GENERAL PHYSICS 1 Module 1: Physics: An Introduction LESSON 1: WHAT IS PHYSICS? INTRODUCTION AND FOCUS QUESTION(S) Physics is considered as one of the most fundamental of the sciences. It involves universal laws and the study of the behavior and relationships among a wide range of important physical phenomena. In addition to its intrinsic beauty, physics also leads to an understanding of many practical applications and ideas in other areas of science. It is the laws of physics that govern many principles involved in chemistry, biology, astronomy, and geology among others. Imagine a world without telephones, televisions, and computers. How do you think would people communicate with one another, entertain themselves, and process vital information. Achievements in modern science and technology have made life more convenient for people. As a result, people are able to communicate regardless of distance, order take-out food or pay bills over the phone, send important documents using E-mail, and even have a damaged internal organ replaced. Behind these products and services people utilize are science principles. Through the results of scientific discoveries, various tools, processes and products have been invented and enhanced. In what way is physics considered a scientific field? What tools is used to formulate the laws of nature? Can students like you specialize in physics and make a career out of it? How significant is an accurate and precise measurement? What mathematical principles are also used in physics? What relationships or variations exist among variables? LESSONS AND COVERAGE: In this module, you will examine those questions as you take the following lessons: Lesson 1.1 – Physics: A Basic Science Lesson 1.2 – Mathematics in Physics Lesson 1.3 – Measurement: A Universal Language Lesson 1.4 – Equations: Relationships in a Capsule In this lesson, you will learn the following: ● Relate physics to other branches of natural science ● Discuss how physics and technology change people’s way of living ● Discuss the developments of physics from the early part of the 17th century to the early part of the 20th century. ● Explain the interrelationship between science, technology and the society Lesson 1.2 ● Tell the number of significant figures in a given measurement ● Express very large or very small numbers using the scientific notation form Lesson 1.3 ● Enumerate the fundamental and derived quantities and give their corresponding SI units ● Differentiate between accuracy and precision ● Convert a particular unit into another unit ● Cite sources of errors and limitations in measurement ● Estimate errors from multiple measurements of a physical quantity using variance. Lesson 1.4 ● Determine the relationship between quantities ● Change the subjects of a formula ● Express the relationship between quantities graphically MODULE MAP: Lesson 1.1 Here is a simple map of the lessons you will cover: EXPECTED SKILLS: To do well in this module, you need to remember and do the following: 1. Read all the instructions carefully before starting anything. 2. Complete all the activities and worksheets. Follow instructions on how to submit them. 3. Look up the meaning of words that you do not know. 4. You will frequently come across process questions as you go through different lessons. Keep a notebook (or use a Notepad) where you can write (and revise) your answers to these questions. Use also the notebook to jot down short notes, draw diagrams, and summarize what you have just read. 5. For worksheets and reports that need to be submitted, use the provided checklist and rubric to evaluate your work before submission. 6. Allow time for relaxation and recreating when you are mentally tired. Make a timetable to schedule your study and recreation. PRE-ASSESSMENT Let’s find out how much you already know about this module. A. MATCHING TYPE: Match the fields of physics in Column B with the descriptions in Column A. A. Astrophysics Column A ______1. It deals with laws and methods, observations, principles that relate electricity and magnetism. ______2. It deals with the application of physical science to explain life processes. ______3. It deals with the motion of objects with or without reference of force. ______4. It deals with the structure and composition of the Earth and is applied in locating subsurface petroleum, mineral deposits and water supplies. ______5. It is concerned with the properties of highly ionized atoms forming a mixture of bare nuclei and electrons. ______6. It is concerned with the structure and properties of solid materials. ______7. It is concerned with the structure and properties of the atom. ______8. It is concerned with the structure, properties and reactions of the nuclei of atom. ______9. It is concerned with the study of Physics of the astronomical bodies. ______10. It is concerned with the study of the chemical properties of matter and the influence of fluid turbulence, temperature, pressure, electricity and light. B. C. D. E. F. G. H. I. J. Atomic Physics Biophysics Electromagnetism Geophysics Mechanics Nuclear Physics Physical Chemistry Plasma Physics Solid State Physics Column B B. MULTIPLE CHOICE: Choose the letter of the correct answer. ______1. How close a measurement is to the true value is called.. A. Accuracy B. Precision C. Significant D. Estimate ______2. A set of data are all close to each other, and they are close to the actual value. This set of data can be described as... A. accurate C. both precise and accurate B. precise D. estimate ______3. When a measurement is repeatable and consistent it is said to have... A. High precision