General Physics 1, Q1 Week 1 PDF

APPLYING MEASUREMENTS IN PHYSICS for GENERAL PHYSICS 1/ Grade 12 Quarter 1/ Week 1 NegOr_Q1_GenPhysics1_SLKWeek1_v2 NegOr_Q1_GenPhysics1_SLKWeek1_v2 1 ...

APPLYING MEASUREMENTS IN PHYSICS for GENERAL PHYSICS 1/ Grade 12 Quarter 1/ Week 1 NegOr_Q1_GenPhysics1_SLKWeek1_v2 NegOr_Q1_GenPhysics1_SLKWeek1_v2 1  FOREWORD This learning kit will serve as your guide into an in-depth understanding of measurements in Physics. Physicists make observations and ask basic questions like how big is an object? How much mass does it have? How far did it travel? To answer these questions, you need to make measurements with various instruments. There is a great deal in the usefulness of measurements in daily life. The topics herein include solving measurement problems involving conversion of units and expression of measurements in scientific notation and differentiating accuracy and precision. When making careful measurements, the goal is to reduce as many sources of error as possible and to keep track of those errors that cannot be eliminated. Thus, it is useful to know the types of errors that may occur, so that we may recognize them when they arise. In understanding vectors, you are expected to distinguish a vector from a scalar quantity and perform addition of vectors. This learning kit is carefully prepared with set of activities guided with contextualized discussions and illustrations that meet the standards of the K to 12 Curriculum. In using this learning kit, you will realize that physics is a boundless discipline because it covers almost everything man can imagine. The activities included herein are simple, readily understandable, and easy to do. In doing so, you will be given opportunity to broaden your knowledge and enhance your resourcefulness and creativity in performing activities provided. This will enable you to develop your critical thinking skills. The Mathematics involved is simple and does not require you to be Math wizards to fit into analyses. It is hoped that your understanding of the basic concepts will benefit you in many ways and the skills you acquired in using this kit may help you in dealing with practical problems. You are expected to learn from this kit and use this with utmost care while learning from the discussions and tasks which you can apply in your everyday activities. Everyone is capable of learning Physics especially if one takes advantage of one’s unique way of learning. NegOr_Q1_GenPhysics1_SLKWeek1_v2 2 OBJECTIVES At the end of the lesson, you should be able to: K: identify experimental errors and how to estimate errors from multiple measurements of a physical quantity using variance; S: solve measurement problems involving conversion of units and expression of measurements in scientific notation; : demonstrate how to add vectors graphically and by component method; and A: explain the importance of measurements in daily life. LEARNING COMPETENCIES Solve measurement problems involving conversion of units and expression of measurements in scientific notation (STEM_GP12EU-Ia1). Differentiate accuracy from precision (STEM_GP12EU-Ia2). Differentiate random errors from systematic errors (STEM_GP12EU-Ia-3). Estimate errors from multiple measurements of a physical quantity using variance (STEM_GP12EU-Ia-5). Differentiate vector and scalar quantities (STEM_GP12V-Ia-8). Perform addition of vectors (STEM_GP12V-Ia-9). Rewrite vectors in component form (STEM_GP12V-Ia-10). NegOr_Q1_GenPhysics1_SLKWeek1_v2 3 I. WHAT HAPPENED Hi! My name is Rio. I will also be learning with you as we do the activities and tasks this week. We are here to help you learn so allow us to help you in completing different activities Hello STEMates! we will meet along the way Welcome to Physics Can we expect a full blast of Classroom. How are energy and active you today? By the participation from you? way, I am Nairobi. I will help you learn about measurements. That’s good to hear. Come and let us join hands in learning measurements. Let’s begin this with an activity! Are you ready? PRE-TEST Let’s test your stock knowledge! A. Writing Numbers in Different Ways Directions: Read the statements and write the