General Physics 1 Quarter 1 - Module 1 PDF

Senior High School General Physics 1 Quarter 1 - Module 1 Units, Physical Quantities and Measurements General Physics 1- Grade 12 Alternative Delivery Mode Quarter 1 - Module 1: Units, Physical Quantities and Measurements First Edition, 2020 Republic Act 829...

Senior High School General Physics 1 Quarter 1 - Module 1 Units, Physical Quantities and Measurements General Physics 1- Grade 12 Alternative Delivery Mode Quarter 1 - Module 1: Units, Physical Quantities and Measurements First Edition, 2020 Republic Act 8293, section 176 states that: No copyright shall subsist in any work of the Government of the Philippines. However, prior approval of the government agency or office wherein the work is created shall be necessary for exploitation of such work for profit. Such agency or office may, among other things, impose as a condition the payment of royalty. Borrowed materials (i.e., songs, stories, poems, pictures, photos, brand names, trademarks, etc.) included in this book are owned by their respective copyright holders. Every effort has been exerted to locate and seek permission to use these materials from their respective copyright owners. The publisher and authors do not represent nor claim ownership over them. Published by the Department of Education – Division of Cagayan de Oro Schools Division Superintendent: Dr. Cherry Mae L. Limbaco, CESO V Development Team of the Module Author: Melanie B. Comcom Reviewers: Illustrators and Layout Artists: Management Team Chairperson: Cherry Mae L. Limbaco, Ph.D., CESO V Schools Division Superintendent Co-Chairperson: Alicia E. Anghay, Ph.D., CESE Assistant Schools Division Superintendent Members Printed in the Philippines by Department of Education – Division of Cagayan de Oro City Office Address: Fr. William F. Masterson Ave Upper Balulang Cagayan de Oro Telefax: (08822)855-0048 E-mail Address: [email protected]  Senior High School General Physics 1 Quarter 1 - Module 1: Units, Physical Quantities and Measurements This instructional material was collaboratively developed and reviewed by educators from public schools. We encourage teachers and other education stakeholders to email their feedback, comments, and recommendations to the Department of Education at action@ deped.gov.ph. We value your feedback and recommendations.  Table of Contents What This Module is About i What I Need to Know i How to Learn from this Module ii Icons of this Module ii What I Know iii First Quarter Lesson 1: Unit Conversion and Scientific Notation What I Need to Know 1 What’s In: Check It Out! 2 What’s New: Pass the Message 3 What Is It: Learning Concept: Scientific Notation 4 Significant Figures 5 What’s More: Exercises 6 What Is It: Learning Concepts: Unit Conversion 7-9 What’s More: Exercises 10 What I Have Learned: 11 What I Can Do: Performance Task and Enrichment Activity 12 Sample Format for the Performance task ……………………13-14 Lesson 2: Accuracy and Precision What’s In 15 What I Need to Know 15 What’s New 16 What Is It: Learning Concepts: Accuracy & Precision 17-18 What’s More: Data Analysis 19 What I Have Learned: 20 Assessment: (Post-Test) 21 Key to Answers 22 Appendices A &B 23 References 24  Module 1 Units, Physical Quantities and Measurements What This Module is About This module demonstrates your understanding and skill in solving measurement problems involving conversion of units as well as expressing it in scientific notation. Since Physics and measurement are