B. Low precision C. High accuracy D. Low accuracy ______4. A set of data are all close to each other, but they are not close to the actual value. This set of data can be described as... A. accurate C. both precise and accurate B. precise D. significant ______5. A set of data are not close to each other, but the average of the data is very close to the actual value. This set of data can be described as... A. accurate C. both precise and accurate B. precise D. significant ______6. What does SI stand for? A. Science Inquiry C. Southern Igloo B. Safety Issues D. System of International Units ______7. What is the measurement using the correct number of sig. figs.? A. 89cm C. 88.90cm B. 88.9cm D. 88cm ______8. The “bullseye” demonstrates… A. High Accuracy & High Precision B. High Accuracy & Low Precision C. Low Accuracy & High Precision D. Low Accuracy & Low Precision ______9. The “bullseye” demonstrates… A. High Accuracy & High Precision B. High Accuracy & Low Precision C. Low Accuracy & High Precision D. Low Accuracy & Low Precision ______10. The metal is 7.1 cm long. A. 7 is the estimated digit C. 7 is the uncertain digit B. 1 is the estimated digit D. Both 7 and 1 are estimated digits ______11. Which student on the data provided below has the most precise data? A. Student A B. Student B C. Student C D. Cannot be determined ______12. Which student on the data below is the most precise AND accurate in determining the melting point of sucrose? A. Student A B. Student B C. Student C D. Cannot be determined ______13. Find the percent error. Round to the nearest tenth of a percent. Estimated length: 32 in. Actual length: 54 in. A. 27.4% B. 70.4% C. 41.8% ______14. How do you write an ordered pair? A. (X,X) B. (Y,X) C. (X,Y) D. 40.7% D. (Y,Y) ______15. The graph represents the height of a burning candle. What is the meaning of the slope? A. the time it takes to burn the entire candle B. the change in the height of the candle each hour it is burning C. the different heights of the candle D. the original height of the candle ______16. What is the letter of the ordered pair (0, 3)? A. A C. R B. M D. L ______17. The graph below represents… A. direct variation B. inverse variation C. neither direct nor inverse variation D. insufficient data ● ● ● ● ______18. The graph on the right represents… A. direct variation B. inverse variation C. neither direct nor inverse variation D. insufficient data ______19. The graph below represents… A. direct variation B. inverse variation C. neither direct nor inverse variation D. insufficient data ______20. . A. direct variation B. inverse variation C. joint variation D. none of these Lesson 1.1 – Physics: A Basic Science EXPLORE Physics is derived from the Greek word “physika” which means “natural things”. It is a science that deals with the properties of matter and energy, and the interaction between them. You cannot dissociate yourself from the world of physics. Look around you, observe the sky, the houses in your neighborhood, and listen to the sounds that reach you from the street. Everything you see, hear, or feel has some link with physics. Physics plays an important role in your daily life as the natural world is governed by the laws of physics. Consider the following everyday life definitions of physics: Physics is a mathematical science. Physics utilizes mathematical concepts and principles to explain and give solution to problems related to certain natural phenomena Physics is the basis of technology. Our simple appliances at home utilize the natural laws of physics (e.g. a can opener, washing machine, transformer, etc.). Physics is a fundamental science. Many facts and theories of physics are fundamental in the study of other sciences. (e.g. (a) Dentists do not confine their knowledge and study to teeth, they need to have some background on leverage in pulling teeth, (b) Optometrists need to have the knowledge of light and lenses, (c) Lawyers must know their physics if he wanted to sue a contractor for a house that collapsed due to faulty construction). Physics is a way of thinking. It answers the question why, how and what of things (e.g. (a) A bridge collapsed, (b) A plane’s wing suddenly snaps while on flight, (c) A ship at sea just turns on the side and sinks without any visible causes). Investigators of these accidents will have to find reasons for the seemingly unexplainable mishaps. Physics is the study of nature. Just like other scientists, physicists also study how nature works. Knowing that nature works in a systematic and consistent way, physicists were able to formulate the laws of nature. Knowing and understanding these laws will enable us to understand nature and make useful things. Physics is an experimental science. Physicists have to learn to ask appropriate questions and design experiments to answer questions and draw appropriate conclusions from the results. In general, a physicist must have wonder, inquiry, creativity, patience, love for work, perseverance, open-mindedness, reverence for men and nature, and humility. The following activity will solicit your concept of how science, technology and the society are interrelated to one another. ACTIVITY 1 – SCIENCE, TECHNOLOGY AND SOCIETY ACTIVITY 1 - A: THE DEFINITION OF SCIENCE: SCIENCE may be classified into three major branches NATURAL SCIENCES is defined as _______________________________ _______________________________ _______________________________ SOCIAL SCIENCES that includes which is subdivided into 1._____________________ 2._____________________ 3._____________________ 4._____________________ 5._____________________ 6._____________________ BIOLOGICAL SCIENCES 1._____________________ 2._____________________ 3._____________________ 4._____________________ 5._____________________ 6._____________________ 7._____________________ 8._____________________ 9._____________________ Sociology Architecture Meteorology Physiology APPLIED SCIENCES 1._____________________ 2._____________________ 3._____________________ 4._____________________ PHYSICAL SCIENCES NOTE: To fill-in the given boxes, refer to the fields of science listed in the box below. 