numbers in scientific notation on the space provided before each item. _________ 1. The population of the world is about 7,117,000,000. _________ 2. The distance from Earth to the Sun is about 92,960,000 miles. _________ 3. The human body contains approximately 60,000,000,000,000 or more cells. _________ 4. The mass of a particle of dust is 0.000000000753 kg. _________ 5. The length of the shortest wavelength of visible light (violet) is 0.0000004 meters. NegOr_Q1_GenPhysics1_SLKWeek1_v2 4  Directions: Convert the following measurements. Write your solution on the space provided. Do this in your Science Notebook/Answer Sheet. 6. 586 cm = ___m 7. 4.28 m = ___mm 8. 1396 mg = ___kg 9. 1375L = ___kL 10. 12g = ___cg B. Sorting Out Vectors and Scalars Directions: Complete the data table below by sorting out the quantities into scalar and vector. Write the words in their appropriate boxes. Do this in your Science notebook/Activity Sheet. Force Mass Distance Density Velocity Acceleration Speed Temperature Time Direction Scalar Vector II. WHAT I NEED TO KNOW DISCUSSION Scientific Notation Scientific notation offers a convenient way of expressing very large or very small numbers. A positive number is written as a product of a number between I and l0 and a power of 10. For example, 9.63 x 107 and 2.3 x 10-6 are numbers written in scientific notation. NegOr_Q1_GenPhysics1_SLKWeek1_v2 5  Standard notation to scientific notation Convert each number to scientific notation: a. 580,000,000,000m b. 0.000068g Solution: a. Determine the power of l0 by counting the number of places that the decimal must move so that there is a single nonzero digit to the left of the decimal point (11 places). Since 580,000,000,000 is larger than 10, we use a positive power of 10: 580,000,000,000m = 5.8 x 1011m b. Determine the power of l0 by counting the number of places the decimal must move so that there is a single nonzero digit to the left of the decimal point (five places). Since 0.0000683 is smaller than 1, we use a negative power of l0: 0.0000683g = 6.83x10-5g Using Scientific Notation in Computations A. (4 𝑥 1013 )(5 𝑥 10−9 ) (4 𝑥 1013 )(5 𝑥 10−9 ) = 20 𝑥 1013+ −9 ) Product rule for exponents = 20 𝑥 104 Simplify the exponent = 20 𝑥 101 𝑥 104 Write 20 in scientific notation = 20 𝑥 105 Product for exponents B. 1.2 𝑥 10−9 4 𝑥 10−7 1.2 𝑥 10−9 = 1.2 Quotient rule for exponents 4 𝑥 10−7 4 = 0.3 𝑥 10−2 Simplify the exponent = 3 𝑥 10−3 Use 0.3 = 3 x 10-1 A. To convert 56 nm to meters, multiply: 56 𝑛𝑚 𝑥 1𝑚 = 5.6 𝑥 10−8 𝑚 109 𝑛𝑚 B. To convert 2.45 cm to µm, multiply: 2.45 𝑐𝑚 𝑥 1 𝑚 𝑥 106 𝑚 = 2.45 𝑥 104 𝜇𝑚 102 𝑐𝑚 1 𝑚 NegOr_Q1_GenPhysics1_SLKWeek1_v2 6  Accuracy and Precision Two key aspects of the reliability of measurement outcomes are accuracy and precision. These terms are often used and even defined synonymously. By contrast, these terms are consistently differentiated in the literature of engineering and the “hard sciences”. Accuracy It refers to the closeness of the measurements to the true or accepted value. A new spring balance is likely to be more accurate than an old spring balance that has been used many times. Figure 1. The accuracy of hits on the dartboards Precision It refers to the closeness of the measurements of the results to each other. A physicist who frequently carries out a complex experiment is likely to have more precise results than someone who is just learning the experiment. Figure 2. The precision of hits on the dartboards NegOr_Q1_GenPhysics1_SLKWeek1_v2 7  There are certain factors affecting the precision and accuracy of a measurement. These are a.) measuring device used, b.) manner of measurement, and c.) condition of the environment during measurement. Degree of Accuracy and Precision The center of the bull’s-eye represents the accepted value. The closer a dart is to a bull’s-eye, the more accurate the throwing of the dart. The closer the darts are to each other, the more precise the throws. High accuracy and precision High accuracy; Low precision Low accuracy; High precision Low accuracy and precision It would be impossible to make a very precise measurement because the instrument is very sensitive but have that same measurement be