads together. The meter should read “0” �, (Ohms).

5. Carefully touch the appropriate points in the circuit with the tips of the probes to measure the resistance.

6. Read measurement.

7. If the reading is “1”, set the range selector switch to the next higher Ohm (�) position.

8. When testing is complete, turn off the DMM; remove the test leads and store your

DMM. Use of the DMM as an Ammeter (Current meter): To measure current (I) the leads of the meter must be connected into the circuit. Wherever the meter is inserted into the circuit make certain that the red lead is closest to the + end of the battery along the circuit and that the black lead is closest to - end of the battery. It is very important that the multimeter be used in series as part of the circuit when measuring current instead of in parallel outside of the circuit as when measuring voltage differences. Improper use may damage the meter and blow the fuse making the multimeter inoperable.

1. Turn the range Selector Switch to the 10 A (amperes) position. Always start with the highest range if the amperage is unknown.

2. Plug the red cable lead into the top10 A jack. Plug the black cable lead into the

bottom COM jack.

3. Switch the multimeter on via the On-OFF switch.

4. Insert the multimeter in series with the circuit to be tested.

5. Read measurement. If the reading is less than .2 A switch the red cable lead to the center V�mA jack and set the range selector switch to the 200mA.

6. Read and record measurement. If you need a current reading in Amps instead of

milliAmperes, simply divide the mA reading by 1000.

7. When testing is complete, turn off the DMM; remove the test leads and store your DMM.

Here is an example of how easily you can blow a fuse if your DMM is used incorrectly. Assume you started in the 200mA (0.2A) position and used the DMM as a current meter for a circuit with a 1.5V battery and a 1ohm resistor; you would blow its fuse immediately! Ohm’s law, V = IR, is also stated as I = V/R. Thus I = 1.5V/1Ƙ = 1.5A or 1,500 mA. This is 7.5 times the limit of the 0.2A setting. For this example circuit you would need to use the 10A setting.

Always turn off your DMM when you have completed your measurements by moving the switch to the “off” position. Otherwise the DMM battery will be used up prematurely and have to be replaced.

Maintenance: x Remove battery if not in use for long periods. x Store unit in dry location x Other than the battery and the fuse, this DMM has no replaceable parts. x Repairs should be done by a qualified technician.

Battery/fuse Replacement:

x Remove the test leads form the multimeter x Turn the unit over and remove both screws with Philips screwdriver. x Remove the back cover x Remove the battery or fuse and replace with a new 9V battery or 250mA fast-acting

fuse. x Replace cover and retighten screws.

Your DMM may also be used to make AC Voltage Measurements; Transistor (hFE) measurements, battery charge measurements, and diode measurements. However, these measurements will not be used in any of the physics experiments in this LabPaq.

Exercise 1

PROCEDURE:

1. Place the sheet of graph paper on a table and center the clear tray over the grid.

2. Attach the end of each jumper cable to a metal nut by clamping the free alligator clip onto it as shown in the photo at right.

3. Place the two metal nut conductors in opposite ends of

the clear tray. They should be approximately centered and about 2.5 cm away from the ends of the tray.

4. Position the battery holder with a 1.5V battery outside of and slightly away from the

tray so it cannot get wet. Attach the jumper cables from the two conductors to the battery holder, one to the positive terminal and the other to the negative terminal.

5. Fill the tray with sufficient water to just barely cover the conductors.

6. Set your DMM to measure voltage by moving the dial to DCV, and its range to a

voltage equal to or higher than that of the 1.5V battery.

7. Attach the negative black lead from the DMM to the negative terminal of the battery holder.

8. Attach a jumper cable to the positive red lead that comes from the DMM. To the

other end of the jumper cable attach the washer. See photo below.

9. With the DMM’s positive red lead, touch each of the conductors in the tray and record your findings.

a. Touching the negative conductor in the tray should result in a zero volt reading, b. Touching the positive conductor should result in a reading that is the same as the

battery output, and

c. Touching a distance halfway between the conductors should record a voltage equal to approximately one-half the voltage of the battery. If it does not, stir a few grains of salt into the water in the tray.

10. Using the second sheet of graph paper, draw the conductors’ locations and label

them with the voltage readings of your voltmeter.

11. Place the positive red lead of the DMM in the water again and note the voltage reading. Move the lead around in such a way that the voltage reading is kept at the same value. How far does this path go? Sketch this pattern on your graph paper and label the line with the voltage you chose.

12. Move the positive lead along additional voltage value paths and similarly sketch their

patterns on the graph paper until you have well mapped out the area between and around the conductors.

13. With a color pen or pencil draw a point any place on your map to represent a

moveable positive charge. Predict the path it would take by drawing a line with your colored pen or pencil.

Note: Your results will look different from the sample at left since you will use a rectangular dish, place your conductors in different positions, and use a 1.5V battery, but it still illustrates the concept of electric field mapping.

Optional: If time permits, repeat this experiment with differently shaped conductors and compare their electric field maps. Questions: A. What generalizations can you make from this exploration? B. Where would a positive test charge have the least potential energy? C. How much energy must you add to the system to move 1 electron 1 m in a direction

along one of the equal potential lines? D. If lightning strikes a tree 20 m away would it be better to stand facing the tree, your back

to the tree, or your side to the tree? Assume your feet are a comfortable shoulder width apart. Explain your answer.

Introduction to Electrical Circuits

�

Peter Jeschofnig, Ph.D. Version 09.1.04

Review the safety materials and wear goggles when working with chemicals. Read the entire exercise before beginning. Take time to organize the materials needed and set

aside a safe work space in which to complete the exercise.

Experiment Summary:

Students will have the opportunity to understand the principles of an electric circuit. They will then explore how to use the various functions of a digital

multimeter, including ammeter, voltmeter, and ohmmeter. They will learn how to draw and read circuit diagrams, read the codes on resistors, and assemble

simple circuits following schematic diagrams.�

Objectives

x To build and understand the principles of a simple electric circuit, and x To learn to use the various functions of a digital multimeter (DMM),

including ammeter, voltmeter, and ohmmeter.

Materials

Materials From: Label or Box/Bag: Qty Item Description:

Student Provides 1 Computer with spreadsheet software From LabPaq 3 Batteries 1.5V, AA 3 Battery holders 5 Cables, jumper - banded 1 Multimeter-Digital 1 100 Ƙ Resistor

Discussion and Review

Reading and understanding a circuit diagram and then building an electric circuit from it is a skill similar to reading a construction blue print. In this laboratory exercise, we’ll become familiar with the basic terms and symbols needed to build electric circuits. Some of the most common symbols used in the circuit diagrams you will be using are shown below. Name Symbol(s) Example

DC Power (Battery) VDC

Flashlight Batteries

AC Power, VAC

Wall Power Outlet

Resistor, R

Heating Element, lamp, etc.

Lamp

Light Bulb

On/Off Switch

Light Switch

Wire Any Wire

Capacitor

Current Storage

Diode

Digital Thermometer

Inductor

Wire Coil

Meter Symbols: We will be using a digital multimeter (DMM) which can be used as a voltmeter to measure voltage, an ammeter to measure current, and an ohmmeter to measure resistance. The symbols for individual meters are: Voltmeter to measure voltage Ammeter to measure current

�

Circuit Drawings: The illustrations in this manual reflect the way circuits are traditionally drawn to show how components are connected. Your actual circuits will not look as nice and neat as the diagrams since connecting cables will not be in perfectly straight lines and angles. At right is a photo of how an

actual circuit might look. The left photo shows how two sets of jumper cables are connected to one resister in parallel.

Reading and understanding the color codes of resistors: To calculate the value of a resistor, use the color-coded stripes on the resistor and the following procedures, plus the table on the following page:

1. Turn the resistor so that the gold or silver stripe is at the right end of the resistor. 2. Look at the color of the first two stripes on the left end. These correspond to the first

two digits of the resistor value. Use the following table to determine the first two digits.

3. Look at the third stripe from the left. This corresponds to a multiplication value. Find

the value using the table below. Multiply the two-digit number from Step 2 by the number from Step 3. This is the value of the resistor in ohms.

4. The fourth band indicates the tolerance of the resistor. Tolerance is the precision of

the resistor and it is given as a percentage. For example, a 200Ƙ resistor with a silver band indicates a tolerance of ±10% . It will have a value within 10% of 200Ƙ, between 200 - 20 = 180Ƙ and 200 + 20 = 220Ƙ.

A gold band means a tolerance of ± 5% from the value given by the stripes. A silver band indicates a tolerance of ± 10%; red means ± 2%; brown means ± 1%. If no fourth band is shown the tolerance is ±20%.

�

Resistor Color Codes: Read the code with gold or silver stripe on right end.

With a little practice you soon will be able to quickly determine the value of a resistor by just a glance at the color -coded stripes. Assume you are given a resistor whose stripes are colored from left to right as brown, black, orange, and gold. To find the resistance value: ¾ Turn the resister to where its gold stripe is on the right. ¾ The first stripe on the left is brown, which has a value of 1. The second stripe

from the left is black, which has a value of 0. Since the first two digits of the resistance value are 1 and 0, this means this value is 10.

¾ The third stripe is orange, which means to multiply the previous value by 1,000. ¾ Thus the value of the resistance 10 time 1000 or 10 x 1000 = 10,000 ohms.

10,000 ohms can also be expressed as 10 kilohms or 10 k Ƙ ohms. ¾ The stripe in Step 1 is gold, i.e. ±5% tolerance; this means the actual value of the

resistor will be somewhere between 9,500Ƙ and 10,500Ƙ. DIGITAL MULTIMETER OPERATING INSTRUCTIONS: It is important that you read and understand the following instructions plus pay attention to the special cautions noted below or you could damage the multimeter and/or blow a fuse. Replacement fuses can be purchased at electronics stores. Direct any use specific questions to your course instructor.

�

Digital Multimeters (DMM): A digital multimeter, DMM, is used in this and future experiments. It is important to familiarize yourself with the DMM’s operations now so you can take accurate measurements without damaging the meter. Multimeters are so called because they can measure three different qualities of a circuit. These qualities, their symbols, and their basic units of measurement are summarized in the table below: A different model of multimeter may be included in your LabPaqs, so generic DMM operating instruction as well as those specific to the Cen-Tech DMM are included here. Regardless of the DMM model in your LabPaq, you should thoroughly review its accompanying instructions in addition to the ones discussed below. Lead Wires (Cen-Tech): Lead wires must be connected correctly. The black lead is normally connected to the bottom terminal labeled COM for common which is also called ground. The red lead must be connected to the corresponding terminal for what you want to measure. For voltage, resistance and low DC current, use the middle terminal labeled V�mA. (V=volts, �=resistance in ohms, mA=milli-ampere). For DC current above 200mA, use the top 10ADC terminal. Detailed instructions as to when to use the middle vs. the upper terminal for the red lead are given for each of the specific measurement instructions below. Always read instructions carefully to be certain you plug the leads into the correct terminals for the appropriate quantity of what you want to measure. Basic Operations: The CEN-TECH digital multimeter (DMM) has a circular range dial knob and a separate On-OFF switch. The central dial must be in the appropriate position for the operation you want to perform. The dial has the following positions starting with DCV and going clockwise:

x DCV - To measure DC voltage: settings 200mV, 2000mV(2V); 20V, 200V, 1000V x ACV To measure AC voltage: settings: 200 & 750V

x 1.5V(4.0mA) & 9V(25mA) - To measure battery charge for 1.5V & 9V batteries only

x DCA – To measure DC current – settings: 200µA, 2000 µA (=2mA); 20mA, and 200mA (= 0.2A)

Symbol: V I and A R Measurement:

Units: Voltage

Volt Current Ampere

Resistance Ohm or �

�

x 10A – To measure DC current greater than 200mA x hFE – To measure transistor values x To measure diode voltage drop x Ƙ - To measure resistance – settings: 200 Ƙ, 2000 Ƙ, 20K Ƙ, 200K Ƙ, 2000K Ƙ

2. Plug the red cable lead into the center V�mA jack. Plug the black cable lead into the

bottom COM jack.

3. Switch the multimeter on via the ON-OFF switch.

4. To measure the voltage, carefully touch the appropriate points in the circuit with the tips of the multimeter’s probes.

5. Read and record the measurement.

6. When testing is complete, turn off the DMM; remove the test leads, and store your

1. Turn the range selector switch to an appropriate � setting higher than the expected ohms. For a 100 Ƙ resistor, set the range switch on the 2000 Ƙ setting, etc.

2. Plug the red cable lead into the center V�mA jack. Plug the black cable lead into the

bottom COM jack.

�

3. Switch on the multimeter via the On-OFF switch.

4. Touch the test leads together. The meter should read “0” �, (Ohms).

5. Carefully touch the appropriate points in the circuit with the tips of the probes to measure the resistance.

6. Read measurement.

7. If the reading is “1”, set the range selector switch to the next higher Ohm (�)

position.

8. When testing is complete, turn off the DMM; remove the test leads and store your DMM.

Use of the DMM as an Ammeter (Current meter): To measure current (I) the leads of the meter must be connected into the circuit. Wherever the meter is inserted into the circuit make certain that the red lead is closest to the + end of the battery along the circuit and that the black lead is closest to - end of the battery. It is very important that the multimeter be used in series as part of the circuit when measuring current instead of in parallel outside of the circuit as when measuring voltage differences. Improper use may damage the meter and blow the fuse making the multimeter inoperable.

1. Turn the range Selector Switch to the 10 A (amperes) position. Always start with the highest range if the amperage is unknown.

2. Plug the red cable lead into the top10 A jack. Plug the black cable lead into the

bottom COM jack.

3. Switch the multimeter on via the On-OFF switch.

4. Insert the multimeter in series with the circuit to be tested.

5. Read measurement. If the reading is less than .2 A switch the red cable lead to the center V�mA jack and set the range selector switch to the 200mA.