inseparable, measurement entails accuracy and precision. This module emphasizes the difference of the two; accuracy and precision and illustrates its equal importance in taking measurement. This module will help you explore the basic concepts on topics that will help you solve measurement problems in the succeeding topics in Physics. This module has two (2) lessons: Lesson 1- Unit Conversion and Scientific Notation Lesson 2- Accuracy and Precision What I Need to Know After going through this module, you are expected to: 1. Solve measurement problems involving conversion of units, expression of measurements in scientific notation (STEM_G-12EU-Ia-1) 2. Differentiate accuracy from precision (STEM_G-12EU-Ia-2) How to Learn from This Module Below, are guide steps for you to attain the learning competencies in going about the module: 1. Read the lessons and follow the instructions carefully. 2. Take the pretest to determine how much you know about the content. A multiple-choice test was provided for you. Be honest. 3. Perform all the activities diligently to help you understand the topic. 4. Take the assessment test (post test) at the end of the module. Icons of this Module Here are the Icons used as your guide in every part of the lesson: What I Need to This part contains learning objectives that Know are set for you to learn as you go along the module. What I know This is an assessment as to your level of knowledge to the subject matter at hand, meant specifically to gauge prior related knowledge What’s In This part connects previous lesson with that of the current one. What’s New An introduction of the new lesson through various activities, before it will be presented to you What is It These are discussions of the activities as a way to deepen your discovery and under- standing of the concept. What’s More These are follow-up activities that are in- tended for you to practice further in order to master the competencies. What I Have Activities designed to process what you Learned have learned from the lesson What I can do These are tasks that are designed to show- case your skills and knowledge gained, and applied into real-life concerns and situations.  What I Know MULTIPLE CHOICE: Directions: Read and understand each item and choose the letter of the correct answer. Write your answers on a separate sheet of paper. 1. Which of the following is equivalent to half a meter? A. 500 𝑐𝑚 B. 50 𝑐𝑚 C. 100 𝑚𝑚 D. 10 𝑚𝑚 2. A book has a mass of 500 𝑔, how many kilograms does it weigh? A. 5 𝑘𝑔 B. 1 𝑘𝑔 C. 0.5 𝑘𝑔 D. 0.25 𝑘𝑔 3. Which of the following has the smallest value? A. 29 𝑐𝑚 B. 0. 0025 𝑘𝑚 C. 4.5 × 10−3 𝑚 D. 10,000 𝑚𝑚 4. The average thickness of the leg of an ant is 0.035 𝑐𝑚. How many millimeters is this? A. 35 𝑚𝑚 B. 3.5 𝑚𝑚 C. 0.0035 𝑚𝑚 D. 0.35 𝑚𝑚 5. Which of the following relationships of quantities is TRUE? A. 200 𝑔 = 0.2 𝑘𝑔 C. 1 𝑘𝑔 < 900 𝑔 B. 5 000 𝑔 > 5 𝑘𝑔 D. 0.5 𝑘𝑔 = 5 000 𝑔 6. Which of the following is the BEST example of a number expressed in scientific notation? A. 15.2 × 102 C. 0.71 × 10−2 3 B. 8.43 × 10 D. 0.039 × 10−3 7. What is 7.236 × 10−3 written in standard form? A. 72.36 B. 0.7236 C. 0.007236 D. 0.07236 8. The speed of light in a vacuum is about 299, 800, 000 𝑚/𝑠. Which of the following values in scientific notation is its equivalent? A. 2.998 × 106 𝑚/𝑠 C. 2.998 × 108 𝑚/𝑠 7 B. 2.998 × 10 𝑚/𝑠 D. 2.998 × 109 𝑚/𝑠 9. MOR radio station in Cagayan de Oro city operates at a frequency of 91.9 Mega Hertz. What is 91.9 × 106 𝐻𝑧 written in standard form? A. 