inaccurate because the instrument was uncalibrated or you made a wrong reading. The precision of an instrument is limited by the smallest division on the measurement scale while the accuracy of an instrument depends on how well its performance compares to a currently accepted value. Experimental Errors All experimental uncertainty is due to either random errors or systematic errors. Random errors are statistical fluctuations (in either direction) in the measured data due to the precision limitations of the measurement device. NegOr_Q1_GenPhysics1_SLKWeek1_v2 8  Measurement errors may be classified as either random or systematic, depending on how the measurement was obtained (an instrument could cause a random error in one situation and a systematic error in another). Random errors usually result from the experimenter’s inability to take the same measurement in exactly the same way to get exact the same number. Random errors are statistical fluctuations (in either direction) in the measured data due to the precision limitations of the measurement device. Random errors can be evaluated through statistical analysis and can be reduced by averaging over a large number of observations. Systematic errors, by contrast, are reproducible inaccuracies that are consistently in the same direction. Systematic errors are often due to a problem which persists throughout the entire experiment. Systematic errors are reproducible inaccuracies that are consistently in the same direction. These errors are difficult to detect and cannot be analyzed statistically. If a systematic error is identified when calibrating against a standard, applying a correction or correction factor to compensate for the effect can reduce the bias. Unlike random errors, systematic errors cannot be detected or reduced by increasing the number of observations. Source:https://lawrencekok.blogspot.com/2014/03/ib-chemistry-on-uncertainty-error.html NegOr_Q1_GenPhysics1_SLKWeek1_v2 9  Source: https://lawrencekok.blogspot.com/2014/03/ib-chemistry-on-uncertainty-error.html When making careful measurements, our goal is to reduce as many sources of error as possible and to keep track of those errors that we cannot eliminate. It is useful to know the types of errors that may occur, so that we may recognize them when they arise. Common sources of error in physics laboratory experiments are: Incomplete definition (may be systematic or random) — One reason that it is impossible to make exact measurements is that the measurement is not always clearly defined. For example, if two different people measure the length of the same string, they would probably get different results because each person may stretch the string with a different tension. The best way to minimize definition errors is to carefully consider and specify the conditions that could affect the measurement. Failure to account for a factor (usually systematic) — The most challenging part of designing an experiment is trying to control or account for all possible factors except the one independent variable that is being analyzed. For instance, you may inadvertently ignore air resistance when measuring free-fall acceleration, or you may fail to account for the effect of NegOr_Q1_GenPhysics1_SLKWeek1_v2 10 the Earth's magnetic field when measuring the field near a small magnet. The best way to account for these sources of error is to brainstorm with your peers about all the factors that could possibly affect your result. Environmental factors (systematic or random) — Be aware of errors introduced by your immediate working environment. You may need to take account for or protect your experiment from vibrations, drafts, changes in temperature, and electronic noise or other effects from nearby apparatus. Instrument resolution (random) — All instruments have finite precision that limits the ability to resolve small measurement differences. For instance, a meter stick cannot be used to distinguish distances to a precision much better than about half of its smallest scale division (0.5 mm in this case). One of the best ways to obtain more precise measurements is to use a null difference method instead of measuring a quantity