6. Read and record measurement. If you need a current reading in Amps instead of

milliAmperes, simply divide the mA reading by 1000.

7. When testing is complete, turn off the DMM; remove the test leads and store your DMM.

�

Ohm’s law, V = IR, is also stated as I = V/R. Thus I = 1.5V/1Ƙ = 1.5A or 1,500 mA. This is 7.5 times the limit of the 0.2A setting. For this example circuit you would need to use the 10A setting.

Always turn off your DMM when you have completed your measurements by moving the switch to the “off” position. Otherwise the DMM battery will be used up prematurely and have to be replaced. Maintenance:

x Remove battery if not in use for long periods. x Store unit in dry location x Other than the battery and the fuse, this DMM has no replaceable parts. x Repairs should be done by a qualified technician.

Battery/fuse Replacement:

fuse. x Replace cover and retighten screws.

PROCEDURE: Set up the following data table to use for these experiments:

DATA TABLE: Resistance based on color bands: ____Ƙ; % uncertainty ____ (from color band) DMM-Measured Resistance ______ Ƙ Measured V (V) Measured Current (A) Calculated R = V/I 1.5V battery 3V battery 4.5V battery

Part 1: Before assembling the following circuits, set the DMM as an ohmmeter. Slide the function switch to Ƙ and the dial range to 2 kƘ. Check the resistance of the resistor by touching the two DMM leads to the two wires extending from each side of the resistor. Record this value. 1. Your first circuit will consist of a 1.5V battery in its holder and a 100-ohm resistor. You

will use 3 separate jumper cables to set up the circuit as shown below in the illustration below. a. Set the DMM as an ammeter. Slide

the function switch to A and the dial range to mA.

b. Connect the first jumper cable (1) to

the negative end of the battery holder and to the 100 Ƙ resistor. Do this by simply opening the jaw of an alligator clip at one end of a jumper cable and firmly clasping that jaw around the metal tail, wire, or extender of the item to be connected into the circuit. Metal must touch metal in all connections.

c. Connect the second jumper cable (2) to the other end of the resistor and the black

lead of the DMM.

d. Connect the third jumper cable to (3) the red lead of the DMM and the positive end of the battery holder.

e. Remember that it is very important when measuring current to use the multimeter in

series, which means that it is inside and part of the circuit as shown above. When measuring voltage differences the meter must be in parallel, which means it is outside of the circuit as shown in B. below. If you confuse these procedures you will blow out the DMM’s fuse!

f. Take the mA reading and record it in the data table.

g. You measured the current at only one point, call it point “P.” Is the current the same everywhere in a simple circuit like this? To find out, rearrange the jumper cables and meter to measure the current at a second point, call it point “Q.” Discuss your findings in your conclusions.

2. Remove the DMM from the above circuit and close the circuit by connecting the jumper

cables’ alligator clips that previously connected the DMM within the circuit.

a. Set the DMM as a voltmeter. Slide function switch to V , and the range dial to 2V. b. Set up the DMM as a voltmeter, which requires that it be parallel to and outside of

the main circuit as shown in the next illustration. Touch the DMM’s positive red lead to the jumper cable connection at the positive end of the battery holder (A) and touch the DMM’s negative black lead to the jumper cable connection at the negative end of the battery holder (B). Now take the V reading between points A and B and record in the data table.

c. Reverse the DMM leads at points A and B by

moving the black lead to point A and the red lead to point B. Observe, then record and explain your observation.

d. Reposition the voltmeter to take a voltage reading between A and C, first with the

leads in one position and then with the leads reversed. Record and explain these voltage readings.

e. Reposition the voltmeter to take a voltage reading between C and D, first with the

leads in one position and then with the leads reversed. Record and explain these voltage readings. Note: You will want to thoroughly discuss these observations in your lab report summary.

Part 2: 1. Again set up the DMM as an ammeter within a

circuit as in the previous Part 1, Step 1.a., but this time you will add a second 1.5V battery in series with the first 1.5V battery as shown at right.

a. To do this you will simply insert a second battery holder and jumper cable next to the

original battery holder so that two batteries are in the circuit between the ammeter and the resister.

b. When the circuit is again complete, take the mA reading and record in the data table.

2. Remove the DMM from the circuit shown in Part 2, Step 1 above and close that circuit.

a. Set up the DMM as a voltmeter parallel to the circuit with the leads attached around both batteries as shown at right.

b. Set the function switch on V and the

range dial to 20V. c. Take a V reading and record in the data

table. Part 3: 1. Again set up the DMM as an ammeter as in Part 2, Step 1, but this time add a third 1.5V

battery in series with the other two 1.5V batteries.

a. To do this you will simply insert a third battery holder and jumper cable next to the original battery holder so that three batteries are now in the circuit between the ammeter and the resister.

b. When the circuit is again complete, take the mA reading and record in the data table.

2. Remove the DMM from the three batteries and the resistor connected in Part 3, Step 1,

above and close that circuit.

a. Set up the DMM as a voltmeter parallel to the circuit with the leads attached around all three batteries.

b. Set the function switch to V and the range dial to 20V. c. Take a V reading and record in the data table.

Calculations and Graphing: For each of the three previous procedures calculate the resistance from the measured current and voltage: R = V/I. 1. Use an xy scatter graph to graph voltage on the y-axis versus current on the x-axis. 2. Use the linear fit trendline function of Excel® to add the slope of the line to the graph. 3. What is the significance of the slope? 4. How do the graph and the slope of the line relate to Ohm’s law? 5. Can this series of experiments be considered a verification of Ohm’s law? Why or why

not? Save the 100 Ƙ resistor, it may be used in another experiment!

Resistors in Series and Parallel

Experiment Summary:

Students will have the opportunity to learn how to use resistors in parallel

and in series and how to calculate the total resistance of an electric current. They will perform a series of experiments with different configurations of

resistors, measuring the voltage and current across each resistor. Students will use Ohms Law to determine calculated values and compare them with

actual readings taken with the digital multimeter.�

�

Peter Jeschofnig, Ph.D. Version 09.1.02

Review the safety materials and wear goggles when working with chemicals. Read the entire exercise before you begin. Take time to organize the materials you will need and set

aside a safe work space in which to complete the exercise.

Objectives

x To learn how resistors are used in series and in parallel.

Materials

Materials From: Qty Item Description:

From LabPaq 1 Batteries 1.5V, AA 6 Cables, jumper - banded 1 Battery Holder 1 Multimeter-Digital Resistor Bag 1 Resistor Set (4)-PK

Discussion and Review

A resistor is an electrical component that limits or regulates the flow of electrical current in an electronic circuit. Resistors can also be used to provide a specific voltage for an active device such as a transistor. All other factors being equal, in a direct-current (DC) circuit the current through a resistor is inversely proportional to its resistance and directly proportional to the voltage across it. This is the well-known Ohm's law, V=IR. Resistors can be fabricated in a variety of ways. The most common type in electronic devices and systems is the carbon composition resistor. Fine granulated carbon graphite is mixed with clay and hardened. The resistance depends on the proportion of carbon to clay - the higher this ratio, the lower the resistance. Another type of resistor is made from winding Nichrome or similar wire on an insulating form. This component, called a wire wound resistor, is able to handle higher currents than a carbon-composition resistor of the same physical size. However, because the wire is wound into a coil the component acts as an inductor as well as exhibiting resistance. This does not affect performance in DC circuits, but it can have an adverse effect in AC circuits because inductance renders the device sensitive to changes in frequency. In experiment Introduction to Electrical Circuits, you learned how the color-coded stripes of an individual resistor are read and calculated to determine its value strength. Review those procedures now if you need reinforcement. To effectively work with resistors, it is often necessary to combine resistors of different values to form new resistance values. As you will learn in this experiment, new resistance values can be obtained by combining resistors in series, in parallel, or in both. Resistors in Series Connection: When two resistors are connected in series, as shown at right, the resistance equivalent, Req, is the sum of the two resistors: Req = R1 + R2. If R1 = 500 Ƙ and R2 = 250 Ƙ, then the resistance between points A and B is: Req = R1 + R2 = 500 Ƙ + 250 Ƙ = 750 Ƙ. Resistors in Parallel Connection: When two or more resistors are connected in parallel as shown at right, the new resistance is smaller than the value of the individual resistors. The inverse of the resistance equivalent is equal to the sum of the inverse values of the resistors in parallel. Using the values from our example above, the new resistance, Req, between points A and B is now calculated as: 1/Req= 1 / R1 + 1/ R2. If R1 = 500 Ƙ and R2 = 250 Ƙ then the A to B resistance is: 1/ Req = 1/500 Ƙ + 1/250 Ƙ 1/ Req = .002 Ƙ + .004 Ƙ = .006 Ƙ 1/ Req = .006 Ƙ R = 167 Ƙ

Jumper cables connecting a resistor in parallel ȸ When only two resistors are in parallel, their combined resistance can more simply be calculated as Req = (R1 x R2) / (R1 + R2). If we use the same two resistors from above, R1 = 500 Ƙ and R2 = 250 Ƙ then the A to B resistance is: Req = (500 Ƙ x 250 Ƙ) / (500 Ƙ + 250 Ƙ) = (125,000 Ƙ) / (750 Ƙ) = 167 Ƙ. If R1 = R2 then the new resistance is simply R1/ 2. Do the math to confirm this.

Exercise 1

PROCEDURE: This lab uses a 1.5V battery, which means that some current readings will be very low. You can double or triple these current readings by using a stronger battery. For example, you can connect two or three 1.5V batteries in series for a 3V or 4.5V circuit. A 6V lantern battery can also be used. When using a voltage greater than 1.5 remember to set the voltmeter to the appropriate voltage setting. Part I: Resistors in Series: Set up the following table to record your observations. Remember to properly adjust your DMM for each different measurement required. Data Table 1: Resistors in Series Battery voltage: _____V. Expected current (from V=IR): ______ mA Resistor value (Ƙ)

color code; % variance

R value (Ƙ)

DMM

R value Ƙ) calculated from R=V/I

DMM Current, mA

DMM voltage, V

Calculated voltage, V from V=IR

R1 R2 R3 Req N.A.

1. Use the color code and identify the Ƙ-value of each resistor used in the circuit and record

in the data table. 2. Use the DMM set as an ohmmeter and measure the Ƙ-value of each resistor used in the

circuit and record results in the data table. 3. Connect the three resistors in series. Then without connecting them to a battery

measure their total combined resistance, Req. Record the results in the data table. 4. Build a series circuit as shown at right by using a 1.5V

battery in a holder and three resistors, then connecting them with four jumper cables.

5. Measure the currents in mA through each resistor and record it. Remember, you must insert the DMM in series into the circuit. Also, in a series circuit the current at any point of the circuit is the same at every point of the circuit. Further, when using the equation V=IR, you must convert current to A instead of mA.

6. Measure the voltage across each resistor and record the values. They will NOT be the

same. Record the results in your data table. Note: you will later calculate the resistance of each resistor using Ohm’s law.

Part II: Resistors in Parallel: Set up the following table to record your observations. Remember to properly adjust your DMM for each different measurement required. Data Table 2: Resistors in Parallel Battery voltage: _____V

R value (Ƙ) DMM

DMM Voltage, V DMM Current, mA

Calculated Current, A from V=IR

R1 I1 = I1 = R2 I2 = I2 = R3 I3 = I3 = Req I = I =

1. Connect the three resistors in Parallel as shown at right, using

two jumper cables. Without connecting them to a battery measure the total combined resistance, Req, of the circuit. You may place the DMM leads at any two opposite points in the circuit to make this measurement. For example, you may use A and B, or C and D, or E and F, or even A and D, or A and F, etc., but you may not use A and C, or B and D, etc. Record the result.

Resistors in parallel with R-measuring pointsȸ 2. Build a parallel circuit by using a 1.5V battery in its holder, three

resistors, and a total of 6 jumper cables. The first set of jumper cables will clip to the battery and first resistor’s leads. The second set of jumper cables will clip from the first resistor to the second, and the third set of jumper cables will clip from the second resistor to the third. The numbers in the drawing at right represent connections for each jumper cable.

Resistors in parallel circuit Æ 3. Measure the voltage across each resistor and record the values.

You should remember that the voltage across each resistor is the same for all pairs of resistors and that the equivalent resistance will be the same regardless of where you place your leads, as long as they are opposite the other as

described in Step 2A above. Record all results in the data table. 4. Measure the current through each resistor by taking

measurements only at the specific points indicated as shown in the drawing at left. These will not be the same unless the resistors are the same. Record all results in the data table.

Å Current meter locations

Part III: Resistors Combined in Series and Parallel: Set up the following table to record your observations. Remember to properly adjust your DMM for each different measurement required. Data Table 3: (Resistors in Combination) Battery voltage: _____V.

R Value (Ƙ) DMM

DMM Voltage, V DMM Current, A Calculated Current, A from V=IR

R1 R2 R3 R2 + R3 Parallel

R1 + R2 + R3

Req 1. Set up the resistors in combination but without a

battery as shown in the illustration to the right. Measure the parallel resistance between E and F or C and D, and then measure the total resistance (Req) of the circuit between A and D or A and F. Record all the result.

2. Build a circuit that includes a combination of series and parallel resisters as shown in

the illustration below by using a 1.5V battery in its holder, three resistors, and five jumper cables.

3. Measure the voltage across each resistor and record the values. The voltage across each

resistor will NOT be the same for all. Record all values.

ȸ Resistors in series and parallel circuit 4. Measure the current through each resistor. The current through each resistor will NOT be

the same, either. Record all values.