1._____________________ 2._____________________ 3._____________________ 4._____________________ 5._____________________ Astronomy Morphology Linguistics Chemistry Archaeology Phylogeny Engineering Geology Physics Genetics Criminology Biology Economics Histology Veterinary Medicine Psychology Botany Zoology Dentistry Embryology ACTIVITY 1 - B: THE DEFINITION OF TECHNOLOGY 1. Define technology:___________________________________________________________________ 2. Give five examples of technology: _______________________ ______________________ _______________________ _______________________ ______________________ 3. Give five advantages of technology: _______________________ _____________________ _______________________ _______________________ ______________________ 4. Give five disadvantages of technology: _______________________ _____________________ _______________________ _______________________ ______________________ 5. Give at least five (5) helpful ways to reduce or lessen the harmful effects of technology to the environment.________________________________________________________________________ ___________________________________________________________________________________ ___________________________________________________________________________________ ___________________________________________________________________________________ ACTIVITY 1 - C: HOW DO SCIENCE, TECHNOLOGY AND THE SOCIETY INTERRELATE WITH EACH OTHER? A. Complete the diagram below by stating the interconnectedness of science, technology and society. SCIENCE Science to Technology Society to Science Technology to Science Science to Society TECHNOLOGY SOCIETY Society to Technology Technology to Society B. Put a check next to each statement with which you agree. _______1. During ancient times technology existed before science. Explain:___________________________________________________________ _______2. Many products and process of technology have created serious environmental problems. Explain:___________________________________________________________ _______3. Unemployment is another consequence of technology. Explian:___________________________________________________________ _______4. Undesirable effects of technology cannot be totally eliminated. Explian:___________________________________________________________ _______5. Physics through modern technology has been beneficial in many ways. Explian:___________________________________________________________ _______6. Humans can be able to control some aspects of nature. Explian:___________________________________________________________ C. PROBLEM SOLUTION CHART: List down problems commonly encountered in the use of technology in the first column. Then, list solutions to solve the problems in the right column. POSSIBLE PROBLEMS POSSIBLE SOLUTION FIRM UP PHYSICS AND ITS BRANCHES Physics is divided into two main branches – classical physics and modern physics. Classical physics refers to the traditional topics in physics that were recognized and developed before the beginning of the 20th century. These topics are concerned with matter and energy under normal conditions. Modern physics, on the other hand, refers to concepts in physics that have surfaced since the beginning of the 20th century. This branch is mostly concerned with the behavior of matter and energy under extreme conditions. BRANCHES AND SUBBRANCHES OF PHYSICS All fields of science have been developing rapidly and links between them were established. Chemists and astronomers then had to be knowledgeable about physics. Biologists had to be familiar with chemistry and physics. The inclusion of astronomy, chemistry geology, and biology to physics thus became necessary. These gave birth to the recently known branches of physics such as: astrophysics, physical chemistry, geophysics, biophysics, etc. ACTIVITY 2 – FILIPINO AND FOREIGN PHYSICISTS A. Match the names of the following foreign physicists/scientists with their invention by choosing from the box below. Telephone Laws of Elasticity Atomic Bomb Wave Theory of Light Laws of Motion and Gravitation Computer Software Transistors Existence of Radio Waves Gas Laws Originator of the Atomic Theory Steam Engine Technology Laws of Planetary Motion Ohm’s Law Electrochemical Cells 1. John Bardeen 2. Robert Boyle 3. Henry Cavendish 4. James Rutherford 5. John Dalton 6. Alexander Graham Bell 7. Bill Gates 8. Robert Hooke 9. Georg Simon Ohm 10. Alessandro Volta Diesel Engine Earth’s Gravitational Constant Lightning is a Form of Electricity Electromagnetism Theory of Relativity, Quantum Theory Electromagnetic Induction 11. Heinrich Hertz 12. Rudolf Diesel 13. Albert Einstein 14. Michael Faraday 15. Benjamin Franklin 16. Christian Huygens 17. Isaac Newton 18. Hans Christian Oersted 19. James Watt 20. Johannes Kepler B. Match the following Filipino physicists/scientists in the box with their inventions/studies conducted. Write the letter of your choice on the space provided. A. Eduardo San Juan D. Diosdado Banatao G. Dr. Apolinario Nazarea J. Dr. Casimiro del Rosario M. Fe del Mundo B. Dr. Melecio Magno E. Dr. Josefino Comiso H. Amador