directly. Calibration (systematic) — Whenever possible, the calibration of an instrument should be checked before taking data. If a calibration standard is not available, the accuracy of the instrument should be checked by comparing with another instrument that is at least as precise, or by consulting the technical data provided by the manufacturer. Zero offset (systematic) — When making a measurement with a micrometer caliper, electronic balance, or electrical meter, always check the zero reading first. Re-zero the instrument if possible, or at least measure and record the zero offset so that readings can be corrected later. It is also a good idea to check the zero reading throughout the experiment. Failure to zero a device will result in a constant error that is more significant for smaller measured values than for larger ones. Physical variations (random) — It is always wise to obtain multiple measurements over the widest range possible. Doing so often reveals variations that might otherwise go undetected. These variations may call for closer examination, or they may be combined to find an average value. Parallax (systematic or random) — This error can occur whenever there is some distance between the measuring scale and the indicator used to obtain a measurement. If the observer's eye is not squarely aligned with the pointer and scale, the reading may be too high or low (some analog meters have mirrors to help with this alignment). Instrument drift (systematic) — Most electronic instruments have readings that drift over time. The amount of drift is generally not a concern, but occasionally this source of error can be significant. NegOr_Q1_GenPhysics1_SLKWeek1_v2 11  Lag time and hysteresis (systematic) — Some measuring devices require time to reach equilibrium and taking a measurement before the instrument is stable will result in a measurement that is too high or low. A common example is taking temperature readings with a thermometer that has not reached thermal equilibrium with its environment. A similar effect is hysteresis where the instrument readings lag behind and appear to have a "memory" effect, as data are taken sequentially moving up or down through a range of values. Hysteresis is most commonly associated with materials that become magnetized when a changing magnetic field is applied. Personal errors come from carelessness, poor technique, or bias on the part of the experimenter. The experimenter may measure incorrectly, or may use poor technique in taking a measurement, or may introduce a bias into measurements by expecting (and inadvertently forcing) the results to agree with the expected outcome. For example, if you are trying to use a meter stick to measure the diameter of a tennis ball, the uncertainty might be ± 5 mm, but if you used a Vernier caliper (measuring tool), the uncertainty could be reduced to maybe ± 2 mm. The limiting factor with the meter stick is parallax, while the second case is limited by ambiguity in the definition of the tennis ball's diameter (it's fuzzy!). In both of these cases, the uncertainty is greater than the smallest divisions marked on the measuring tool (likely 1 mm and 0.05 mm respectively). Unfortunately, there is no general rule for determining the uncertainty in all measurements. Experimental Errors Systematic Random Errors Errors Reduces Accuracy Reduces Reliability Estimating Uncertainty in Repeated Measurements Suppose you time the period of oscillation of a pendulum using a digital instrument (that you assume is measuring accurately) and find: T = 0.44 seconds. This single measurement of the period suggests a precision of ±0.005s, but this instrument precision may not give a complete sense of the NegOr_Q1_GenPhysics1_SLKWeek1_v2 12 uncertainty. If you repeat the measurement several times and examine the variation among the measured values, you can get a better idea of the uncertainty in the period. For example, here are the results of 5 measurements, in seconds: 0.46, 0.44, 0.45, 0.44, 0.41. 