Part IV: Calculations: Now using the equation V = IR, calculate the expected values of the currents and voltages of all resistors tested above. Create new tables for these results. Use only the voltage supplied by the 1.5V battery and the resistance values for the three resistors. When using the current in calculations (V=IR), you must convert mA to A by dividing the mA value by 1000. For example, in a circuit with a 1.5V battery and a 500 Ƙ resistor, what is the expected current? V = IR or I = V/R = 1.5/500 = 0.003A or 3 mA. Series Resistors: Req = R1 + R2 + R3. First, find the equivalent resistance Req for all resistors involved. Then find the current through Req. The voltage for each resistor can be calculated using the resistor value, current and the equation V=IR. Parallel Resistors: 1/Req = 1/R1 + 1/R2 + 1/R3. This method of calculation can be used for calculating any number of individual resistances connected together within a single parallel network. If however, there are only two individual resistors in parallel then a much simpler and quicker formula can be used to find the total resistance value, and this is given as:

Req = R1 x R2/(R1 + R2)

Using the measured voltage, calculate the currents for each resistor. The total circuit current, I, is simply the sum of the currents through each resistor I1, I2, and I3. Combination: First, find the equivalent resistance R23 of the parallel resistors, then the equivalent resistance Req for the entire circuit. Next, find the current through Req, and this should be the current through R1 and R23. Using that current, find voltages across R1 and R23.Then you can find the current through R2 and R3. Lab Report: Summarize all findings, discrepancies, errors, and the significance of the experiment in your lab report’s conclusions.

Semiconductor Temperature Sensor

Experiment Summary:

Students will have the opportunity to learn about diodes and how to calibrate diodes with a glass thermometer to measure changes in temperature.

Students will learn how to construct an electric thermometer using a silicon diode, a 10K resistor, and a 1.5V battery connected in series. Students will

explore the relationship between voltage and temperature.�

�

Peter Jeschofnig, Ph.D. Version 09.1.01

Review the safety materials and wear goggles when working with chemicals. Read the entire exercise before you begin. Take time to organize the materials you will need and set

aside a safe work space in which to complete the exercise.

Objectives

x To construct an electric thermometer consisting of a silicon diode, 10K : resistor, and 1.5V battery connected in series, and

x To find the voltage vs. temperature relationship of the diode

Materials

Materials From: Qty Item Description: Student Provides 1 Computer and spreadsheet program 1 Desk lamp with exposed light bulb 1 Soldering iron and solder (optional) 1 Tape, clear or masking From LabPaq 1 Thermometer-in-cardboard-tube Dissection Tray 1 Batteries 1.5V, AA 2 Cables, jumper - banded 1 Battery Holder 1 Capacitor, LED, diode, and photocell in bag 1 Multimeter-Digital 1 Resistor Set (4)-PK

Discussion and Review

Diodes are specialized electronic components with two electrodes called the anode and the cathode. Most diodes are made of semiconductor materials such as silicon, germanium, or selenium. The fundamental property of a diode is its tendency to conduct electric current in only one direction. Silicon diodes have a forward voltage drop that is nominally 0.6 VDC at ambient temperature. The voltage drop varies inversely with temperature. As the ambient temperature increases, the voltage drop of the diode decreases slightly. Diodes are ideal for use as temperature probes because they are small, sensitive, and there is a reliable relationship between their electrical characteristics and temperature. Diodes can be calibrated as a temperature sensor for degrees C or F and a resolution of 0.1 deg C is achievable. At room temperature the voltage across the diode should read between 0.45V and 0.6V, depending on battery strength, wire, solder connection, etc. The voltage across a silicon diode changes at approximately – 2 mV/ºC or minus 2 millivolts per degree Celsius. For example, if the voltage across a diode is 0.60V at 25 ºC, then as shown below the voltage would be 0.65V at 0ºC, and 0.45V at 100 0ºC. This experiment will introduce you to the diode which is part of many electronic devices and give you a feel for today’s technology in modern electronics. It will also introduce a calibration procedure that is fairly common in laboratory work. Many laboratory instruments need to be calibrated at regular intervals and calibration procedures always require a standard substance or device against which the instrument to be calibrated is checked. In this case, we will calibrate the diode thermometer against a regular glass thermometer in order to study the relationship between temperature and voltage.

��25ºC�diode�voltage�=��0.60V�� 25ºC�diode�voltage��=��0.60V�� Ͳ25��degrees�x�Ͳ.002�=�0.05V� �+75��degrees�x�Ͳ.002�=�Ͳ0.15V�� 0ºC��diode�voltage��=�0.65V�� 100ºC��diode�voltage�=��0.45V��

Exercise 1

PROCEDURE: 1. Assemble a circuit as shown below. . +anode end - cathode end

a. Attach a jumper cable to the negative end of an empty battery holder and to the negative cathode end of a diode. The wide stripe on a diode indicates its cathode or negative end.

b. Connect one end of a 10K : resistor to the positive anode end of a diode. The end

opposite to the wide stripe is the diode’s anode or positive end.

c. If you have access to a soldering iron, solder the contact between the diode and resistor. If you do not have a soldering iron, twist the ends of the diode and resistor wires together and wrap tape around them to stabilize the connection.

d. Attach a jumper cable to the resistor end that is opposite to the diode connection and

to the positive end of the empty battery holder.

e. Put the battery inside the battery holder to complete the circuit. 2. Touch the black lead of the digital multi-meter (DMM) to the diode’s cathode wire and

the red lead of the DMM to the diode’s anode wire. Secure these connections with a small amount of tape. Turn the DMM to voltage measurements and it will then give you a measurement of the potential difference across the diode.

3. Place the bulb of your thermometer next to the diode and secure it to the diode with a

small piece of tape. This will allow you to measure the external temperature of the diode and relate it to the voltage. Record the temperate and voltage in a data table.

4. Position a desk lamp with a hot light bulb close to the diode/thermometer assembly. 5. As the external temperature of the diode rises, with approximately every 5oC increase

record the exact temperature from the thermometer and the corresponding voltage from the DMM.

6. When the temperature is no longer increasing, stop the experiment and record the final temperature and voltage readings.

7. Using a computer spreadsheet program, graph the voltage vs. temperature using an X-Y

scatter graph. Plot voltage in mV on the y-axis and temperature in oC on the x-axis. Use the trendline function to calculate the slope. Do not try to force the line through the origin (0). Display the slope on your graph.

Creative Challenge: Think about and design a modification of this experiment that allows you to insert the diode in a small beaker or pot of water. You could start with boiling water and lower the temperature by adding ice cubes. Do NOT allow the probes from the multimeter to come in contact with water! Record data and prepare a graph as before. How do the results from the two experimental methods compare?

Capacitance in a Circuit

Experiment Summary:

Students will have the opportunity to learn about capacitors and how they are

used to store electric charges. They will observe and describe the charging and discharging process for a capacitor in a resistor–capacitor circuit.

Students will determine the time constant of the RC circuit and the internal resistance of the digital multimeter used in the experiment. �

�

Peter Jeschofnig, Ph.D. Version 09.1.03

Review the safety materials and wear goggles when working with chemicals. Read the entire exercise before you begin. Take time to organize the materials you will need and set

aside a safe work space in which to complete the exercise.

Objectives

x To observe and describe the charging and discharging process for a capacitor in an RC circuit.

x To show that voltage across a discharging capacitor decreases exponentially with time.

x To determine the time constant (W ) of the RC circuit.

x To determine the internal resistance of the DMM used.

Materials

Materials From: Label or Box/Bag:

Qty Item Description:

Student Provides 1 Stopwatch or watch with second hand 1 Computer with spreadsheet/graphing

program 1 An assistant (optional) From Labpaq 2

2 Batteries 1.5V, AA Battery holders

4 Cables, jumper - banded 1 Multimeter-Digital

Capacitor Bag Capacitor Bag 1 Capacitor Bag-PK (47 uF capacitor) Resistor Bag Resistor Bag 1 100-ohm resistor from Resistor Set (4)-PK

Discussion and Review A capacitor is a relatively simple electronic component with the ability to store electrical charge.

In its simplest form a capacitor is a pair of parallel, conducting plates which are separated by insulating material referred to as dielectric. The capacitance is the measurement of capacitors’ capability to store a charge. It is directly proportional to the plates’ surface area, and inversely proportional to the space between the plates. Another consideration is the dielectric constant of the material between the plates. When a voltage is applied across a capacitor, an amount of charge (Q) is stored by the capacitor. The amount of charge is given by the equation: Q = CV, where Q is the charge in Coulombs; C is the capacitance in Farads; and V is the voltage in Volts across the capacitor. When a DC circuit with a capacitor is closed, an uncharged capacitor will start charging. As the charge on the capacitor increases, the current decreases; and when the capacitor is fully charged, no more current will flow through the circuit. The time it takes for a capacitor to be fully charged can be determined from the following equation:

time constant RCW where W is in seconds, R = resistance in Ƙ C =capacitance in Farad

For example, a 10 uF capacitor in a 1-K ohm resistor circuit will be fully charged in 10 milli- seconds. (1000*10x10-6) = .01 sec = 10 ms The size of a capacitor, its capacity, is measured in farads and one farad, F, equals one Coulomb per volt. However, one farad is a very large quantity and so it is more convenient to work with smaller sizes such as a microfarad which is abbreviated as µF where 1 µF = 10-6 F or a picofarad which is abbreviated as pF where1 pF = 10-12 F. Capacitors have many uses, one of which is to protect circuits from sudden voltage losses. Another use is in computer memories where millions of low capacitance capacitors may be part of integrated circuit chips. Larger capacitors are used in the power supplies of electronic equipment, where they produce steady DC from rectified AC.

A circuit which consists of resistors, capacitors, and a current source (battery) is referred to as a RC circuit. The simplest type of RC is made up of one resistor and one capacitor and is called “first order” RC circuit. RC circuits are extremely useful electric circuits. They are incorporated into equipment as diverse as audio equipment or heart pacemakers. Additionally, they are used for their precise timing and signal filtering abilities. As mentioned above, when an RC circuit is closed, charges build up on the capacitor over a period of time. �During the charging process, the charge and voltage across a capacitor as a function of time is given by,

where the RC time-constant is given by

Notice that the time-constant has units of time. During the discharge process, the charge and voltage across a capacitor decay exponentially according to,

Taking the natural log of the last equation gives

) t

ln(V) ln(Vo W § ·

�¨ ¸ © ¹

The above equation shows that a plot of the natural logarithm of voltage vs. time yields a straight line and the slope of that line is . Note that the time constant can be found experimentally by observing the charging or discharging process. For the charging process, is equal to the time for V(t) to reach

or 63% of its final value. For the discharging process is equal to the time it takes for V(t) to fall to or 37% of its initial value.

As a capacitor is charging, at a time period of 4 the is practically fully charged and the voltage across the capacitor is approximately 99% of its maximum voltage. After a charging

time of 5 the capacitor is fully charged and the voltage across the capacitor is the same as the battery voltage. We can use the following equation to calculate the voltage across a charging capacitor at any time during the charging process:

� V = voltage across the capacitor Vs = source or battery voltage t = time in seconds from the start of the charging process RC = = the time constant Example: The voltage across a 470 µF capacitor in an RC circuit with a 100KƘ resistor and a 3- V battery after 20 sec = 3(1 – e -20/47) = 1.04 V When taking measurements with a digital voltmeter, it is usually assumed that the measurements have no effect on the circuit under study. An ideal voltmeter has an infinite resistance and draws no current from the circuit under study. However, in practice, voltmeters have a very high, but finite, internal resistance, and we will make use of that internal resistance to observe the discharge of an RC circuit.

In this experiment a capacitor first will be placed in series with a resistor and then in series with an LED. The discharge time will be determined and graphed as the capacitor discharges into the internal resistance of the DMM.

Exercise 1

PROCEDURE: Part I:

1. Using 4 jumper cables set up a series circuit with two 1.5V batteries in holders, a 100-ohm resistor, and capacitor. a. Use one jumper cable to connect the two battery holders with batteries in place.

b. Connect a second jumper cable to the black wire of the connected battery holders

with batteries to one of the 100-ohm resistor wires.

c. Connect the third jumper cable to the second wire of the 100-ohm resistor and one of the tails of the capacitor.

d. Connect the forth jumper cable to the second tail of the capacitor and when ready

to start the experiment to the final, unused wire of the second battery holder. This final connection should only be made after the DMM is connected – as shown in step 2.

2. Set the DMM to read as a voltmeter. Using two additional jumper cables connect the

DMM leads to the capacitor: Do this by attaching an alligator clip of one jumper cable to one tail of the capacitor and the other alligator clip to one of the leads of the DMM. Then attach an alligator clip of a second jumper cable to the other tail of the capacitor and attach its second alligator clip to the other lead of the DMM. At this point the capacitor is connected between the two leads of the DMM.

3. Leave the circuit open until ready to observe. Then watch the voltmeter while connecting the last wire to close the circuit. Record the voltage.

4. Observe the voltmeter again after disconnecting a wire from the battery. The capacitor is now discharging through the internal resistance of the DMM. Have an assistant record the voltage every 5 or 10 seconds as it is being read out aloud off the voltmeter. Record the voltage changes until the voltmeter reads zero again.

Note: If there is no assistant, place a watch beside the circuit where it can be seen easily. Disconnect a wire from the circuit and simultaneously begin timing. Remember, the DMM leads must remain attached to the capacitor. Data Table: Time (sec) Voltage Time (sec) Voltage 0 110 10 120 20 130 30 140 40 150 50 160 60 170 70 180 80 190 90 200 100 210 Continue until V=0

5. Use a computer graphing program to draw an xy-scatter graph of the capacitor

voltage on the y-axis vs. time on the x-axis. Since the capacitor will charge very quickly but discharge very slowly, the graph may look similar to the sample graph below.

6. Note: It is a good idea to discharge the capacitor between experiments. To quickly discharge a capacitor, connect the alligator clips from the ends of a wire to the capacitor’s two tails. The capacitor’s tails may also be bent out to where they can be touched simultaneously with the metal stem of an insulated screwdriver.