Muriel, Ph. D. K. Dr. Jose Juliano N. Agapito Flores C. Gregorio Zara F. Roberto del Rosario I. Dr. Eduardo Padlan L. Daniel Dingle 1. Theory of Turbulence 9. Ethernet Controller Chip 2. Effects of Typhoon 10. Incubator 3. Researched on Soft X-rays 4. Radioactiviation and photoneutron counting in analyzing sulfur and calcium 5. Detection of Climate Changes 11. Moon Buggy 6. Basis of Synthetic Vaccine 14. One-Man-Band (OMB) 7. Human antibodies and their potential treatment 15. Solar Water Heater 12.Flourescent Lamp 13. Water Powered Car 8. Two-Way Videophone GUIDE QUESTIONS: 1. Who do you think among the scientists mentioned above has contributed a lot in the field of physics? How did he change the world? ________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 2. If you will invent an instrument or gadget (supported by the government) that will benefit your countrymen, what will it be? Why? ____________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ Lesson 1.2 – Mathematic in Physics FIRM UP Physics without mathematics is unthinkable. In fact, throughout your study of physics, you will find out that the basic rules governing the behavior of nature are readily expressed in mathematical form. SIGNIFICANT FIGURES Numerical values of measurement results are composed of digits known with complete certainty and those considered an estimate. These digits are called significant figures. RULES IN COUNTING THE NUMBER OF SIGNIFICANT FIGURES 1. All nonzero digits are significant. Example: 2 596 4 significant figures 2. All zeros between nonzero digits are significant. Example: 60.08 4 significant figures 3. Zeros to the right of a nonzero digit but to the left of an understood decimal point are not significant unless indicated significant by a bar. Example: 200 000 1 significant figure 200 000 5 significant figures ₱2000 4 significant figures 4. All zeros to the right of a decimal point but to the left of a nonzero digit are not significant. Example: 0.004 21 3 significant figures 5. All zeroes found to the right of the decimal point and to the right of a nonzero digit are significant. Example: 0.003 080 4 significant figures 6. Exponential numbers have no effect on the number of significant figures. Example: 5.20 x 10-3 3 significant figures Why is counting the number of significant figures necessary? It is because the result or final answer to a mathematical problem should be expressed in accordance with the least number of significant figures among the quantities given in the problem. In general, the number of significant figures of a numerical quantity is the number of reliably known digits and is based on the precision of the instrument used in measuring the quantity. ACTIVITY 3 – COUNTING THE NUMBER OF SIGNIFICANT FIGURES A. Count the number of significant figures in the following: 1. 0.000 203 2. 500.00 3. 600 000 000 4. 20 010 5. 63 237 6. 80 002 7. 0.000 000 000 2 8. 5.64 x 10-15 9. 3.0045 10. 0.000 470 = ______________ = ______________ = ______________ = ______________ = ______________ = ______________ = ______________ = ______________ = ______________ = ______________ 11. 463.55 12. 20.050 13. 500 000 14. 0.000 00755 15. 1.00 x 1020 16. 12 000 000 17. 1 000 045 18. 621.00 19. -7.45 x 10-9 20. 0.002 006 = ______________ = ______________ = ______________ = ______________ = ______________ = ______________ = ______________ = ______________ = ______________ = ______________ SCIENTIFIC NOTATION The shorter way of writing a very large and very small number, in the form: N x 10 K called scientific notation. HOW TO WRITE NUMBERS IN SCIENTIFIC NOTATION 1. Move the decimal point after the first significant digit. 2. Indicate the number of times the decimal point is moved as the power of 10. RULE 1: FOR NUMBERS < 1 N x 10 –K power k is always NEGATIVE RULE 2: FOR NUMBER > 1 N x 10 K power k is always POSITIVE ACTIVITY 4 – EXPRESSING NUMBERS IN SCIENTIFIC NOTATION A. Express the following numbers in scientific notation. B. Rewrite the following into standard decimal form. 1. 102 000 000 = ______________________ 1. 8.05 x 10 -11 =_____________________ 2. 0.000 000 708 = ______________________ 2. 4.00 x 10 5 3. 8 145 000 000 = ______________________ 4. 0.002 14 = ______________________ =_____________________ 3. 6.60 x 10 -3 =_____________________ 4. 5.03 x 10 -5 =_____________________ 5. 0.000 000 1002 = ______________________ 5. 7. 304 x 10 10 =_____________________ 6. 360 500 000 = _______________________ 6. 3.15 x 10 -6 =_____________________ 7. 1 200 = _______________________ 7. 2.09 x 10 8 =_____________________ 8. 34 000 000 = _______________________ 8. 5.5 x 10 -13 =______________________ is 9. 0.000 000 808 = _______________________ 9. 3.45 x 10 12 =_____________________ 10. 0.000 005 045 = _______________________ 10. 