𝑥1 + 𝑥2 + ⋯ + 𝑥𝑁 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 (𝑚𝑒𝑎𝑛) = 𝑁 For this situation, the best estimate of the period is the average, or mean. Whenever possible, repeat a measurement several times and average the results. This average is generally the best estimate of the "true" value (unless the data set is skewed by one or more outliers which should be examined to determine if they are bad data points that should be omitted from the average or valid measurements that require further investigation). Generally, the more repetitions you make of a measurement, the better this estimate will be, but be careful to avoid wasting time taking more measurements than is necessary for the precision required. Consider, as another example, the measurement of the width of a piece of paper using a meter stick. Being careful to keep the meter stick parallel to the edge of the paper (to avoid a systematic error which would cause the measured value to be consistently higher than the correct value), the width of the paper is measured at a number of points on the sheet, and the values obtained are entered in a data table. Note that the last digit is only a rough estimate, since it is difficult to read a meter stick to the nearest tenth of a millimeter (0.01 cm). Observation Width (cm) #1 31.33 𝑠𝑢𝑚 𝑜𝑓 𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑 𝑤𝑖𝑑𝑡ℎ𝑠 #2 31.15 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 = 𝑛𝑜. 𝑜𝑓 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛𝑠 #3 31.26 155.96 𝑐𝑚 = = 31.19 𝑐𝑚 #4 31.02 5 #5 31.20 This average is the best available estimate of the width of the piece of paper, but it is certainly not exact. We would have to average an infinite number of measurements to approach the true mean value, and even then, we are not guaranteed that the mean value is accurate because there is still some systematic error from the measuring tool, which can never be calibrated perfectly. So how do we express the uncertainty in our average value? NegOr_Q1_GenPhysics1_SLKWeek1_v2 13  One way to express the variation among the measurements is to use the average deviation. This statistic tells us on average (with 50% confidence) how much the individual measurements vary from the mean. ̅ |𝑥1 − 𝑥̅ | + |𝑥2 − 𝑥̅ | + ⋯ + |𝑥𝑁 − 𝑥| 𝑑̅ = 𝑁 However, the standard deviation is the most common way to characterize the spread of a data set. The standard deviation is always slightly greater than the average deviation, and is used because of its association with the normal distribution that is frequently encountered in statistical analyses. To calculate the standard deviation for a sample of N measurements: 1. Sum all the measurements and divide by N to get the average, or mean. 2. Now, subtract this average from each of the N measurements to obtain N "deviations". 3. Square each of these N deviations and add them all up. 4. Divide this result by (N − 1) and take the square root. We can write out the formula for the standard deviation as follows. Let the N measurements be called 𝑥1 , 𝑥2 , … , 𝑥𝑁. Let the average of the N values be called 𝑥̅. Then each deviation is given by 𝛿𝑥𝑖 = 𝑥𝑖 − 𝑥, ̅ 𝑓𝑜𝑟 𝑖 = 1,2,... , 𝑁. The standard deviation is: (𝛿𝑥12 + 𝛿𝑥22 + ⋯ + 𝛿𝑥𝑁2 ) ∑ 𝛿𝑥12 𝑠=√ = √ 𝑁−1 (𝑁 − 1) In our previous example, the average width 𝑥̅ is 31.19 cm. The deviations are: Observation Width (cm) Deviation (cm) #1 31.33 +0.14 = 31.33 – 31.19 #2 31.15 -0.04 = 31.15 – 31.19 #3 31.26 +0.07 = 31.26 – 31.19 #4 31.02 -0.17 = 31.02 – 31.19 #5 31.20 +0.01 = 31.20 - 31.19 The significance of the standard deviation is this: if you now make one more measurement using the same meter stick, you can reasonably expect NegOr_Q1_GenPhysics1_SLKWeek1_v2 14 (with about 68% confidence) that the new measurement will be within 0.12cm of the estimated average of 31.19 cm. In fact, it is reasonable to use the standard deviation as the uncertainty associated with this single new measurement. However, the uncertainty of the average value is the standard deviation of the mean, which is always less than the standard deviation. Identifying Scalars and Vectors Physical quantities can be specified completely by giving a single number and the appropriate unit. For example, “a TV program lasts 40 min” or “the water tumbler holds 500 mL” or “the distance between two posts is 50 m.” A physical quantity that can be specified completely