7. Analyzing the graph: We know that Ƴ is equal to the time it takes for V(t) to fall to 37% of its initial value. Example: If the maximum voltage was 10.0V, 37% of 10.0V = 3.7V If we enter the Y-axis at 3.7 V and draw a horizontal line to the discharge curve, and go down from this intersection to the x-axis time scale, we can read off the value of the time constant, Ƴ in seconds. Figure 1: Sample graph – Voltage vs. Time

In this example, a horizontal line at 3.7 V intersects the discharge curve at ~103 seconds = time constant, Ƴ = ~ 103 seconds. Another, slightly more accurate method is to prepare another graph where the voltage is plotted as “ln V” vs. time. This will produce a straight line graph. Then using the spreadsheet’s capability to add a trend line, we can have Excel calculate the equation of the line. Finally, by taking the negative inverse of the slope we get W .

Figure 2: ln V vs. Time

In this example, the slope of the line is -0.0096; taking the negative inverse gives a W - value of – 1/-.0096 = 104 sec. From W = RC, we can calculate either the value of the resistor or the capacitor. In this case, if we used a 100 µF capacitor, the DMM resistance would be 104/100 x 10-6 = ~ 1 M-�, which is a reasonable value for a low-cost DMM. Questions:

A. What was the voltage across the capacitor when the circuit was first closed?

B. Was the voltage across the capacitor the same as the voltage of the battery? C. What was the voltage across the capacitor when the battery was disconnected?

D. What is the time constant, Ƴ for this circuit?

E. What is the internal resistance of your DMM?

Part II:

1. Set the DMM as an ammeter – 200mA will work best.

2. Refer to the illustration below and use four jumper cables to set up the capacitor, an LED, two batteries in holders, and an ammeter in a series circuit:

a. Use one jumper cable to connect the two battery holders with batteries in place.

b. Connect a second jumper cable to the black wire of the connected battery holders

with batteries to one of the LED contacts.

c. Connect the third jumper cable to the second contact of the LED and one of the tails of the capacitor.

d. Connect the forth jumper cable to the second tail of the capacitor and to the

black lead of the DMM set as an ammeter.

e. When you are ready to observe in this experiment, close the circuit by touching the red lead of the ammeter to the red wire of the connected battery holders.

3. Observe the meter while you touch the DMM lead to the battery and complete the

circuit. Record your observations.

4. You may need to repeat this experiment several times before you realize what is happening. Do not forget to discharge the capacitor after each trial.

Questions:

A. Did the LED light up? Why or why not?

B. What did the ammeter show when the circuit was first closed?

C. What did the ammeter show after a few seconds?

D. How can your observations be explained?

Electric Motor

Experiment Summary:

Students will have the opportunity to simulate a simple electric motor by constructing an armature out of coiled wire. They will use a magnet to cause the armature to spin and will then learn how to reverse the direction of the

spinning motor. �

�

Peter Jeschofnig, Ph.D. Version 09.1.01

Review the safety materials and wear goggles when working with chemicals. Read the entire exercise before you begin. Take time to organize the materials you will need and set

aside a safe work space in which to complete the exercise.

Objectives

x To make a simple electric motor and to investigate how it works.

Materials

Materials From: Qty Item Description: Student Provides 1 Scissors or pliers From LabPaq 1 Batteries 1.5V, AA 2 Cables, jumper - banded 1 Battery Holder 1 Cardboard square, 4-in. Magnet wire bag 1 Magnet Wire-2 piece-PK

1 Magnet bar-PK 2 Paper Clip Large 2 Push Pins 1 Sandpaper - 1" x 1"

PROCEDURE: 1. Cut the length of magnet wire into two 50-cm pieces. 2. Beginning about 2½ cm from one end of a piece of the insulated wire, wrap the wire for

7 to 10 tight and close turns around a AA battery or something similar that will make a coil with a diameter of about 1½ cm. Leave a ~2½-cm tail at the end of your coil.

3. Carefully slip the coil off of the round battery. On opposite sides of the coil, wrap the

beginning and ending wire tails around the coil once or twice and then pull the tails straight out and away from the coil as shown in the illustration at left. It is important that

about 2 cm of wire tail stick out from each side of the coil. The wire knot created around the coil helps to hold it together and the wire tails form an axle around which the coil will rotate. The coil and its built-in axle are called an armature.

4. Take a small piece of sandpaper and sand the coating off of one of the two wire tails beginning at their tips and working inward for only 1 to 1½ cm. Make sure that all of the coating is sanded off all sides from one of the tails. Next, use the sandpaper to strip off only half of the insulation of the other tail. Be very careful that you do not accidentally sand or damage the coil in this process.

(Note: It is very important that the orientation of the exposed wire corresponds to the orientation described here: If the coil is held in the vertical plane, the insulation must be removed from only the top or only the bottom of the secondwire tail.) If you accidentally remove more than half of the insulation, you may use a black permanent marker to color any portion of the wire that was intended to remain insulated (Note: marker doesn't last very well once the armature starts spinning. 5. Next you must open a pair of paper clips and bend them to use as supports for the coil.

a. Open the paper clip to where the large end is perpendicular to the small end and the clip stands steadily on its smaller end as shown at right.

b. Next open out the paperclips’ large end and form it into an

open hook to support the tails from your coil, or more correctly, the arms of your armature. A pair of pliers or scissors is helpful for this task.

c. The hooks of both modified paper clip supports must be the same height.

6. Arrange the paper clip supports on a support base that will not conduct electricity, such

as a small piece of wood or Styrofoam®, or the piece of cardboard supplied in the

LabPaq. The paper clip supports must be spaced in such a way that the sanded wire tails can lie in their open hooks turn freely and securely. Also, the sanded areas of the wire tails must be in contact with the metal of the hooks.

7. When you have appropriately spaced the paper clip supports fasten them to the support

base with two thumbtacks as shown in the illustration. 8. After the paper clip supports are well fastened to your base, position the coil within their

hooks as shown in the illustration. Make certain that the armature can spin evenly and is not lop-sided.

9. Lay the magnet on the support base directly under the coil. 10. Take the two jumper cables and attach one to each connection of the battery holder.

Then attach the other ends the paper clip armature supports. It is best to attach the alligator clips close to the bottom of these paper clip supports to increase their stability and not stress the hooked ends.

11. Spin the armature to start the motor. If all goes well the armature will then continue to

spin and you will have a functioning mini motor! If it does not work correctly, you will need to make adjustments to the magnet position, the supports, and/or the armature to get the motor running smoothly. A second piece of insulated wire is included in your LabPaq should you need it. Keep trying!

For your reference, here is a photo of a motor constructed in a similar but slightly different way. It does not use paper clips for supports and it is certainly not as attractive as the motor you constructed! If you enjoyed this experiment, visit the website listed below for it has instructions on how to build several different electric motors. This photo comes from the website: www.scitoys.com/scitoys/scitoys/electro/electro.html.

Questions:

A. How can you make your motor run in reverse? Make sure to try it.

B. Try making various armatures for your motor. Note: The wire can be straightened and rewound several times; also a second wire is included in your LabPaq for this purpose. Increase or decrease the number of turns in the armature. What effect does this have?

C. How do you think this motor operates?

Reflection and Refraction

Experiment Summary:

Students will have the opportunity to verify the law of reflection by measuring incident and reflection angles from a mirror and determine the relationship between the refraction of light and Snell’s law. Students will use a laser to

study how various angles of light reflect off a mirror and determine whether the image in the mirror is real or virtual. Students will also study refraction

through both water and a translucent block. Students will use Snell’s law to calculate the refractive indexes for these materials and compare the indexes

to those of other materials. �

�

Peter Jeschofnig, Ph.D. Version 09.1.02

Review the safety materials and wear goggles when working with chemicals. Read the entire exercise before you begin. Take time to organize the materials you will need and set

aside a safe work space in which to complete the exercise.

Objectives

x To verify the law of reflection by measuring some incident and reflection angles off of a mirrored surface and to determine the relationship between the refraction of light and Snell’s law.

Materials

Materials From: Qty Item Description: Student Provides 1 Card board: 8.5x11-in or larger

1 Several sheets of white paper 1 Scotch® tape or masking tape

From LabPaq 1 Petri dish, divided 1 Ruler with center groove

Dissection Tray 1 Laser pointer 1 Mirror 1 Protractor

2 Clothespin 1 Dissection pins, package of 6 1 Refraction block, Acrylic

VERY IMPORTANT WARNING: This experiment uses a laser pointer.

x Laser beams can seriously damage vision if pointed directly into eyes! x NEVER LOOK INTO A LASER BEAM! View it only from a side or rear angle. x NEVER POINT A LASER TOWARD THE EYES OF PEOPLE OR ANIMALS! x Keep this laser pointer away from the reach of all children at all times!

Discussion and Review

When light hits the surface of a material some of the light is reflected. The reflection of light rays from a plane surface like a glass plate or a plane mirror is described by the law of reflection: "The angle of incidence is equal to the angle of reflection," or Ƨi = Ƨr. These angles are measured from a line perpendicular or “normal,” N, to the reflecting surface at the point of incidence as shown in the illustration on the right. The velocity of light, v, is less in glass, water, or any material other than the vacuum of empty space. We label this speed of light in vacuum as c. The speed of light in a material is usually described by the index of refraction, n, defined by n = c/v. In any homogeneous material, light travels in straight lines. However, when light encounters a change in material, a boundary between materials, some of the light reflects back and some of the light is transmitted forward into the new material. The transmitted light does not travel in the same direction as the original light. Instead it is bent at the boundary and travels in a slightly different direction as shown in the illustration at left. When light is bent in this way the phenomenon is called refraction. The refraction of light at the boundary between two materials is described quantitatively by Snell's law. It relates how a ray of light will behave when passing from one medium to another. It is given by: n1 sinƧi = n2 sinƧr, where n1 and n2 are the indices of refraction for the two different media. In this experiment, we will trace sets of light rays originating from an object (pin) before and after it strikes a mirror surface. From this we can find the "apparent" image formed due to the reflected or refracted rays originating from the object. We will do this by properly aligning a set of pins.

Exercise 1

PROCEDURE: Part I- Reflection:

1. Tape a sheet of white paper onto the card board.

2. Draw a straight line about 20 cm long across the paper about one-third down from the top. This will be the baseline. Draw another line perpendicular to the first line using the protractor. This second line will be normal, 90o, to the first line.

3. From the intersection of the two lines, use your protractor to draw 20-cm long lines that form 30°, 45°, and 60° angles from the normal line as shown at right.

4. Attach a clothes pin along the bottom edge of each side of the mirror so it will stand

up straight. Then approximately center the mirror about the normal on the base line with the reflecting surface facing the angle lines.

5. Push two pins vertically through the paper and cardboard on the 30° line, one

approximately 20 cm and the other approximately 10 cm from the mirror. Label these points P1 and P2.

6. Look at the mirror from the right side of the normal

line so you can see the reflection of the first two pins. Stick two pins into the paper so that they appear to be co-linear with the reflection of the first two pins. They should appear to be in a straight line with the images in the mirror. Label the new pin points P3 and P4. It is important that the mirror not move from the baseline. This would change the angle of reflection.

7. Remove the pins and draw a line that connects points P3 and P4. This line represents

the reflected ray. Use a protractor and carefully measure the angle of reflection, Ƨr. Compare it to the angle of incidence. Are they the same?

8. Repeat the procedure by placing pins 1 and 2 on the 45°-line and then on the

60°-line of incidence. Record the angles of reflection on your drawing. Transfer the results to the data table that follows.

Data Table 1:

Incident angle, Ƨi 30 45 60

Reflected angle, Ƨr

9. What can you conclude about the relationship of Ƨi and Ƨr? Does this verify the law of reflection?

10. Repeat Part I using your laser pointer. In order to see the laser beam, you must hold

the laser pointer low enough to track the angle line and also be visible on the paper. This will allow the track of the beam to be reflected out onto the paper. When using the laser you will not need the pins, just draw the angle lines.

Part II - Reflection: You will now locate the image of an object as seen in a mirror.

1. Tape a new sheet of paper to the cardboard, draw a straight line approximately 20 cm long across the paper about one-third down from the top. Again place the mirror in an upright position by attaching clothes pins to each side of its bottom edge.

2. Place a pin which will be called the

object pin about 10 cm in front of and near the center of the mirror as seen at right.

3. Close one eye and use the other to site

the object image in the mirror while you look at it from the right side of the mirror. Place one pin that will be called a locator pin near the mirror and in line with the reflected ray of the object image.

4. Place a second locator pin about 10 cm in front of the mirror and also in line with the

image pin. The image must be along a straight line you will draw through the pins. 5. Now site the object image again, but this time from the left side of the mirror. Use

two more locator pins to mark a line with the reflected ray of the object image.

6. Circle the locations of all pins on the paper: label the object pin with “O” and the locator pins with "L" as shown in the illustration at right. Remove the mirror and the pins.

7. Draw straight lines through each of the

two pairs of locator pins and extend them as dashed lines behind the mirror line. The lines must be sufficiently long to intersect each other.

8. Draw a ray from the object pin to the point on the mirror that meets the lines from the

pairs of locator pins. The image reflection light that originated at the object pin reached your eye through this path.

9. Find the image location, circle that point and label it “I”. Measure and record the object distance do and the image distance di. What can you say about the location of the image?

10. Is the image real or virtual?

Part III - Refraction and the Refractive Index of Water: In this part we will trace rays through a semi-circular tray or petri dish of water using the pin technique.

1. Tape a fresh sheet of paper to the cardboard.

2. Draw a horizontal line near the center of your paper and then a second normal line perpendicular to and crossing the first line.

3. Use a protractor to draw a line from

the intersection of the above perpendicular lines at an angle of 20o to the left of the normal.

4. Fill one side of a divided petri dish about 2/3 full with water. Place the straight edge

of the petri’s divide along the horizontal line with the water on the opposite side from the pins. The petri dish should be centered close to the normal line as shown above. Place Pin 1 at the edge of the empty side of the dish and its intersection with the line from Step 3. Place a second pin 1 cm farther out the line.