1.64 x 10 -15 =_____________________ Lesson 1.3 – Measurement a Universal Language FIRM UP ACTIVITY 5 – WHAT IS MEASUREMENT? A. PARTS OF THE BODY AS UNITS OF MEASUREMENT Fill in the blank spaces in the table by measuring the parts of your own body. It was originally measured as the length of three barley grains placed end to end. Distance from tip of the thumb to first knuckle. INCH My INCH = _______________________________ INCHES Length of foot from tip of the longest toe to heel. FOOT My FOOT = _______________________________ INCHES Distance from the shoulder to end of the middle finger with arm outstretched. YARD My YARD = _______________________________ INCHES Width of one hand, including thumb. HAND My HAND = _______________________________ INCHES Distance from pinkie to thumb tip with hand spread out. SPAN My SPAN = _______________________________ INCHES Length from elbow to the middle finger. CUBIT My CUBIT = _______________________________ INCHES Spanish for “upper arm”. BRAZO My BRAZO = _______________________________ INCHES From the Anglo-Saxon word for “embrace,” it was the length of rope held between two hands with two hands with the arms outstretched. FATHOM My FATHOM = _______________________________ INCHES Length of a single step. In Roman times one pace was a double step. PACE My PACE = _______________________________ INCHES QUESTIONS: 1. Compare your results with your classmates. Explain your observations. __________________________________________________________________________________________________ __________________________________________________________________________________________________ __________________________________________________________________________________________________ __________________________________________________________________________________________________ 2. How do you think will the use of body parts affect measurement results in general? __________________________________________________________________________________________________ __________________________________________________________________________________________________ __________________________________________________________________________________________________ __________________________________________________________________________________________________ 3. What is measurement? __________________________________________________________________________________________________ __________________________________________________________________________________________________ __________________________________________________________________________________________________ __________________________________________________________________________________________________ ACTIVITY 6 – ACCURACY AND PRECISION DEFINITIONS: A. Accuracy – how close a measurement is to _______________________________ B. Precision – how close a measurement to _________________________________ PRECISION VS. ACCURACY “Bull’s Eye” Analogy: Look at each target and decide whether the “hits” are precise, accurate, both accurate and precise, or neither accurate nor precise. Put a check on the space provided. (Note: An accurate hit is a bull’s eye!) Accurate? - __________ Precise? - ___________ Accurate? - __________ Precise? - ___________ Accurate? - __________ Precise? - ___________ Accurate? - __________ Precise? - ___________ ACTIVITY 7 – CALCULATING FOR THE DEGREE OF PRECISISON 1. Several lab groups measured the density of aluminum. Here are there data: TEAM 1 2.65 g/cm3 TEAM 2 2.75 g/cm3 TEAM 3 2.80 g/cm3 TEAM 4 2.77 g/cm3 TEAM 5 2.80 g/cm3 TEAM 6 2.65 g/cm3 TEAM 7 2.68 g/cm3 The average length is ______________g/cm3. (This is the mean or average.) Subtract the lowest value from the highest value: _________ g/cm3 (This is the range or spread.) Divide this by 2: __________ g/cm3 (This is the approximate ± deviation from the average.) The precision of the measurement can be shown as Average ± Deviation from the Average. The precision of the measurement was ___________ ± _________ g/cm3. 2. Here is more data. Is this more precise, less precise or the same precision as the above data? ___________ TEAM 1 TEAM 2 2.60 g/cm3 2.70 g/cm3 Show your process. TEAM 3 2.80 g/cm3 TEAM 4 2.75 g/cm3 TEAM 5 2.65 g/cm3 TEAM 6 2.62 g/cm3 TEAM 7 2.78 g/cm3 Note: To compare the precision of data, take a look at the ± Deviation from the average. The larger the deviation, the farther apart are the values making them less precise. ACTIVITY 8 – CALCULATING FOR THE DEGREE OF ACCURACY Accuracy in measurement is determined by calculating the Percentage of Error. The greater its value, the less accurate the measurement is. The lesser its, the more accurate the measurement is. % error = | | x 100 % 1. A student estimated the mass to be 250 g, but upon carefully measuring it, he found the actual mass to be 240 g. What is his percentage of error? 2. A student measured the temperature of boiling water and got an experimental reading of 97.5 OC, however the true boiling point of water is exactly 100 OC. What is the percent error? EXERCISES: A measurement was taken three times. The correct measurement was 68.1 mL. Circle whether the set of measurements is accurate, precise, both or neither. a. 78.1 mL, 43.9 mL, 2 mL accurate precise both neither b. 68.1 mL, 68.2 mL, 68.0 mL accurate precise both neither c. 98.0 mL, 98.2 mL, 97.9 mL accurate precise both neither d. 72.0 mL, 60.3 mL, 68.1 mL accurate precise both neither FIRM UP ERRORS IN MEASUREMENT No measurement is said to be accurate! Errors occur because of the following: 1. Parallax error (incorrectly sighting the measurement). 2. Calibration error (if the scale is not accurately drawn). 3. Zero error (if the device doesn’t have a zero or isn’t correctly set to zero). 4. Damage (if the device is damaged or faulty). 5. Limit of reading of the measurement device (the measurement can only be as accurate as the smallest unit of measurement of the device). Errors are generally categorized into (3) major types: 1. GROSS ERROR • generally the fault of the person using the instruments • such as incorrect reading, incorrect recording, and incorrect calculation • They can be avoided only by taking care in using and reading all instruments. 