9, 190, 000 𝐻𝑧 C. 919, 000, 000 𝐻𝑧 B. 91, 900, 000 𝐻𝑧 D. 9, 190, 000, 000 𝐻𝑧 10. Which of the following is equal to 0.051 × 10−3 ? A. 5.1 × 10−1 B. 5.1 × 10−4 C. 5.1 × 10−5 D. 5.1 × 10−6  Lesson Unit Conversion and 1 Scientific Notation What I Need to Know Physics is an experimental science. Thus, experiments are performed in order to test hypotheses. How do we make conclusions? Conclusions in experiment are derived from measurements. Experiments are performed to measure physical quantities. Physical quantities can be expressed in terms of a number of fundamental quantities. Mass, distance, time are some of these fundamental quantities. A physical quantity will only make sense if compared to a reference standard. For example, a 3.5 𝑚 cloth you bought from Everbest Store means that the cloth’s length is 3.5 times a meter stick (or a tape measure that is 1-m long). Here, the meter stick is considered as our reference standard. Therefore, stating that the cloth is 3.5 is not as informative. Look at the figure to the right. How difficult will it be without a standard? To make sure that scientist throughout the world means the same thing when referring to a measurement; standards have been defined for measurements of time, mass and length. In this lesson, you are to solve measurement problems involving conversion of units, expression of measurements in scientific notation.  What’s In You have learned in your Grade 11 Chemistry the rules of significant figures. Recall that when we say significant figures these are the digits in a number that indicates reliability of a measurement. Check It Out! Determine the number of significant figures of the values given below: 1. 0.0025 🡪 ___________ 2. 12. 00030 🡪 ___________ 3. 3.1416 🡪 ___________ 4. 20.20 🡪 ___________ 5. 0. 4 🡪 ___________ Rules in Determining the Number of Significant Figure: (A short recall) 1. All nonzero digits are significant. 2. All zeros between nonzero digits are significant. 3. All zeros before the first nonzero digit are NOT significant. 4. All zeros to the right of the last nonzero digit are significant. This concept which you learned in your previous science subject will be used in our entire topic involving measurement. Thus, it is important to remember and apply these rules.  What’s New PASS THE MESSAGE A. Situation: You received a text message from your service “You are nearing the provider as shown in the screen of your cellular phone. end of your payment period and you only You need to send the message below but the have one text message message is too long to send as one text message. Shorten left before you go over this to create the shortest text message possible. the limit!” “Hi Kayla! Today, I got drenched in the rain while walking home from school since I forgot to bring my umbrella. I can’t believe it! My bag wasn’t zipped all the way. When I got home all my papers got soaked. I cannot read our homework to be passed tomorrow. Kindly send it to me. Thank you so much!” Write you message in the space provide in the screen of your cellular phone below. _______________________________ _______________________________ _______________________________ _______________________________ _______________________________ _______________________________ _______________________________  What Is It If we shorten a message, we should do it in a way that the message will be useful and easy to understand. Physical quantities vary from very large numbers (e.g. the speed of light in