5. With one eye look through the petri dish and water from the water-filled side. You

should be able to see both pins through the water. Make sure you are looking through the water; it is very easy to confuse looking through with looking over the water. Move your eye down from the top of the dish until you see the ray from the two pins on the opposite side pass through the water.

6. Place Pin 2 at the edged of dish in line with the rays you see through the dish from

the pins on the other side. Place a second pin about 1 cm farther out on the same sight line. Circle the positions of the pins both behind and in front of the petri dish.

7. Remove the dish and draw a straight line through the pins from the water-filled side

of the dish to the intersection of the perpendicular lines. You previously drew the incident ray and angle, Ƨi, from the empty side of the dish. The new line from the filled side of the dish represents the refracted ray. Measure the angle of refraction, Ƨr. Notice that this ray strikes the curved surface normal to the surface and passes through without being bent.

8. The angle of incidence and the angle of refraction are related by Snell’s law, or

Descarte’s law as it is known in France: ni sin Ƨi = nr sin Ƨr. For our example, ni, the index of refraction for the medium of the incident ray is the index of the refraction of air, which is ni = nair = 1.00. Therefore, we can solve for nr, the index of refraction for the medium that is water in this case: nr = sin Ƨi/sin Ƨr.

9. Perform the experiment two more times using different angles of incidence and

complete the following data table. Remember, the known value of the index of refraction for water is nwater = 1.33.

Data Table 2

Experiment Incident angle, Ƨi Refracted angle, Ƨr Index of refraction, n 1 2 3

Average value of the index of refraction, navg = _______________________.

10. Find the percent difference between the known value and your average experimental value.

11. Repeat this experiment using your laser pointer. Place a few drops of milk in the

water to make it cloudy and allow you to see the laser beam as it passes through the water. Extend the 20o angle line from Step 3 so it will pass beyond the entire petri dish when it is in place. Shine the laser down that line through the empty side of the petri dish. When you look down into the petri dish, you will actually see how the light has bent. Place a pin where the laser beam exits the curved part of the petri dish and then proceed with the previous calculations.

Part IV - Refraction and Refractive Index: In this part we will trace rays through a refraction block and measure its refractive index.

1. Tape clean paper to the cardboard and on the center of that paper trace around the large side of the refraction block.

2. Remove the protective paper or plastic from the translucent

ends of the refraction block.

3. About 1 cm from the upper left corner of the traced square, draw a normal line (N) to the outline of the cube that passes through the outline as shown in Figure 1.

Figure�1�

4. Draw a diagonal line up and to the left of the intersection of the normal line and outline. Mark the line with Pins P1 and P2. See Figure 2.

5. Place the refraction block on the out line so you will look through and to its translucent ends. Look through it from the opposite side of the first pins and place two pins, P3 and P4, along the path that appears to be a straight line from P1 and P2 when viewed from this angle. See Figure 3 below.

Figure 3

Figure�2�

Place� P3� and� P4� in� line� with� this� view.�

6. Draw a line through the P3 and P4 path to the edge of the square. At that point, draw a second normal line to the outline of the cube that passes through the outline. See Figure 4.

7. Draw a line from the intersections of the two normal lines with the outline. See Figure 5.

8. Measure the incident angles (Ƨi) the transmitted rays outside the outline make to their respective normals. See Figure 6.

Figure�4�

�

Figure�5�

9. Measure the refracted angles (Ƨr) between the normal lines and the ray drawn inside the outline. Use these angles to calculate the index of refraction of the material. See Figure 6 for guidance.

10. Perform the experiment two more times using different angles of incidence and complete the following data table.

Data Table 3

Experiment Incident angle, Ƨi Refracted angle, Ƨr Index of refraction, n 1 2 3

Average value of the index of refraction, navg = _______________________.

11. Find the percent difference between the known value of 1.49 and your average experimental value.

Figure�6�

Diffraction Grating

Experiment Summary:

Students will observe the interference pattern produced by passing a laser beam through a diffraction grating. They will determine the distance between slits in the grating and determine the wavelength of the laser light. Students

will calculate the number of grooves in an audio CD by measuring the diffraction of light spectra on a wall.�

�

Peter Jeschofnig, Ph.D. Version 09.1.03

Review the safety materials and read the entire exercise before you begin. Take time to organize the materials you will need and set aside a safe workspace in which to complete

the exercise.

�

Objectives

x To observe the interference pattern produced by passing a laser beam through a diffraction grating To determine the distance between the slits in the grating given the wavelength of the laser light, and determine the wavelength of the laser light given the distance between the slits in the diffraction grating

x To determine the number of grooves on a CD

�

Materials

WARNING: This experiment involves the use of a laser beam pointer.

x Never look into the laser beam. Laser beams may cause serious damage to vision if pointed directly into the eyes.

x Never point the laser beam toward people or animals.

x Unless otherwise instructed, do not allow the laser beam to strike a reflective or smooth surface as this may cause the laser beam to be redirected to the eyes.

x Keep the laser pointer out of reach of children at all times.

Materials Provided by:

Label or Box/Bag: Qty Item Description:

Student 1 1

Any music CD Room with table adjacent to a wall

LabPaq 1 Laser pointer 1 Tape measure, 3-m

Photo Card Bag Photo Card Bag 1 Diffraction grating card

�

Discussion and Review A diffraction grating is composed of numerous narrow, evenly spaced slits used to diffract light into its component energies. The number of slits used on a diffraction grating usually ranges from several hundred to a thousand slits per millimeter. When monochromatic light, such as the light from a laser, passes through the narrow slits, an interference pattern forms. Refer to Figure 1.

Figure 1. Light diffused into an interference pattern. An interference pattern is comprised of a distinctive pattern of sharp bright maxima. The points of constructive interference in a diffraction pattern are called diffraction maxima, which are mathematically expressed:

��ሺ ሻǡ� � �ͳǡ�ʹǡ�͵ǤǤǤ�� O T where n is the order of the diffraction maximum; d is the separation between slits; O is the wavelength of the light, and T n is the angular displacement from the center of the pattern (zeroth-order maximum) to the center of the nth order maximum. Refer to Figure 2.

�

Figure 2. Angular displacement of diffracted maxima. For example, assuming angle

ͳ� T is 40° and the wavelength O of the laser is 633 nm,

calculate d (distance between slits) as follows:

� � �u u u

ͻ ͻ ͹͸͵͵� �ͳͲ � ͸͵͵� �ͳͲ �� ͻǤͺͶͶͷ� �ͳͲ ��

��ͶͲ Ǥ͸Ͷ͵ �

Assuming the line spacing is 9.8445 × 10-7 m, calculate how many lines there are per millimeter of grating. 1000 mm equals 1 m; convert 9.8445 × 10-7 m to millimeters by multiplying by 1000. Thus, 9.8445 × 10-4 mm. If the line spacing is 9.8445 × 10-4 mm, then determine how many line spaces there will be in 1 mm.

Ͷ ͳ�� ͳͲͳ͸��ൌ� � �ͳͲͲͲ��Ȁ��

ͳ��ͻǤͺͶͶͷ� �ͳͲ �� |

1 Laser 2 Diffractive grating 3 Wall

�

PROCEDURE: In this experiment, you will determine the number of lines per millimeter for the diffraction grating provided in the LabPaq. Use Data Table 1 to record observations into the lab report. Assume that the pocket laser pointer used in this lab produces red light of wavelength ~ 633 nm. Data Table 1. Data from recorded observations.

O of laser (nm) L (m) ' x (m) T (tan-1 ( ' xavg/L) Part I: 1. Arrange a table or other level surface perpendicular to and adjacent to a blank wall.

Position the diffraction grating slide perpendicular to the table as shown above in Figure 2, Item 2.

2. Secure the slide by gently wedging it between two books lying on their sides on the table.

See Figure 3, Item 2. To avoid damage to the diffractive grating, secure the slide only by its cardboard edges.

3. Place the laser pointer upon another book adjacent to the diffraction grating slide. Use a

slightly thicker book to position the laser so that its beam will pass through the center of the diffractive grating slide. See Figure 3, Items 1 and 2.

Figure 3. Laser beam positioned to pass through center of diffraction grating. Wall and table surface are positioned perpendicular to one another. Note that items are not to scale.

1 Laser beam pointer 2 Books for positioning laser

beam pointer and diffraction grating

3 Diffraction grating frame 4 Diffraction grating 5 Diffracted laser beam

energies 6 Wall 7 Table or similar flat surface

4. Turn on the laser and point it into the center of the diffractive grating. Its beam passes through the diffraction grating, and the interference pattern from the diffraction grating appears on the wall. If you are too far from the wall, the interference pattern may be too spread out to be visible. If this is the case, position your laser beam pointer and books closer to the wall.

5. Use the tape measure to measure the distance, L, in a straight line between the diffraction grating slide and wall. Record the result into the lab report.

6. Use a tape measure to measure the distance ( ' x) between the zeroth order position (n0)

to the highest order position observable ( ��ሺ ሻǤ�

Angle measurement accuracy improves as ' x increases. For example, a ' x value between n0 and n3 or n4 would give a more accurate angle measurement than a ' x value between n0 and n1.

7. Calculate the angle T between n0 and nmax in the interference pattern and record the

result into Data Table 1 in the lab report. Use this equation:

T � 'ͳ�� ൌ��ሺ�� ሻ��

8. Using d sin T = O = 633 nm, calculate the distance d between the slits in the grating

and record the result into Data Table 1 in the lab report. Questions A. Convert the wavelength O of the laser pointer from nm to m.

Note: 1 nm = 1 × 10–9 m. B. Calculate the average value for ' x from the various individual measurements.

C. Calculate the angle Ƨ from T '�� ൌ� ��

D. Find ��T .

E. Solve for � using �� O T . For example, �� O T

F. Use � to find ͳ� � . In other words, how many lines are there per millimeter of diffraction

grating?

Part II: A compact disc (CD) consists of a series of evenly spaced grooves and ridges that can act as a diffraction grating. In this experiment, you will calculate the number of grooves in a CD.

Figure 3. Laser pointing at flat-lying CD surface to produce diffraction pattern on a wall. 1. Place the CD onto a table with the “rainbow” side facing up. 2. As in Part I, the wall onto which the interference pattern appears must be perpendicular

to the table surface on which the grating will rest. 3. Turn on the laser pointer and point it at the CD using a very low angle of incidence. 4. Rotate the CD until a series of red laser dots appear on the wall. For better contrast, turn

off or dim the lights in the room.

If you are too far from the wall, the interference pattern may be too spread out to be visible. If this is the case, position your laser beam pointer and books closer to the wall.

5. The first dot on the wall is a direct reflection of the laser beam off the CD and represents the zeroth diffraction order; this dot is called the “specular dot.” The other dots above n0 are numbered n1, n2, and so forth. If necessary, adjust the angle of the laser beam to make the dots more visible.

6. Take measurements only after the dots are seen clearly. First, determine the baseline. This is the spot on the wall that represents the top surface of the CD (See Figure 3). Mark the baseline on the wall and record the following measurements into Data Table 2:

L = the distance from the laser—CD intersection to the wall h0 = the height from the baseline to the lowest red laser dot on the wall h1 = the height from the baseline to the second laser dot on the wall

Data Table 2. Data from recorded observations. O of laser (nm) L (m) ho

(m) h1 (m)

On = d (cos Ƨi – cos Ƨn)

7. Compute the number of grooves in the CD. The number of grooves per millimeter is usually 625. Because two angles are involved in the projection of the interference pattern off a CD, use this formula:

�� ሺ�� ሻ�� O T T �

where n is the diffraction order; O is the wavelength of light; d is the groove spacing; �T is the angle of incidence and the angle of refraction (from the table); and �T is the angle of diffraction of the nth order maximum. Hypothetical Calculation: Assuming L = 0.8 m; h0 = 0.32 m; h1 = 1.33 m, follow the steps below for this hypothetical calculation. Calculate Ƨ

ͳ ͳͲ�� ͲǤ͵ʹ�� ʹʹǤʹ ሺ��ሻ ͲǤͺ��

� �

� � § · § ·

Ǧͳ Ǧͳͳ�� ͳǤ͵͵�� ൌ�� ͷͺǤͻ͹�ൌ�ͷͻ ሺ��ሻ ͲǤͺ��

� �

��ʹʹǤʹι�ൌ�ͲǤͻʹ͸ ��ͷͻι�ൌ�ͲǤͷͳͶ͸ͻ ��ൌ�ͲǤͶͳͳͲͶ

Calculate d

O T

� � � �§ · § ·u u u u¨ ¸ ¨ ¸

�© ¹ © ¹

ͻ ͻ ͸ ͵͸͵͵� �ͳͲ �� ͸͵͵� �ͳͲ ��ൌ� �ൌ�ͳǤͷͶ� �ͳͲ ��ൌ�ͳǤͷͶ� �ͳͲ ��

��ʹʹǤʹι� ��ͷͻι ͲǤͶͳͳͲͶ��

Calculate number of grooves per millimeter

� ��u ͵ ͳ ൌ�

ͳǤͷͶ� �ͳͲ �� ͸ͷͲ��Ȁ��

Questions: A. Calculate Ƨi:

ͳ Ͳሺ�� ሻ�� ሺ��ሻ

B. Calculate Ƨn :

ͳ ͳሺ�� ሻ�� ሺ��ሻ

�� § · ¨ ¸ © ¹

C. Calculate d:

� ��

�� Ȃ �� O

T T

D. Calculate number of grooves per mm:

ͳ �

E. Calculate number of grooves on CD:

��Ȁ��

Extra Assignments:

A. Take the diffraction grating slide outside in the evening. Look through the grating at streetlights, car lights, or neon lights. Observe the diffraction spectra. Remember that the spectrum for each gas with which the lights are filled is unique. These unique properties provide the ability to easily differentiate between mercury vapor, neon, and other light sources.