2. SYSTEMATIC ERROR • Systematic errors in experimental observations usually come from the measuring instruments and environmental factors. • Instrumental errors occur due to wrong construction of the measuring instruments. These types of errors include loading effect and misuse of the instruments. In order to reduce the errors due to faulty instruments, the extreme condition instrument must be recalibrated carefully. • The external conditions of the instrument can result to instrumental errors. External conditions mainly include pressure, temperature, humidity or due to magnetic fields. In order to reduce the environmental errors • Try to maintain the humidity and temperature constant in the laboratory by making some arrangements. • Ensure that there shall not be any external electrostatic or magnetic field around the instrument. 3. RANDOM ERRORS • These errors are due to unknown causes and occur even when have been accounted for. • This variation cannot be corrected by any method of calibration or of control. • Random errors may be avoided by increasing the number of statistical means to obtain the best approximation of the true value measurement. all systematic errors other known method readings and using of the quantity under ACTIVITY 9 – REDUCING ERRORS IN MEASUREMENT Accomplish the graphic organizer below by identifying the problems you encountered in measurement and listing your solutions to each problem. POSSIBLE PROBLEMS POSSIBLE SOLUTIONS QUESTIONS: 1. What is the significance of using a measuring instrument? __________________________________________________________________________________________________ __________________________________________________________________________________________________ __________________________________________________________________________________________________ __________________________________________________________________________________________________ __________________________________________________________________________________________________ 2. To make measurements more accurate can you ask several people to do the measuring process and then take the average of their reading? Why or why not? __________________________________________________________________________________________________ __________________________________________________________________________________________________ __________________________________________________________________________________________________ __________________________________________________________________________________________________ __________________________________________________________________________________________________ 3. Why is it important to perform the measuring process carefully and systematically? __________________________________________________________________________________________________ __________________________________________________________________________________________________ __________________________________________________________________________________________________ __________________________________________________________________________________________________ __________________________________________________________________________________________________ Lesson 1.4 – Equations: Relationship in a Capsule FIRM UP KINDS OF PROPORTION OR VARIATION BETWEEN VARIABLES A. DIRECT PROPRTION – as one quantity increases, the other quantity also increases Expressed in the equation: y = kx where: k – constant of the variation; y – dependent variable; x – independent variable In equation form the relationship may be expressed as: C = kD B. INVERSE PROPORTION – as one quantity increases, the other quantity decreases, and vice versa. Expressed in the equation: = expressed as: In equation form the relationship mayybe V=k/P C. DIRECT SQUARE PROPORTION – as the square of one quantity increases, the other quantity also increases Expressed in the equation: y = kx2 In equation form the relationship may be expressed as: A = kr2 D. INVERSE SQUARE PROPORTION – as the square of one quantity increases, the other quantity decreases, and vice versa Expressed in the equation: y= In equation form the relationship may be expressed as: mv2 = k then, m = k / v2 In all cases given above: k (the constant of variation, which is equivalent to the slope of a line) is determined by taking two known points P1 (x1,y1) and P2 (x2,y2). Then, using the formula for slope (m) = ᐃy / ᐃx, or m = (y2 – y1) / (x2 – x1) ( ) ( ) FIRM UP FORMULA is a set of algebraic symbols representing a mathematical fact, rule or principle. The symbol for the unknown quantity is written on the left-hand side of the equal sign. The symbols of the known quantities are written on the right-hand side of the equal sign FORMULA TRANSFORMATION is the process of rearranging the symbols in a given formula to change its subject. ACTIVITY 10 – MANIPULATING EQUATIONS Transform the following formula. Then, determine the relationship between the indicated variables. 1. GIVEN: A = lw FIND THE EQUATION FOR: a. l b. W DETERMINE THE RELATIONSHIP BETWEEN: a. Length and Area b. Width and Length c. Area and Width 2. GIVEN: d = gt2 FIND THE EQUATION FOR: a. g b. t DETERMINE THE RELATIONSHIP BETWEEN: a. Distance and square of time b. Acceleration due to gravity and square of time c. Distance and acceleration due to gravity 3. GIVEN: Fe = k FIND THE EQUATION FOR: a. c. b. d. k DETERMINE THE RELATIONSHIP BETWEEN: a. k and Fe c. Fe and q1·q2 b. Fe and r2 d. q1·q2 and r2 4. GIVEN: d = 2π √ FIND THE EQUATION FOR: a. m b. k DETERMINE THE RELATIONSHIP BETWEEN: a. d2 and m c. m and k b. d2 and k DEEPEN ACTIVITY 11 – CAREERS IN PHYSICS INSTRUCTION: Name five (5) fields of specialization related to physics and the corresponding careers that one could pursue after college. FIELD OF SPECIALIZATION CAREERS TRANSFER KINDS OF DATA: A. QUALITATIVE DATA – are non-numerical information describing objects or situations B. QUANTITATIVE DATA – data expressing a certain quantity, amount or range. A graph provides a picture of the relationships existing between the variables in a given set of data. A smooth-line graph displays information as a series of data points called 'markers' and how they are connected to form a line (may take the shape of a parabola, hyperbola or a smooth-straight line graph) used to determine the trend of the variation between variables, rather than how the points are plotted in the graph. STEPS IN PREPARING A GRAPHICAL REPRESENATION OF EXPERIMENTAL DATA 1. Identify the dependent and independent variables. 