a vacuum = 299, 800, 000 𝑚/𝑠) to very small numbers (length of a certain wavelength of visible light of 0.0000004 𝑚). For scientists and students like you writing large or very small numbers in its standard form can be a waste of time, energy and even your resources like ink and paper. Scientific Notation Scientific notation also called exponential notation is a convenient way of writing values using the power of ten notation wherein we can determine the number of significant digits as well as the place value of the digit. Place values are denoted by prefixes. (See appendix A for the SI prefixes found in the last page of this lesson) Format: 𝐶. 𝑀𝑀𝑀𝑀𝑀 × 10𝑒 where: 𝐶 - the characteristic digit, may be any digit from 0-9 𝑀 – the mantissa digits, may be any digit from 0-9 10 – base 𝑒 – exponent, the number of times the decimal point is moved to either towards left or right Rules in expressing standard notation to scientific notation: 1. When the decimal point is moved from right to left, the result is positive exponent. Example: 7806. 123 = 7. 806123 × 103 = 7.81 × 103 2. When the decimal point is moved left to right, the result is negative exponent. Example: 0.00007806123 = 7.806123 × 10−5 = 7.81 × 10−5 Rules converting scientific notation back to standard notation are shown below. 1. Move the current decimal point according to the number of places based on the exponent (+) positive exponent – move to the RIGHT Example: (−) negative exponent – move to the LEFT Example: Rules in Addition and Subtraction involving scientific notation 1. When two or more quantities are added or subtracted, make sure the exponents are the same. [𝐼𝑓 𝑛𝑜𝑡, 𝑐ℎ𝑜𝑜𝑠𝑒 𝑜𝑛𝑒 𝑡𝑜 𝑎𝑑𝑗𝑢𝑠𝑡 𝑡ℎ𝑒 𝑑𝑒𝑐𝑖𝑚𝑎𝑙 𝑎𝑛𝑑 𝑒𝑥𝑝𝑜𝑛𝑒𝑛𝑡. 𝑈𝑠𝑒 𝐿𝐴𝑅𝑆 (𝐿𝑒𝑓𝑡 𝐴𝑑𝑑, 𝑅𝑖𝑔ℎ𝑡 𝑆𝑢𝑏𝑡𝑟𝑎𝑐𝑡)] 2. Add/subtract the number. Keep the exponent the same. Example: (a) (6.2 × 103 ) + (1.74 × 103 ) = (6.2 + 1.74) × 103 = 7.94 × 103 (b) (7.1 × 103 ) + (5.2 × 105 ) = (0.071 × 105 ) + (5.2 × 105 ) = 5.271 × 105 -Since exponents are not the same, choose one to adjust. -LARS-𝐿𝑒𝑓𝑡 𝐴𝑑𝑑, 𝑅𝑖𝑔ℎ𝑡 𝑆𝑢𝑏𝑡𝑟𝑎𝑐𝑡 (here we will adjust 7.1 × 103 to have an exponent of 105 ) -From 103 𝑡𝑜 105 , we will move two decimal places to the left since we added two to the exponent, that becomes 0.071 × 105 Rules in Multiplication and Division involving scientific notation 1. Powers of ten are added in multiplication Example: (1.50 × 102 ) (1.20 × 103 ) = (1.50)(1.20) × 102+3 = 1.80 × 105 2. Powers of ten are subtracted in division 1.50×102 1.50 Example: =( ) × 102−3 = 1.25 × 10−1 1.20×103 1.20 Significant Figures 1. In adding or subtracting quantities, the least number of decimal places in any of the numbers being added or subtracted should also be the number of the decimal places in the answer. Example: 2.15 𝑚 (two decimal places) + 1.8 𝑚 (one decimal place) → LEAST 0.4367 𝑚 (four decimal places) 4.7 𝑚 (ONE decimal place) 2. In multiplying or dividing quantities, the least number of significant figures in the input number should also be the number of significant figures in the answer. Example: 10.58 𝑐𝑚 (four significant figures) x 2.14 𝑐𝑚 (three significant figures) (LEAST) (three significant figures) 22.6 𝑐𝑚2  What’s More Exercises: Write you answer on a separate sheet of paper. 1. Apply the rules in identifying the number of significant figures in each of the following: (a) 0. 00054 (d) 0. 016500 (b) 830 (e) 32.0040 (c) 356, 000 (f) 5.130 × 105 2. Express the following numbers in scientific notation: (Answers should include three significant figures) (a) 65, 000 (c) 2, 450, 000 (b) 0. 