B. Shine the white light of a flashlight or desk lamp through the diffraction grating onto a

nearby wall in a partially darkened room. Notice the white light breaks up into its rainbow-colored components. Notice the grating diffracts white light the same way a prism does.

C. Include your observations for the above activities in the lab report.

Polarized Light

Experiment Summary:

Students will have the opportunity to explore the polarization of light, polarizing filters, and light intensity changes. They will use both qualitative and quantitative methods to determine the amount of light able to pass

through crossed polarizers. Students will determine quantitative measurements of resistance using a cadmium sulfide photocell with

electrical readings collected by a digital multimeter. �

�

Peter Jeschofnig, Ph.D. Version 09.1.01

Review the safety materials and wear goggles when working with chemicals. Read the entire exercise before you begin. Take time to organize the materials you will need and set

aside a safe work space in which to complete the exercise.

Objectives

x To study the polarization of light, polarizing filters, and light intensity changes through polarizing filters.

Materials

Materials From: Qty Item Description:

Student Provides 1 Flashlight or desk lamp From LabPaq 2 Cables, jumper - banded 1 Laser pointer 1 Multimeter-Digital 1 Protractor Capacitor Bag 1 Capacitor, LED, diode, and photocell in bag

Miscellaneous Supplies Bag

2 Clothespin

Photo Card Bag 1 Polarizing cards (2)-PK VERY IMPORTANT WARNING: This experiment uses a laser pointer.

Discussion and Review

Ordinary light such as that from a light bulb is a form of wave motion that consists of electric and magnetic fields that vibrate at right angles to the direction of travel of a light beam. This means that the electric field associated with a light wave oscillates in random directions, though always at right angles to the direction of the propagation of the light. A light wave which is vibrating in more than one plane is referred to as unpolarized light. Light emitted by the sun, by a light bulb, or by a candle flame is unpolarized light. Polarized light waves are light waves in which the vibrations occur in a single plane. They can be produced by passing light through a special “polarizing” filter. A polarization filter is a device with a specified direction, called the polarization axis. The polarizing filter absorbs the wave's incoming electric field not parallel to the polarization axis and transmits the electric field parallel to the polarization axis. So no matter what the polarization of the light shining into a polarizer might be, the light coming out of the polarizer is always polarized in the direction specified by the polarization axis. Well known applications of polarizing filters are found in photography and in polarized sunglasses. Regular sunglasses cut down glare and light intensity on a bright sunny day. In polarized sunglasses the light waves that vibrate in the same plane as the polarizing material can pass through, but other waves are reflected or absorbed. This helps to reduce unwanted reflected glare off strongly reflecting surfaces like water, asphalt roads, snow fields, etc.

PROCEDURE: Part I - Crossed Polarizers – Qualitative:

1. Find the polarization axis mark on each filter, and then put one polarizing filter on top of the other so that the axes marks are on top of each other. With the polarization axes in the same direction light will be transmitted.

2. With two filters together and their polarization axes aligned look through them at a

bright light such as a strong flash light or desk lamp. 3. Slowly rotate one of the filters through a 360o angle while keeping the other one still.

Observe and record what happens. Part II - Crossed Polarizers – Quantitative:

1. Find the polarization axis mark on each filter and put one polarizing filter on top of the other so that the axes marks are on top of each. Attach a clothes pin to each side of the bottom edge of the combined filters. The clothes pins should support and allow the filters to rest perpendicular to a table top where you will place them.

2. Arrange a photocell - also called a CdS cell since it contains cadmium sulfide - behind

the filter assembly so that the photocell’s light sensitive surface is unobstructed and faces the Polaroid filter assembly about 5 to 10 cm away from the center of the filters. It may be necessary to support the photocell or tape it to something such as a drinking glass to get it in proper position. The illustration below shows the basic configuration you need to achieve.

Note: Cadmium sulfide (CdS) photocells or photoresistors are used to measure the intensity of light. When light hits the surface of the photocell it causes a decrease in resistance, while darkness produces a higher resistance. We are using this relationship between varying light intensity and resistance changes to obtain quantitative data that can then be displayed graphically. 3. Attach the two wires of the photocell to the DMM via two jumper cables. The DMM

should be set as an ohmmeter. The resistance will be inversely proportional to the incident light intensity.

4. With a flashlight or desk lamp that has with a shade or paper cone to focus the light,

shine light through the polarizing filter assembly at the photocell. Since the two axes are on top of each other the angle between them is zero. Record the angle and the corresponding resistance.

5. Rotate one of the filters 15o and take another angle and resistance reading. The positions of the light source and photocell must not change during the experiment.

6. Take additional readings every 15o though a complete 360o of the rotating filter. 7. Graph light intensity, 1/R vs. angle between polarization axes. Note that the light

intensity indicator 1/R is an arbitrary unit. If we had a true light intensity meter our light intensity units would be in “lux”.

Part III - Polarization by Reflection:

1. Look out the window at a car windshield that is reflecting sunlight. 2. Hold each of the two linear polarizing filters in front of your eyes in a way that best

reduces the glare from the window. Make note of the orientation mark on each filter. These lines mark the transmission axis of the filter.

3. Notice how the best glare reduction is achieved from a filter with its transmission axis

in a vertical position. Light reflected from a horizontal surface is horizontally polarized. This experiment illustrates the way polarized sunglasses reduce glare from snow, ice, water and the front of your car.

4. Record your observations.

Part IV - Polarization of Sky Light:

1. Use one of your polarizing filters to look at the sky at �to the direction of the sun. Never look directly at the sun.

2. Look at different regions of the sky and notice if the intensity of the light changes as

you rotate the polarizer. 3. Record your observations.

Question:

A. If you buy polarizing sunglasses how can you be sure they are truly polarized? Consumer Tip: Never trust labels that say sunglasses are polarizing; a large percentage of them really are not! If you’ve learned this lesson well you will never be fooled by fakes!

Radioactive Decay

Experiment Summary:

Students will have the opportunity to simulate the decay of a hypothetical radioactives element using split peas, graph the results of the simulated

decay, and determine the half-life and decay constant of the element.

�

Peter Jeschofnig, Ph.D. Version 09.1.01

Review the safety materials and wear goggles when working with chemicals. Read the entire exercise before you begin. Take time to organize the materials you will

need and set aside a safe work space in which to complete the exercise.

Objectives

x To simulate the decay of a hypothetical radioactive element; x To graph the results of the simulated decay; and x To determine the half-life and decay constant of the element.

Materials

Materials From: Qty Item Description: Student Provides 1 Coffee cup 1 Paper, pen, tape 1 Computer with spreadsheet software Dissection Tray 1 Split Peas - 50 in Bag 2"x 3"

Discussion and Review

Certain elements are made up of atoms whose nuclei are naturally unstable. These elements are said to be radioactive. The nucleus within an atom of a radioactive element will decay into the stable atomic nucleus of another element by emitting or capturing atomic particles. The unstable element is called the “parent” element and the stable element is called the “daughter” element. The continuous process of disintegration of unstable radioactive nuclei is called radioactive decay. It is impossible to predict which particular nuclei and when any one of the nuclei in a sample will disintegrate. However, it is possible to predict the average rate of nuclei that will decay during a given time period. This percentage, expressed as a decimal, is called the decay constant, . Mathematically, the decay process is modeled exponentially:

where No is the original number of nuclei present and N is the number of nuclei present at time t. The half-life, t1/2 of a radioactive sample is the time required for one half of the nuclei present to decay. If the above exponential equation is solved for t when N = No /2, the result is (Remember “ln” refers to the natural log):

We will assume that once an unstable “parent” decays the resulting “daughter” is stable and can emit no more particles. In more complicated cases the daughter might be unstable as well but we will not deal with that situation now.

Exercise 1

PROCEDURE: In this exercise, you will calculate the decay constant and half-life of a sample using split peas to simulate the decay of radioactive nuclei. Peas lying on their flat side will be “parents” representing nuclei not yet decayed. Peas lying on their rounded side will be “daughters” representing the decayed nuclei. Each trial represents one unit of time. We assume a time interval of 2 minutes for each trial, but since this is a simulation, we could have assumed any time interval we wanted. 1. Set up a data table as follows to record your observations. Data Table: Trials Time -

minutes Parents = Peas lying flat

# per trial Daughters = Peas on rounded side

# per trial cumulative # 0 0 50 0 0 1 2 2 4 3 6 4 8 Etc. 0 50 2. Tape several sheets of white paper to your work table. Having this white background will

make counting the peas easier. 3. Count out exactly 50 individual split peas and put them into a coffee cup. Record 50

peas under time trial 0 on the data table. 4. Cover the cup with your hand, shake the contents for several seconds, and pour the

peas from the cup onto the paper in such a way that a single layer of peas is formed. 5. Count the number of parent peas lying on their flat side, and the number of daughter

peas lying on the rounded side. Record these values under Trial 1 of the Data Table. 6. Set the daughters aside, but put the parent peas from the trial back into the cup. Shake

as before and pour them back onto the paper for another trial. 7. Again, count and record both the flat lying parent peas and the rounded-edge lying

daughter peas. For the parents, record only the number of peas counted. For the daughters, you should record the number counted, then add that number to the previous count so that a running cumulative total of daughters can also be recorded. See the example on the following page for clarification.

8. Repeat this process until no split peas are remaining.

Example: The example below assumes that for trial 1 you had 23 flat lying parents and 27 daughter peas lying on the rounded sides. Next, you used only the 23 parents for trial 2 and got 12 parents and 11 daughters. Under trial 2, you record the 12 parents and 11 daughters, then add the 11 daughters to the previous count of 27 for a cumulative total of 38 daughters. Example DATA TABLE:

Trials Time - minutes

Parents = Peas lying flat # per trial

Daughters = Peas on rounded side # per trial cumulative #

0 0 50 0 0 1 2 23 27 27 2 4 12 11 38 3 6 4 8

Graphing: 1. Graph the results of your experiment. Plot the number of parent atoms (peas) remaining

after each trial on the y-axis. Plot the time on the x-axis. 2. Construct another graph. Plot the number of daughter atoms (peas) after each

observation on the y-axis. Plot the time of the observation on the x-axis. 3. Explain the difference in the two graphs. 4. Determine the half-life of this hypothetical element from your graph.

5. Using the equation calculate the decay constant: (ln 2 = 0.693) ƪ = 0.693/ t ½

APPENDIX

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Using Statistics This short introduction to statistics is designed to assist you in performing a few simple statistical analyses on some of your experiments. This brief introduction to statistics only scratches the surface. If you want to learn more about statistics, consider reviewing a statistics textbook, downloading one of the many statistics tutorials on the Internet, or taking a statistics course. The final section will show you how to use Microsoft® Excel® to calculate most statistics automatically. Statistics is a branch of applied mathematics. It specifically deals with the collection and interpretation of quantitative data and the use of probability theory to estimate population parameters. Statistics can be categorized into two sub-groups: descriptive statistics and inferential statistics. Descriptive statistics describe large amounts of data in an abbreviated form. They describe important characteristics of the data, including the mean, median, range, variance, standard deviation, etc. Inferential statistics use data obtained from a small group of elements called the sample to make estimates and test hypotheses about the characteristics of a larger group of elements called the population. Descriptive Statistics There are a number of measures of central tendency used to describe the center of a distribution and the scatter of observations around the center.

x Mean: The mean is the arithmetic average of all observations in a distribution. The mean is equal to the sum of all observations divided by the sample size.

x Mode: The mode is the most common value or class in the distribution.

x Median: If all of the observations are arranged in rank order from smallest to largest,

the median is the value bound by 50% of the observations on each side. If the number of observations in the distribution is odd, the median is simply the middle value in the ranked observations. If the number of observations is even, then the median is the mean of the two most central observations.

The measurement of the scatter of observations around the center of a distribution is extremely important. What if you had two means from two populations and the means of both were 50, but the values going into sample #1 were 1, 50, 100 and the values going into sample #2 were 49, 50, 51. It would appear that these are two very different distributions, but with the same mean.

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The scatter of observations around the center of a distribution can be depicted in the following ways:

x Range: The range of a distribution is the difference between the largest and the smallest value and is typically expressed as range = 1 – 22, meaning the lowest value was 1 and the highest was 22.

x Variance and standard deviation: The variance is a measure of the average squared

deviation from the mean. Variance differs from the range in that the variance takes into account the distribution of all data points; the range simply describes the single lowest and highest extremes. To calculate variance, take the deviation (or differences) of each value xi (i.e., the ith value of x) from the mean, (i.e., Xi - ). Square these differences and divide by the number of values minus one (i.e., n-1).

The standard deviation (s) is the square root of the variance. The advantage of the standard deviation is that if the data conform to a normal distribution, 95% of the values will fall within two standard deviations (actually 1.96s) on either side of the mean.

If you were contrasting the weight of two populations of acorns, it might be nice to see a statement like" "Acorns from Plot A (mean = 4.58 g, S.D. = .59, range = 3.99 – 4.91) were heavier than the acorns from Plot B (mean = 3.64, S.D. = .71, range = 2.99 – 4.29). At this point you could also give the results of a statistical test comparing these two samples. See the upcoming section on Hypothesis Testing.

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Inferential Statistics There are two types of statistical inferences: hypothesis testing and estimation of population parameters. Hypothesis testing refers to a general class of procedures for weighing the strength of statistical evidence or for determining whether the evidence supporting one hypothesis over another is sufficiently strong. Hypothesis testing is one of the most important tools statistical applications bring to real-life problems. Most often, decisions are required concerning populations on the basis of sample information. Statistical tests are used in arriving at these decisions. There are five ingredients to any statistical test:

1. Null Hypothesis 2. Alternate Hypothesis 3. Test Statistic 4. Rejection/Critical Region 5. Conclusion

Following is a simple example of hypothesis testing and the application of a null hypothesis and an alternative hypothesis.