2. 3. 4. 5. 6. 7. Dependent Variable – the variable being tested in a scientific experiment and whose value depends on another variable (also called the y-variable) Independent Variable - the variable that is changed or controlled in a scientific experiment and whose value does not depend on that of another (also called the xvariable) Use the most convenient scale of the coordinate axis and calibrate each axis equally. Plot the points and draw the graph Line of Best Fit is drawn if the points do not lie on a straight line but show a straight line trend. Determine the kind of relationship existing between the variables of the graph. Express the relationship in equation form. Calculate the constant of variation k. Perform interpolation and extrapolation to estimate other values for the given variables. Extrapolation is a process of estimating values that lie beyond the graph by extending it. Interpolation is the process of estimating values between two points of a graph. EXAMPLE: 1. Consider the dependence of the circumference (C) of the circle on its diameter (D) in the given table. DIAMETER (cm) CIRCUMFERENCE (cm) 1 3.14 2 6.28 3 9.42 4 12.56 5.5 ? ? 8.00 a. Plot the points in a graph b. Describe the relationship that exist between the Circumference (C) and Diameter (D) c. Determine the constant of variation. d. Express the relationship in equation form. e. Determine the diameter if the circumference is 8.00 cm. f. Determine the circumference if the diameter is 5.5 cm. ACTIVITY 12 – GRAPHICAL DATA Draw the graph of the following data. TABLE 1: LENGTH OF VIBRATING STRING AND FREQUENCY OF NOTES LENGTH (l) (m) Frequency (f) (1/s) 7.5 3.14 15 6.28 20 9.42 ? 12.56 80 96 2400 ? a. b. c. d. e. f. Plot the points in a graph Describe the relationship between the variables. Determine the constant of variation. Express the relationship in equation form. Determine the length if the frequency is 128/s (128 Hz). Determine the frequency if the length is 240 m. TABLE 2: STRETCHING FORCE AND ELONGATION OF SPRING FORCE (F) (N) ELONGATION (e) (m) 8 3.2 15 6 25 ? 37.5 15 ? 22 a. b. c. d. e. f. Plot the points in a graph Describe the relationship between the variables. Determine the constant of variation. Express the relationship in equation form. Determine the elongation if the stretching force is 25N. Determine the amount of force applied if the elongation is 22m. ACTIVITY 13 – EXPLORING FURTHER ACCURACY AND PRECISION Explain how accuracy and precision are important to the following occupations: 1. chemist __________________________________________________________ ___________________________________________________________ __________________________________________________________ 2. pilot __________________________________________________________ __________________________________________________________ __________________________________________________________ 3. astronaut __________________________________________________________ __________________________________________________________ __________________________________________________________ 4. dressmaker__________________________________________________________ __________________________________________________________ __________________________________________________________ 5. traffic enforcer_______________________________________________________ __________________________________________________________ __________________________________________________________ 6. news reporter________________________________________________________ __________________________________________________________ __________________________________________________________ 7. civil engineer________________________________________________________ __________________________________________________________ __________________________________________________________ 8. stockbroker_________________________________________________________ __________________________________________________________ __________________________________________________________ 9. accountant__________________________________________________________ __________________________________________________________ __________________________________________________________ 10. geneticist __________________________________________________________ __________________________________________________________ __________________________________________________________ TRANSFER Physical quantities are quantities derived from taking measurements. Fundamental Quantities are quantities that can be measured directly using a specific instrument. Examples are length, mass, time, temperature, luminous intensity, electric current, and amount of substance. Derived quantities are quantities that are based on fundamental measurement; can be a combination of fundamental quantities or a combination of fundamental and derived quantities. Examples are area, volume, density, speed, acceleration weight, etc. CONVERSION FACTORS LENGTH 1 cm = 10 mm 1 in = 2.54 cm 1 ft = 12 in 1 m = 100 cm 1 yd = 3 ft 1 km = 1000 m 1 mi = 1.6093 km MASS 1 g = 1000 mg 1 kg = 1000 g 1 kg = 2.205 lb 1 ton = 1000 kg 1 lb = 16 oz 1 amu = 1.6605402 x 10-24 g VOLUME 1 mL = 1 cm3 1 L = 1000 mL 1 gal = 4 qt 1 gal = 128 oz 1 m3 = 35.3147 ft3 AREA 1 ha = 10 000 m2 1 ha = 2.471 acres 1 km2 = 1 x 106m2 1 m2 = 1 x 104 cm2 1 m3 = 1000 mL 1 L = 1 dm3 1 qt = 2 pt 1 gal = 3.78541 L 1 in3 = 16.4 cm3 FORCE 1N = 100 000 dynes ENERGY 1 kcal = 1000 cal 1 kcal = 4184 J 1 J = 0.2388 cal 1 J = 1 x 107 erg PRESSURE 1 bar = 1 x 105 Pa 1 atm = 1.01325 x 105 Pa 1 atm = 1.01325 bar 1 atm = 760 torr = 760 mmHg TEMPERATURE O F = OC + 32 O C = (OF – 32) K = OC + 273.15 EXAMPLES: 1. 