in this manner is called a scalar quantity. A scalar is a quantity that is completely specified by its magnitude and has no direction. Examples of scalars are mass, volume, distance, temperature, energy, and time. When giving someone directions to your house, you must include both the distance and the direction. The information “two kilometers north” is an example of a vector. A vector is a quantity that includes both a magnitude and a direction. Other examples of vectors are velocity, acceleration, and force. Vectors are arrows that represent two pieces of information: a magnitude value (the length of the arrow) and a directional value (the way the arrow is pointed). In terms of movement, the information contained in the vector is the distance traveled and the direction traveled. Vectors give us a graphical method to calculate the sum of several simultaneous movements. The average deviation is: 𝑑̅ = 0.086 𝑐𝑚. (0.14)2 +(0.04)2+(0.07)2 +(0.17)2 +(0.01)2 The standard deviation is: 𝑠 = √ = 0.12 𝑐𝑚 5−1 NegOr_Q1_GenPhysics1_SLKWeek1_v2 15  We draw a vector from the initial point or origin (called the “tail” of a vector) to the end or terminal point (called the “head” of a vector), marked by an arrowhead. Magnitude is the length of a vector and is always a positive scalar quantity. To sum it up, a vector quantity has a direction and a magnitude, while a scalar has only a magnitude. You can tell if a quantity is a vector by whether it has a direction associated with it. Adding Vectors Using Pythagorean Theorem Consider the following examples below. Example 1: Blog walks 35 m East, rests for 20 s and then walks 25 m East. What is Blog’s overall displacement? Solve graphically by drawing a scale diagram. 1 cm = 10 m Place vectors head to tail and measure the resultant vector. Solve algebraically by adding the two magnitudes. We can only do this because the vectors are in the same direction. R= 35 m East + 25 m East = 60 m East Example 2: Blog walks 35 m [E], rests for 20 s and then walks 25 m [W]. What is Blog’s overall displacement? x + x 1 2 Using algebraic solution, we can still add the two magnitudes. We can only do this because the vectors are parallel. We must make one vector negative to indicate opposite direction. R = 35 m East + 25 m West = 35 m East + – 25 m East = 10 m East (Note that 25 m West is the same as – 25 m East) NegOr_Q1_GenPhysics1_SLKWeek1_v2 16  If the vectors occur such that they are perpendicular to one another, the Pythagorean theorem may be used to determine the resultant. Example 3: Eric leaves the base camp and hikes 11 km, north and then hikes 11 km east. Determine Eric's resulting displacement. This problem asks to determine the result of adding two displacement vectors that are at right angles to each other. This can be added together to produce a resultant vector that is directed both north and east. When the two vectors are added head-to-tail as shown below, the resultant is the hypotenuse of a right triangle. The resultant can be determined using the Pythagorean theorem; it has a magnitude of 15.6 km. Source: https://www.physicsclassroom.com The Pythagorean theorem works when the two added vectors are at right angles to one another - such as for adding a north vector and an east vector. Consider the vector addition problem: Example 4: A student drives his car 6.0 km, North before making a right-hand turn and driving 6.0 km to the East. Finally, the student makes a left-hand turn and travels another 2.0 km to the north. What is the magnitude of the overall displacement of the student? When these three vectors are added together in head-to-tail fashion, the resultant is a vector that extends from the tail of the first vector (6.0 km, North, shown in red) to the arrowhead of the third vector (2.0 km, North, shown in green). The head-to-tail vector addition diagram is shown below. NegOr_Q1_GenPhysics1_SLKWeek1_v2 17  Source: https://www.physicsclassroom.com The resultant vector (drawn in black) is not the hypotenuse of any right triangle yet it would be possible to force this resultant vector to be the hypotenuse of a right triangle. To do so, the order in which the three vectors are added must be changed. The vectors above were drawn in the order in which they were driven. But if the three vectors are added in the order 6.0 km, N + 2.0 km, N + 6.0 km, E, then the diagram will look like this: Source: https://www.physicsclassroom.com After rearranging the order in which the three vectors are added, the resultant vector is now the hypotenuse of a right triangle. The lengths of the perpendicular sides of the right triangle are 8.0 m, North (6.0 km + 2.0 km) and 6.0 km, East. The magnitude of the resultant vector (R) can be determined using the Pythagorean theorem. 