One may wish to test whether or not a coin is fair (that is, whether there is an equal chance of it coming up heads or tails when tossed). The null hypothesis is that the coin is fair; the alternative hypothesis is that the coin is biased. If a series of coin tosses produce a result that is only 4% likely given a fair coin, one would reject the null hypothesis, assuming 95% confidence is required. By contrast, if the experiment produces a result that is 30% likely given a fair coin, one would fail to reject the null hypothesis that the coin is fair. It is not permissible to accept the alternative hypothesis. Only acceptance or failure to reject the null hypothesis is allowed in hypothesis testing. If a test fails to reject the null hypothesis, it is said to lack sufficient power to accept the alternative hypothesis.

The null hypothesis states that there is no effect or difference between procedures and is denoted by H0. The objective of hypothesis testing is to either accept or reject the null hypothesis The alternative hypothesis states that there is a statistically significant difference in the outcome of an experimental procedure. Typically, the null hypothesis is stated first, followed by the alternative hypothesis (Ha). This alternative can be stated simply as there is a true difference. Only one of the two statistical hypotheses can be true.

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Consider a simple example in which one wishes to compare the size of male and female fish. The null hypothesis might be that the males and females are the same size (i.e., the samples obtained were drawn from the same underlying population). The alternative hypothesis is that males and females are different sizes. The null hypothesis is tested with an appropriate statistic. If one rejects the null hypothesis, one is left with the alternative that there is a difference (i.e., males and females are of different sizes). This sounds pretty simple, but statistical tests provide a formal means to tell us if the evidence is sufficiently compelling to reject the null and decide that something is going on and might be worthy of further investigation.

Hypotheses can be directional (e.g., males are smaller than females) or non-directional (e.g., males and females are of different sizes), and this determines whether to use what is called a one-tailed or a two-tailed test.

x Example: Two-Tailed Hypothesis Ho = There is no difference in size between male and female fish. Ha = There is a difference in size between male and female fish.

x Example: One-Tailed Hypothesis

Ho = Male fish are not smaller than female fish. Ha = Male fish are smaller than female fish.

In the example for a one-tailed test, failure to reject the null hypothesis might mean that there was no difference in size of male and female fish or that female fish were bigger than male fish. Decision Making and the Level of Significance After stating the hypothesis, one must select and carry out an appropriate statistical test. Each test is based upon a different test statistic [e.g., given the symbols, t (for a t-test), F (in an analysis of variance), r (for a correlation analysis), ƶ2 (for a chi-square test), etc.]. By plugging the values from a sample into a formula for the statistical test, one ends up with an observed value for the test statistic. One must then compare the observed value of the test statistic with a theoretical distribution of values that one would obtain if the null hypothesis was true. This distribution of expected values is generated from the assumptions that underlie the test and, in the case of parametric tests, from some of the data that was collected, such as the variance among multiple observations within a group. These distributions are typically summarized in tables that are published in statistics books or are readily available on the Internet (search: Statistical Tables).

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With these tables, one can ask how likely is it that we would have obtained the observed results. The table provides the entire distribution and determines how much of the distribution lies beyond the observed value of the test statistic. This yields the P-value, or the probability of obtaining one’s observed results or something more extreme under the assumption that the null hypothesis is correct. For example, a P-value of 0.13 means that if the null hypothesis were true, 13% of all possible samples would lead to results as extreme as those found (i.e., with the same or more extreme differences between the two groups). The smaller the P-value, the less likely it is that the null hypothesis is true. But how small should the P-value be before one rejects the null hypothesis? This cut-off is given the symbol Ơ (alpha), which by convention is typically set at 0.05. In other words, 5% of the times when the null hypothesis is correct, one will conclude that the null hypothesis is wrong. This is called a Type I error. The probability of a Type I error is equal to Ơ. To interpret the results, one compares the P-value to Ơ. If P<Ơ (i.e., if P<0.05) then one rejects the null hypothesis. If P> Ơ or P= Ơ, one tentatively accepts the null, recognizing that it might be wrong, but there is insufficient evidence to reject it. If able to calculate a P-value exactly from a distribution or from a statistics software program, it's useful to report the exact value as P=0.05 rather than P<0.05 or P>0.05. In the second and more common case, the entire distribution is not published, so one cannot exactly determine the P-value. Instead, the tables provide particular values of the test statistic associated with different P- values or levels of significance or Ơ. If one’s observed test statistic is greater than this critical value of the test statistic, one can reject the null hypothesis because P < Ơ.

The T-Test One of the most common comparative statistical tests is the t-test. Also called the student’s t-test, it is used when there are just two sets of normally-distributed data to compare. Normally-distributed data means that the data distribution looks like a bell-shaped curve. There are several types of t-tests, each designed mathematically for a specific application. Here we will look at the t-test used to compare two independent samples, which one would use in an experiment where the average height of plants in the two squares sampled are compared. In this exercise you will ask if the difference between the mean heights of the plants in the two plots is statistically significant. Your null hypothesis is that the species of plants present and the conditions in which they have grown have made no difference in their height and that the mean heights of the two plots are essentially the same, allowing for some minor variance:

Ho: µ1 = µ2 The alternative hypothesis is that differences in the plant species and growing conditions have made a difference and that the mean heights are not the same:

Ha: µ1 � µ2

If the mean heights are not the same, then the question is whether the mean height of one sample is significantly larger or smaller than the other. As you have two means, you will use a two-tailed test. Don’t worry if this sounds confusing. Following are step-by-step examples of how this analysis is performed. Sample Problem 1: Weights of acorns collected from two different plots 1. Calculate the mean (average) of the weights in grams. Add all data point values for each

plot and divide by the number of data points.

x Plot A: (2.33 + 2.51 +2.12 +2.7 +2 +2.42 +2.54 +2.6 +2.44 +2.53)/10 = 2.419

x Plot B: (2.02 +1.9 +2.13 +2.5 +2.3 +2.5 +2.3 +2.21 +2.21

+1.8 +2.64+2.14)/10 = 2.185

2. Calculate the variance (s²) of each plot:

a. Square each data value and enter it in a data table: 2.33² = 5.4289, etc.

b. Add all the data values in the last row: 2.33+2.51+2.12 +……= 24.19.

c. Add all the squared data values: 5.4289 + 6.3001 + ------- = 58.94 (rounded).

3. Enter the values calculated in Step 2 into the equation:

Plot A Plot B 2.33 2.02 2.52 1.90 2.23 2.13 2.70 2.50 2.00 2.30 2.42 2.21 2.54 2.21 2.60 1.80 2.44 2.64 2.53 2.14

Plot A Plot B X x2 x x2 2.33 5.4289 2.02 4.0804 2.51 6.3001 1.9 3.61 2.12 4.4944 2.13 4.5369 2.7 7.29 2.5 6.25 2.0 4.0 2.3 5.29 2.42 5.8564 2.21 4.8841 2.54 6.4516 2.21 4.8841 2.6 6.76 1.8 3.24 2.44 5.9536 2.64 6.9696 2.53 6.4009 2.14 4.5796 24.19 58.9359 21.85 48.3247

Plot A: s2 = {58.94 – [(24.19*24.19)/10]/9} = 0.047 Plot B: s2 = {48.32 – [(21.85*21.85)/10]/9} = 0.065

4. Calculate the t-value.

a. Calculate the numerator of the equations above: . Subtract the mean of plot B from the mean of plot A: 2.419 - 2.185 = 0.234.

b. Multiply the difference of the means (0.234) by the ¥ n (for the sample in the

example n=10, and the ¥10 is 3.162) which = 0.74.

c. Calculate the denominator: Take the square root of the sum of the two variances calculated earlier: ¥(0.047 + 0.065) = 0.334.

d. Divide the numerator by the denominator: 0.74/0.334 = 2.24 = t.

e. The calculated t-value is 2.24.

5. Now look at the table of critical values for t and compare the values in the table to your

calculated t.

In order to use the critical values table, you need alpha (Ơ) and degrees of freedom (df). The total number of data points is n, in your case 20 acorns. For a t-test involving two independent means, df = n – 2. In your case, n = 20 so df = 20 – 2 = 18.

Alpha refers to the degree of confidence. The degree needed to accept the null hypothesis is normally 5% or 0.05. Since you are using a two-tailed test, your alpha has to be split between the two tails, giving an alpha of 0.025 for each tail. Go to the table and look under 0.025 and 18 df. You can find such tables on the Internet with a search of t-test critical values.

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From the table you see that the value under Ơ = 0.025 and df = 18 is approximately 2.1 Interpretation of the results: Since the calculated t-value of 2.24 is greater than the critical value of 2.1, accept the null hypothesis that the two means are statistically equal. It indicates that the difference between the means is insignificant at the 95% level (100% minus alpha). In other words, the means of the two samples differ by less than can be accounted for by minor variations and the size of the sample. Sample Problem 2: Weights of acorns collected from two different plots with different number of data points in each plot. 1. Calculate the mean (average) of the weights in grams. Add all data point values for each

plot and divide by the number of data points. Plot A: (2.33 + 2.51 +2.12 +2.7 +2 +2.42 +2.54 +2.6 +2.44 +2.53+2.5+2.55)/12 = 2.437 Plot B: (2.02 +1.9 +2.13 +2.5 +2.3 +2.5 +2.3 +2.21 +2.21 +1.8 +2.64+2.14)/10 = 2.185

2. Calculate the variance (s²) of each plot:

a. Square each data value and enter it in a data table, Ex: 2.33² = 5.4289, etc. b. Add all the data values: 2.33+2.51+2.12 +……= 29.24 c. Add all the squared data values: 5.4289 + 6.3001 + ------- = 71.69 (rounded).

Sample 1 Sample 2 2.33 2.02 2.51 1.9 2.12 2.13 2.7 2.5 2.0 2.3 2.42 2.21 2.54 2.21 2.6 1.8 2.44 2.64 2.53 2.14 2.5 2.55

3. Enter the values calculated in Step 2 into the equation:

Plot A: s2 = {71.69 – [(29.24*29.24)/12]/10} = 0.04 Plot B: s2 = {48.32 – [(21.85*21.85)/10]/9} = 0.065

4. An additional step is needed to calculate pooled variance since you have an unequal number of data points in each plot.

sp2 = (n1-1)s12 + (n2-1)s22 n1 + n2 – 2

So, what does this mean?

x n1-1 = number of data points in plot A minus 1 x s12 = variance for plot A x n2-1 = number of data points in plot B minus 1 x s22 = variance for plot B x n1 + n2 – 2 = number of data points in plot A + plot B minus 2 (which also = df)

sp2 = (11)0.04 + (9)0.065 = 1.025 = 0.051

12 + 10 – 2 20

5. Now, having adjusted the variance for different sample sizes, you can calculate the t- value using a slightly different equation.

t(pooled) =

= 2.437 – 2.185 = 0.2545

= 0.051/12 + 0.051/10 = .00935

¥.00935 = 0.0967

Final step: 0.2545/0.0967 = 2.63 calculated t = 2.63

6. Now find the critical t-value in the table. Using alpha = 0.05/2 = 0.025 and df = 22 – 2 =

20, ee find that tcritical = 2.086. Interpretation of the results: Since the calculated t-value of 2.63 is greater than the critical value of 2.086 you reject the null hypothesis that the two means are equal. It indicates that the difference between the means is significant at the 95% level (100% minus alpha).

The Chi-Square Test The chi-square (X2) test is one of the most useful non-parametric statistical tests for the biologist. It is used with count data or frequencies organized in a matrix defined by two or more variables. The chi-square test is based on the differences between the observed results and the expected values (those results that would be obtained if the null hypothesis were true). The formula for X2 is as follows:

where o is the observed frequency and e is the frequency expected under the null hypothesis of no difference between groups.

Example: Suppose a fisheries biologist samples adult fish from two lake populations: 100 from Lake 1 and 150 from Lake 2. The biologist records whether or not the lakes are infested with a nematode parasite that encysts in their muscles. The biologist wants to know whether the presence of the parasite is independent of the lake from which they were taken. A. Arrange the data in a data table. B. Calculate the sums for each table row and column. Data Table 1 – Observed values Site # fish w/parasites #fish w/out parasites Total Lake A 15 85 100

Lake B 50 100 150 Totals 65 185 250 C. Compute the table of expected values. For example, the expected value for the number

of fish with parasites in Lake 1 = (100x65)/250=26 [i.e., (the row total x the column total)/total].

Data Table 2 – Expected values Site # fish w/parasites #fish w/out parasites Total Lake A 26 74 100 Lake B 39 111 150 Totals 65 185 250

Notice the row and column totals are the same in the tables of expected and observed values.

D. Compare the observed and expected frequencies using the �2 statistic. �2= (15-26)2/26 + (85-74)2/74 + (50-39)2/39 + (100-111)2/111 = 10.5

E. Determine the degrees of freedom for the test = (2 rows-1) x (2 columns-1) = 1 df. F. Compare the calculated �2 value (10.5) with the value for 1 degree of freedom from a

stats table. Since your calculated value is greater than 3.84 (from the table), you can reject the null hypothesis that the presence of parasites in fish is independent of the lake.

Table 2 – Chi-square

Microsoft Excel and Statistics Microsoft Excel spreadsheets can be used to perform most statistical calculations. Analysis ToolPak add-in MS Excel provides a set of data analysis tools, the Analysis ToolPak, which can save steps when one is developing complex statistical or engineering analyses. One provides the data and parameters for each analysis, and the tool uses the appropriate statistical or engineering macro functions before displaying the results in an output table. Some tools generate charts in addition to output tables. To view a list of available analysis tools, go to the Tools > Data Analysis. If the Data Analysis menu item is missing from the Tools menu, the Analysis ToolPak must be installed. Install and Use the Analysis ToolPak 1. Select Tools > Add-Ins > Analysis ToolPak.