67.5 gal = _________ pt 67.5 gal x x 71 kg x = 540 pt x = 2504.88 oz 2. 71 kg = _______ oz 3. 67.5 OF = ______ K Step 1: Convert OF measure to OC (67.5OF-32) = 19.72 OC Step 2: Convert OC measure to K 19.72 OC + 273.15 = 292.87 K ACTIVITY 14 – CONVERSION OF UNITS Convert the following. 1. 0.310 ton = _____ g 6. 22.5 mi = __________ m 2. 450 torr = _____ Pa 7. 48 oz = __________ kg 3. 84 OF = _____ K 8. 10 pt = __________ cm3 4. 327 oz = _____ m3 9. 105 bar = __________ Pa 5. 45 ha = _____ cm2 10. -78 OF = __________ OC Note: Round-off your final answers to the nearest hundredths. END OF TRANSFER In this module, you have examined the nature of physics, its significant contributions to world, the mathematical principles it requires, and the significance of accuracy and precision in measurement. According to Colossians 4:2-6, “Devote yourselves to prayer, being watchful and thankful. And pray for us, too, that God may open a door for our message, so that we may proclaim the mystery of Christ, for which I am in chains. Pray that I may proclaim it clearly, as I should. Be wise in the way you act toward outsiders; make the most of every opportunity. Let your conversation be always full of grace, seasoned with salt, so that you may know how to answer everyone.” Processing Questions: 1. What is the message of the scripture text? 2. Why is prayer the most important guide in anything we do? 3. How can you be sensible to others? 4. How would you relate the text in the development of science and technology? You have completed this lesson. Before you go to the next lesson, you have to answer the following post-assessment questions. EXIT CARDS The most important thing I learned… The most challenging part of the lesson… I would like to learn more about… I wish… POST-ASSESSMENT Now, it’s time to evaluate your learning. ______1. What is the constant of proportionality? A. 45 B. 50 C. 27 D. 1 ______2. Concrete building blocks weigh 28 pounds each. If b represents the number of concrete blocks and w represents the weight, what equation relates the two variables? A. 28/w=b B. 28w=b C. 28b=w D. 28bw ______3. Zane walked 2 miles to school yesterday. What is this distance in feet? A. 3520 ft B. 9000 ft C. 10,560 ft D. 15,840 ft ______4. Shawn bought 5 pounds of potatoes. What is this value in ounces? A. 8 oz B. 80 oz C. 40 oz D. 240 oz ______5. It is a measure of how close measurements come to each other when they are made in the same way. A. Accuracy B. Precision C. Error D. Extrapolation ______6. Q. Describe the accuracy and precision of the image A. Accurate and Precise C. Not Accurate and Precise B. Accurate and not precise D. not accurate and not precise ______7. Which Student is the most Precise? A. Alex C. Luis B. Chandra D. Alex and Luis ______8. The students measured length during a science experiment, they got 12 cm. But the actual measurement was 14.25 cm. What was the percent error? A. 15.79% B. 18.75% C. 2.25% D. 18% ______9. This image is an example of... A. precision ONLY C. BOTH precision and accuracy B. accuracy ONLY D. NEITHER precision and accuracy ______10. Q. What does the Direct Variation Equation look like? A. y= kx B. y = mx + b C. y = b D. y = x ______11. Which of the following represents indirect variation? A. y = kx B. y = k/x C. y = x/k D. y = mx + b ______12. What ordered pair does a direct variation always go through when graphed? A. (0, 0) B. (1, 0) C. (0, 1) D. (1, 1) ______13. A chemist measured the amount of caffeine in a new energy drink called FlipOUT to be 84.20 mg. The correct amount of caffeine is 87.10 mg. Calculate the percent error. A. 9.6% B. 3.4% C. 3.3% D. 0.033% ______14. What type of variation does this scenario represent? The outside temperature and the number of layers of clothes you need to wear outside to feel comfortable. A. direct variation C. joint variation B. inverse variation D. none of these ______15. What type of variation does this scenario represent? You and some friends decide to buy 2 pizzas and split the cost evenly. The number of friends who are sharing the cost of the pizzas and the amount of money you pay for your share. A. direct variation C. joint variation B. inverse variation D. none of these ______16. Y varies directly with x, and y is 84 when x is 16. Which equation represents this situation? (Find k first.) A. y=1344x B. y=100x C. y=5.25x D. y=4/21x ______17. Determine the type of variation: A. Direct B. Inverse C. Neither D. Both A and B ______18. Which of the given graphs is a direct variation? A. A B. B C. C D. D ______19. Is the given table a direct or inverse variation? What is the constant of variation? (Hint: As the x-values are increasing, what are the y-values doing?) A. Direct, 12 C. Direct, 1/12 B. Inverse, 12 D. Inverse, 1/12 ______20. Is the given table a direct variation? If so, what is the constant of variation? A. Yes; 1/3 C. Yes; 5 B. Yes; 3 D. No - END -