𝑅2 = (8.0 𝑘𝑚)2 + (6.0 𝑘𝑚)2 𝑅2 = 64.0 𝑘𝑚 + 36.0 𝑘𝑚 𝑅2 = 100.0 𝑘𝑚 √𝑅 2 = √100.0 𝑘𝑚2 𝑹 = 𝟏𝟎. 𝟎 𝒌𝒎 The size of the resultant was not affected by this change in order. This illustrates that the resultant is independent by the order in which they are added. Adding vectors A + B + C gives the same resultant as adding vectors B + A + C or even C + B + A as long as all three vectors are included with their specified magnitude and direction, the resultant will be the same. NegOr_Q1_GenPhysics1_SLKWeek1_v2 18 This means that vector addition is commutative (the order of addition is unimportant). The direction of a resultant vector can often be determined by use of trigonometric functions. Recall the meaning of the useful mnemonic SOH CAH TOA of the three common trigonometric functions - sine, cosine, and tangent functions. These three trigonometric functions can be applied to the hiker problem to determine the direction of the hiker's overall displacement. The process begins by the selection of one of the two angles (other than the right angle) of the triangle. Once the angle is selected, any of the three functions can be used to find the measure of the angle. Write the function and proceed with the proper algebraic steps to solve for the measure of the angle. The work is shown below. Source: https://www.physicsclassroom.com Vector Addition: Component Method When vectors to be added are not perpendicular, the method of addition by components described below can be used. To add two or more vectors A, B, C, … by the component method, follow this procedure: 1. Draw each vector. 2. Find the x- and y- components of each vector. 3. Find the sum of the x- components. ⃗𝒙= 𝒗 ∑𝒗 ⃗ 𝟏𝒙 + 𝒗 ⃗ 𝟐𝒙 + 𝒗 ⃗ 𝟑𝒙 4. Find the sum of the y- components. ⃗𝒚= 𝒗 ∑𝒗 ⃗ 𝟏𝒚 + 𝒗 ⃗ 𝟐𝒚 + 𝒗 ⃗ 𝟑𝒚 5. Use the sum of the x- components and the sum of the y- components to find the resultant (magnitude) and its angle (direction). NegOr_Q1_GenPhysics1_SLKWeek1_v2 19  Magnitude: (𝒗 ⃗ 𝑹 )𝟐 = (∑𝒗 ⃗ 𝒙 )𝟐 + (∑𝒗 ⃗ 𝒚 )𝟐 Direction: Use any of the trigonometric functions: sine, cosine, tangent Example 5: An ant crawls on a tabletop. It moves 2 cm East, turns 3 cm 400 North of East and finally moves 2.5 cm North. What is the ant’s total displacement? Given: ⃗⃗𝒅𝟏 = 𝟐 𝒄𝒎 𝑬 ⃗𝒅𝟐 = 𝟑 𝒄𝒎 𝟒𝟎𝟎 𝑵𝑬 ⃗𝒅𝟑 = 𝟐. 𝟓 𝒄𝒎 𝑵 Find: 𝒅𝑹 Solution: Step 1: Draw the vectors Step 2: The 2-cm vector has no component along the y-axis and the 2.5 cm has no component along the x- axis. The components of the 3 cm vector are found this way, NegOr_Q1_GenPhysics1_SLKWeek1_v2 20  ⃗𝒅𝟐𝒚 𝐬𝐢𝐧 𝟒𝟎𝟎 = 𝟑 𝒄𝒎 ⃗𝒅𝟐𝒚 = (𝟑 𝒄𝒎)(𝐬𝐢𝐧 𝟒𝟎𝟎 ) = (𝟑 𝒄𝒎)(𝟎. 𝟔𝟒) ⃗ 𝟐𝒚 = 𝟏. 𝟗𝟐 𝒄𝒎 𝒅 ⃗𝒅𝟐𝒙 𝐜𝐨𝐬 𝟒𝟎𝟎 = 𝟑 𝒄𝒎 ⃗⃗𝒅𝟐𝒙 = (𝟑 𝒄𝒎)(𝐜𝐨𝐬 𝟒𝟎𝟎 ) = (𝟑 𝒄𝒎)(𝟎. 𝟕𝟕) ⃗⃗ 𝟐𝒙 = 𝟐. 𝟑𝟏 𝒄𝒎 𝒅 To show the components of the vectors, you may present them in a table. Vector dx dy 2 cm E 2.00 cm 0 3 cm 40O NE 2.31 cm 1.92 cm 2.5 cm N 0 2.50 cm ⃗⃗⃗⃗𝑥 = 4.31 𝑐𝑚 ∑𝑑 ∑ ⃗⃗⃗⃗ 𝑑𝑦 = 4.42 𝑐𝑚 Step 3: If the sum of the components on each axis is drawn, we get this figure Use the Pythagorean theorem to solve for the magnitude of the resultant. (dR)2 = (∑ dx)2 + (∑ dy)2 = (4. 311 cm) 2 + (4.42 cm)2 NegOr_Q1_GenPhysics1_SLKWeek1_v2 21  dR = √ 18.58 cm 2 + 19.54 cm 2 = √ 38. 12 cm2 dR = 6.17 cm To solve for the direction, Θ, tan Θ = 4.42 cm 4.31 cm = 1.03 Θ = 45.85 o Therefore, the final displacement is … dR = 6.17 cm 45.85o NE. To add vectors that are not in the same or perpendicular directions, we use method of components. All vectors can be described in terms of two components called the x component and the y component. Adding the vectors graphically using their components produces the same result. Components can be added using math methods because all x components are in the same plane as are all y components. Furthermore, x and y components are perpendicular and can be added to each other using Pythagorean theorem. Activity: A. Brain Exercises: Perform these operations using scientific notation. Write your solutions in your notebook. 