If the Analysis ToolPak is not listed in the Add-Ins dialog box, click Browse and locate the drive, folder name. The file name for the Analysis ToolPak add-in, Analys32.xll, is usually located in the Microsoft Office\Office\Library\Analysis folder Run the Setup program if the pak isn't installed.

Excel provides many statistical, financial, and engineering worksheet functions. Some of the statistical functions are built-in and others become available when you install the Analysis ToolPak. It is easy to analyze data using descriptive statistics in Excel, because Excel includes all common statistics, including mean, median, mode, standard deviation, etc. Create a Data File 1. Open Excel. 2. Enter the data at right. 3. Click once in cell C1 to the right of

the Sample 2 column.

4. Click Tools > Data Analysis. The

screen at right will appear.

5. Select Descriptive Statistics.

6. Click OK.

7. Enter the cell reference for the

range of data to analyze. The reference must consist of two or more adjacent ranges of data arranged in columns or rows.

Choose the values for Sample 1 by entering the range, $A$1:$A$11, into the Input Range textbox.

You can also click the drop-down box in the Input Range field and drag the mouse across the desired range.

8. Indicate whether the data in the

input range is arranged in rows or columns by selecting the correct option button. For this exercise, select Columns

9. Indicate whether the input range

contains labels by selecting the Labels in First Column checkbox.

If the input range has no labels, leave the checkbox unmarked. Excel will generate appropriate data labels for the output table.

10. If you want to include a row in the output table for the confidence level of the

mean:

Enter the desired confidence level in the text box.

For example, entering a value of 95% calculates the confidence level of the mean at a significance of 5%.

11. If you want to include a row in the output table for the kth largest value for each

range of data, enter the number to use for k. If you enter 1, this row contains the maximum of the data set.

12. If you want to include a row in the output table for the kth smallest value for each range of data, enter the number to use for k. If you enter 1, this row contains the minimum of the data set.

13. Output Range: Enter the reference for the upper-left cell of the output table.

This tool produces two columns of information for each data set. The left column contains statistics labels, and the right column contains the statistics.

Excel writes a two-column table of statistics for each column or row in the input range, depending on the Grouped By option selected. If you don't enter an output range, Excel might overwrite your data table.

For this example, enter $C$1 in the Output Range text box.

14. Click OK.

After some calculation time, a table will appear in your spreadsheet with all your descriptive statistics.

Perform a t-Test Analysis

This tool is a part of the Analysis ToolPak. When two populations are both normally or approximately normally distributed, and when at least one sample size is small (less than 30), the t-test is used to make decisions about differences between the population means. The Analysis ToolPak provides three tools that can be used to test the means of different types of populations. There are four different ways of doing a t-test in Excel.

x t-test: One Sample t-test x t-test: Two-Sample Assuming Equal Variances Analysis x t-test: Two-Sample Assuming Unequal Variances Analysis x t-test: Paired Two Sample for Means Analysis

Single Sample t-Test x Definition: Used to compare the mean of a sample to a known number (often 0). x Assumptions: Subjects are randomly drawn from a population, and the distribution of the

mean being tested is normal. x Test: The hypotheses for a single sample t-test are:

o Ho: u = u0 o Ha: u < > u0

where u0 denotes the hypothesized value to which you are comparing a population mean.

x Test statistic: The test statistic, t, has N-1 degrees of freedom, where N is the number of

observations. x Results of the t-test: If the p-value associated with the t-test is small (usually set at p <

0.05), there is evidence to reject the null hypothesis in favor of the alternative. In other words, there is evidence that the mean is significantly different than the hypothesized value. If the p-value associated with the t-test is not small (p > 0.05), there is not enough evidence to reject the null hypothesis, and the conclusion is that there is evidence that the mean is not different from the hypothesized value.

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To create a single sample t-test in Excel, you use the tdist function. Example: TDIST (1.96,60,2) equals 0.054645, or 5.46 percent Exercise - Single Sample t-test from http://www.mastep.sjsu.edu/learn/t_test.htm You have been told that the average employee for your industry has an average dexterity score of 100 on a standardized test. You think your employees will score differently, so you give a random sample of 12 the test. The results are: First, we need to construct hypotheses.

Ho: The average dexterity score for our employees is 100. Ha: The average dexterity score for employees is not 100.

1. Open an Excel® spreadsheet and enter the data

from the table.

Subj. Test Score

1 98 2 102 3 120 4 140 5 123 6 101 7 89 8 99 9 119 10 103 11 132 12 107

2. Move the cursor to cell E4. 3. Calculate the sample mean and the standard deviation of our sample. 4. Click Insert > Function.

5. In the left column, click Statistical.

You will see a list of statistical functions appear on the right.

6. Scroll down until you see AVERAGE.

7. Click AVERAGE

8. Either type the range B2:B13

into the Number1 box or use the mouse to select the range from the worksheet.

9. Click OK.

For this example, you should get a mean of 111.0833..

10. Next, click cell E3. 11. Click Insert > Function.

12. In the left column, click Statistical.

You will see a list of statistical functions appear on the right.

13. Scroll down until you see STDEV.

14. Click STDEV.

15. Either type the range B2:B13

into the Number1 box or use the mouse to select the range from the worksheet.

16. Click on OK.

For this example you should get a standard deviation of 15.45938. We are using the standard deviation of a sample [with n-1] because we know it is a sample, not the entire population.

17. Calculate the t ratio using the following formula.

t = Sample Mean – Population Mean Sample SD / (SQRT (sample size))

For our example, this calculation would be t = 111.0833 - 100 15.45938/(SQRT(12))

t = 2.4835

18. To test the hypothesis that our sample is different from the population, we need to find

the two-tailed probability of a t ratio of 2.4835 with 11 degrees of freedom Remember degrees of freedom is Sample Size - 1.

19. Next, click cell E4. 20. Click Insert > Function. 21. In the left column, click Statistical.

You will see a list of statistical functions appear on the right.

22. Scroll down until you see TDIST.

23. Click TDIST.

24. Enter the values at right into the text boxes.

25. Click OK.

You should get a value of 0.030384. This means there is a 3% chance that your sample is representative of the population.

Related to significance levels, you would reject the null hypothesis at the 5% significance level, but you would not reject the null hypothesis at the 1% level. About the t-Test: Two-Sample Assuming Equal Variances Two samples are referred to as independent if the observations in one sample are not in any way related to the observations in the other. This is also used in cases where you randomly assign subjects to two groups, give the first group treatment 1, give the second group treatment 2, and compare the two groups. This analysis tool performs a two-sample student's t-test. This t-test form assumes that the means of both data sets are equal; it is referred to as a homoscedastic t-test. You can use t- tests to determine whether two sample means are equal. For this example, you are going to use the data from the file space.xls. In a NASA-funded study, 7 men and 8 women spent 24 days in seclusion to study the effects of gravity on circulation. Without gravity, there is a loss of blood from the legs to the upper parts of the body. The study started with a 9-day control period in which the subjects were allowed to walk around. This was followed by a 10-day bed rest period in which the subjects' feet were somewhat elevated to simulate weightlessness. The study ended with a 5-day recovery

period in which the subjects were allowed to walk around. Every few days, researchers measured the electrical resistance at the calf, which increases when there is blood loss. The electrical resistance gives an indirect measure of the blood loss. Example from Data Analysis with MS Excel®, p. 137. 1. Open Excel.

2. Enter the data set at right.

3. We are going to use Excel's Analysis ToolPak to perform a 2-sample t-test. Click Tools > Data Analysis.

4. Scroll down until you see t-test: Two-Sample Assuming Equal Variances.

5. Click on this t-test. 6. Define the Variable 1 Range.

This is the cell reference for the first range of data you want to analyze. The range must consist of a single column or row of data. In this case, we are going to select the range $A$2:$A$12. You can either type this range or use the mouse to select the range from the worksheet.

7. Select the Variable 2 Range. We are going to select the range $B2:$B$12.

8. Hypothesized Mean Difference: Enter the number that you want for the shift in sample means. A value of 0 (zero) indicates that the sample means are hypothesized to be equal.

9. Enter 0. 10. Labels: Select the checkbox if the first row or column of your input ranges contains

labels.

Clear this check box if your input ranges have no labels. Excel generates appropriate data labels for the output table. Since your first row contains labels (Sample 1 and Sample 2), check the Labels box.

11. Alpha: Enter the confidence level for the test. This value must be in the range 0 to 1.

The alpha level is a significance level related to the probability of having a type I error (rejecting a true hypothesis). We will enter 0.05 for our Alpha.

12. Output Options: You have three options

for the output range. Generally, it is safer to choose either New Worksheet Ply or New Workbook.

Output Range: If you place a range here, your t-test values will appear on the same worksheet.

Enter the reference for the upper-left cell of the output table. Excel automatically determines the size of the output area and displays a message if the output table will replace existing data.

New Worksheet Ply: Select to insert a new worksheet in the current workbook and paste the results, starting at cell A1 of the new worksheet.

To name the new worksheet, type a name in the box.

New Workbook: Select to create a new workbook and paste the results on a new worksheet in the new workbook.

For this example, select Output Range

A17. This means the results will be displayed below the data table.

Click OK. You should see the information at right in a new worksheet.

Let's translate this data into plain English. Based on the table, we can see that, on the average, the sample 1 acorns have higher weight (2.419g as compared to 2185 g for sample 2 acorns). The variances in the two samples are not exactly the same, so we may want to recheck our calculations using the t-test with unequal variances option in Excel. Generally, if the variance is close, the difference in t value will not be great. The value of the t statistic is 2.217. The two-tailed p-value is given as 0.0397, which is less than 0.05, so the difference is significant at the 5% level. Because the probability level is so small, the null hypothesis of no difference between sample 1 and sample 2 seems incompatible with the data. Therefore, you would reject the null hypothesis and state that the weights are different for sample 1 and sample 2 acorns.

About the t-Test: Two-Sample Assuming Unequal Variances One would use this test if the variances in the two groups are extremely different. The worst situation would be if the two samples are of very different sizes, and the small sample has a much larger standard deviation. We will use the same data file as above, Space.xls, to do this calculation.

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1. Open Excel and use the same acorn data as before. 2. Click Tools > Data Analysis. 3. Scroll down until you see t-test: Two-

Sample Assuming Unequal Variances. 4. Click once on this t-test.

5. Enter the same data as you did in the t-

test: Two Sample Assuming Equal Variances example.

6. Click OK. You should see the information at right in a new worksheet.

As you can see, the values are identical to those for equal variances, and our assumption about equal variances was correct. If the variances had been unequal, we might have gotten slightly different results. But as long as the standard deviations and the sample sizes are close, the results will often be very close to those of the equal variances t-test. t-Test: Paired Two Sample For Means Analysis This analysis tool and its formula perform a paired two-sample student's t-test to determine whether a sample's means are distinct. This t-test form does not assume that the variances of both populations are equal. You can use a paired test when there is a natural pairing of observations in the samples, such as when a sample group is tested twice — before and after an experiment. Another reason data is dependent is when results on one measure are presumed to be related to another measure. For example, if a student does well in one subject, English, it is likely that he will do well in another subject, for example, history. In fact, this is the situation we are going to use to demonstrate this t-test.

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Paired t-test

x Definition: Used to compare means on the same or related subject over time or in differing circumstances.

x Assumptions: The observed data are from the same subject or from a matched

subject and are drawn from a population with a normal distribution.

x Characteristics: Subjects are often tested in a before-after situation (across time, with some intervention occurring such as a diet), or subjects are paired such as with twins, or with subject as alike as possible. An extension of this test is the repeated measure ANOVA.

x Test: The paired t-test is actually a test that shows the differences between the two

observations is 0. So, if D represents the difference between observations, the hypotheses are: Ho: D = 0 (the difference between the two observations is 0) Ha: D 0 (the difference is not 0)

The test statistic is t with n-1 degrees of freedom. If the p-value associated with t is low (< 0.05), there is evidence to reject the null hypothesis. Thus, you would have evidence that there is a difference in means across the paired observations. Sample Calculation: We want to find out whether a student's performance in English is, on the average, different from his/her performance in history. Suppose that a sample of 11 students is selected and their grades for these two subjects are obtained. 1. Open Excel and enter the data at right.

2. Click Tools > Data Analysis. 3. Scroll down until you see t-Test: Paired

Two-Sample for Means. 4. Click once on this t-test.

5. In this case, we are going to select the range $B$3:$B$14. You can either type this

range or use the mouse to select the range from the worksheet.

6. Next, select the Variable 2 Range, and select the range $C$3:$C$10.

7. Hypothesized Mean Difference: Enter the number that you want for the shift in sample means. A value of 0 (zero) indicates that the sample means are hypothesized to be equal. Enter 0.

8. Labels: Select if the first row or column of your input ranges contains labels.

Clear this check box if your input ranges have no labels; MS Excel generates appropriate data labels for the output table.

Since our first row contains labels (English and History), you should check the Labels box.

9. Alpha: Enter the confidence level for the test. This value must be in the range 0...1.

The alpha level is a significance level related to the probability of having a type I error (rejecting a true hypothesis).

We will enter 0.05 for our Alpha.

10. Output Range: As before, you have three options for the output range. Generally, it is safer to choose either New Worksheet Ply or New Workbook.

Output Range: If you place a range here, your t-test values will appear on the same worksheet. Enter the reference for the upper-left cell of the output table. MS Excel® automatically determines the size of the output area and displays a message if the output table will replace existing data.

New Worksheet Ply: Click to insert a new worksheet in the current workbook and paste the results starting at cell A1 of the new worksheet. To name the new worksheet, type a name in the box.

New Workbook: Click to create a new workbook and paste the results on a new worksheet.

11. Choose New Worksheet Ply and type

the name, paired t-test, to the right. 12. Click OK. You should see the information at right in a new worksheet.

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