001327 (d) 0. 00001997 3. Perform the indicated operations: (All answers should be expressed in scientific notation. Apply the rules for significant figures in your final answer.) (a) (4.0 × 10−6 ) × (3.0 × 104 ) = (b) (32 × 106 ) − (2 × 107 ) = (3×108 )(8×104 ) (c) = (6×105 ) (d) 0.868 𝑘𝑔 + 2.35 𝑘𝑔 − 21.5 𝑘𝑔 = (e) (3.25 𝑚)(2.1 𝑚) = 4. Convert the given standard notation below to scientific notation. Then, perform the indicated operation. Apply the rules for significant figures in your final answer. 150, 000 × 0.0025 × 20 = 3, 000, 000 × 0.015 × 150  What Is It Unit Consistency and Conversion of Units There are two major systems of units in the world namely; SI (derived from French Syteme International) units also known as Metric system and the English system. Although the system of units used by engineers and scientists is the metric system since 1960, some countries continue to use the English system of units like for example the United States of America. However, the conversions between the SI unit and English system of units have been well- defined. (See appendix B found in the last page of this lesson for conversion factors) Multiplying and/or dividing units just like ordinary algebraic expressions give an easy way to convert a quantity from one unit to another to be dimensionally consistent. Example: (a) To convert 0.58 𝑚 to 𝑚𝑚 Conversion factor to be used: 1𝑚 = 1 000 𝑚𝑚 1000 𝑚𝑚 0.28 𝑚 × = 280 𝑚𝑚 1𝑚 (b) To convert 90 𝑘𝑚/ℎ in meters per second Conversion factors to be used: 1𝑘𝑚 = 1, 000 𝑚 1 ℎ𝑟 = 60 𝑚𝑖𝑛 1 𝑚𝑖𝑛 = 60 𝑠 𝑘𝑚 1000 𝑚 1ℎ 1 𝑚𝑖𝑛 𝑚 90 × × × = 25 ℎ 1 𝑘𝑚 60 𝑚𝑖𝑛 60 𝑠 𝑠 𝑘𝑔 𝑔 (c) To convert 50 to 𝑚3 𝑐𝑚3 Conversion factors to be used: 1 𝑘𝑔 = 1000 𝑔 1 𝑚 = 100 𝑐𝑚 𝑘𝑔 1000 𝑔 1𝑚 3 𝑔 50 3 × × [ ] = 0.05 𝑚 1 𝑘𝑔 100 𝑐𝑚 𝑐𝑚3 (d) Converting units with different prefixes (See appendix A for the SI prefixes found in the last page of this lesson)  (i.) Example: convert 5 Megameter to meter 5 𝑀𝑚 → 𝑚𝑒𝑔𝑎 𝑓𝑟𝑜𝑚 𝑡ℎ𝑒 𝑡𝑎𝑏𝑙𝑒 𝑎𝑏𝑜𝑣𝑒 𝑚𝑒𝑎𝑛𝑠 106 5 𝑀𝑚 = 5 × 106 𝑚 (ii.) Example: convert 7 𝑚𝑖𝑙𝑙𝑖𝑔𝑟𝑎𝑚𝑠 to 𝑔𝑟𝑎𝑚𝑠 7 𝑚𝑔 → 𝑚𝑖𝑙𝑙𝑖 𝑚𝑒𝑎𝑛𝑠 10−3 𝑓𝑟𝑜𝑚 𝑡ℎ𝑒 𝑡𝑎𝑏𝑙𝑒 7 𝑚𝑔=7 × 10−3 𝑔 (iii.) Example: 5 𝑘𝑚 to 𝑐𝑚 kilo means 103 so, 5 𝑘𝑚 = 5 × 103 𝑚 1 𝑐𝑚 = 1 × 10−2 𝑚 1 𝑐𝑚 (5 × 103 𝑚) × = 5 × 105 𝑐𝑚 𝑜𝑟 500, 000 𝑐𝑚 1×10−2 𝑚 * ANOTHER way to do this: 5 𝑘𝑚 to 𝑐𝑚 Step 1: subtract exponents *kilo has exponent of 103 and centi has exponent of 10−2 3 subtract -2 =5 from kilo to centi Step 2: move decimal places according to difference of exponents to the direction of wanted unit. * move the decimal 5 places to the right (toward centi) 5 𝑘𝑚 = 5 0 0 0 0 0 𝑐𝑚 or 5 × 105 𝑐𝑚 5 decimal places to the right  (iv.) Example: 384.0 𝑚𝑔 to 𝑑𝑔 milli means 10−3 so, 384.0 𝑚𝑔 = 384.0 × 10−3 𝑔 conversion factor (See appendix A for the SI prefixes found in the last page of this lesson) 1𝑑𝑔 = 0.1 𝑔 1 𝑑𝑔 (384.0 × 10−3 𝑔) × = 3. 840 𝑑𝑔 0.1 𝑔 * ANOTHER way to do this: 384.0 𝑚𝑔 to 𝑑𝑔 Step 1: subtract exponents *milli has exponent of 10−3 and deci has exponent of 10−1 -1 − -3 =2 deci milli Step 2: move decimal places according to difference of exponents to the direction of wanted unit. * move the decimal 2 places to the left (toward deci) 384.0 𝑚𝑔 = 3. 8 4 0 𝑑𝑔 2 decimal places to the left  What’s More Exercises: Write you answer on a separate sheet of paper. 1. Below are the given measurements. Convert it as indicated. (a) 365 𝑑𝑎𝑦𝑠 into 𝑚𝑖𝑛 (b) 94.3 𝑀𝐻𝑧 into 𝑘𝐻𝑧 (c) 450 𝑐𝑚2 into 𝑘𝑚2 (d) 72 𝑛𝑚 into 𝑚𝑚 (e) 130 𝑚𝑖/ℎ into 𝑘𝑚/𝑠 (f) 40.0 𝐿 to 𝜇𝐿 (g) 5 𝜇𝐿 to 𝑚𝐿 2. Indicate which is greater (>) or lesser (