1. 4.35cm – 0.615cm + 33.7cm 2. 14.08N x 0.52m 3. 50N ÷ (2.4m x 0.008m) B. Solve the following problem and write your answer in your notebook. 1. How heavy in kilogram is a 180lb football player? 2. How many mL are in 0.037 quartz? NegOr_Q1_GenPhysics1_SLKWeek1_v2 22  C. Distinguishing between Vector and Scalar Quantities Directions: Classify each quantity as either a vector or a scalar quantity. Put a check mark in the appropriate box. Do this in your Science notebook/Answer Sheet. VECTOR SCALAR 10 meters 1600 calories 20 degrees Celsius 40 m/sec, East 520 bytes 5 mi., South Northwest D. Adding Vectors Using the Component Method Directions: Solve the given problem. Show your solution in your notebook. Problem: Vicky walks 8 km East, then 5 km South and finally 6 km West. Find her final displacement. The table below shows the components of the vectors. Vector dx dy 8 km E 8 km 0 5 km S 0 - 5 km 6 km W -6 km 0 ∑ dx = ?? ∑ dy = ?? NegOr_Q1_GenPhysics1_SLKWeek1_v2 23 Performance Task: Activity 1: Measurements Directions: Do the activities below. Write your answers of the questions given in your Science notebook. Materials: Book Ruler Procedure: 1. Measure the length, width, and thickness of a book. 2. Record the results on the following table. Questions: 1. How many significant figures did you use in reporting your measurements? 2. Are the results of each measurement (length, width or thickness) close to each other? 3. Were the measurements accurate or precise? Measure the actual length, width, and thickness of the book, and compare the results with this value. 1. Are the results of each measurement (length, width, or thickness) close to the true value? 2. Were the measurements accurate or precise? NegOr_Q1_GenPhysics1_SLKWeek1_v2 24  Activity 2: Materials Needed: Small Ball (You can use paper ball) Stop watch (You can use stop watch of the cellphone, watch) Paper and pen Procedure: 1. Prepare the necessary materials. 2. Get a pen and paper and copy the table below. 3. Get the initial data. Throw the ball upward and use the stop watch to get the time in which the ball reaches the ground. 4. Input the initial data per second. Initial Data:_________seconds Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 5. After 3 minutes, throw the ball again to get the data for Trial 1. 6. Repeat the step 5 for the succeeding trials. Example: Initial Data: 6 seconds Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 5 seconds 4 seconds 7 seconds 3 seconds 6 seconds *Please observe the data on the table. Guide Questions: 1. What can you observe on the data you’ve gathered? 2. Why do you think the data is not consistent? NegOr_Q1_GenPhysics1_SLKWeek1_v2 25  III. WHAT I HAVE LEARNED EVALUATION/POST-TEST A. Directions: Read the statements and write the numbers in scientific notation on the space provided before each item. Write your answers in your notebook. _________ 1. The population of the world is about 7,117,000,000. _________ 2. The distance from Earth to the Sun is about 92,960,000 miles. _________ 3. The human body contains approximately 60,000,000,000,000 or more cells. _________ 4. The mass of a particle of dust is 0.000000000753 kg. _________ 5. The length of the shortest wavelength of visible light (violet) is 0.0000004 meters. B. Convert the following measurements. Write your solutions in your notebook. 1. 586 cm = ___m 2. 4.28 m = ___mm 3. 1396mg = ___kg 4. 1375L = ___kL 5. 12g = ___cg C. List down at least 2 common sources of errors and how to prevent them. Example of Systematic Error Example of Random Error (1) (1) (2) (2) D. Solve the given problem below. Write your answers in your notebook. Merly leaves her house, drives 26 km due North, then turns onto a street and continues in a direction 30O NE for 35 km and finally turns onto the highway due East for 40 km. What is her total displacement from her house? NegOr_Q1_GenPhysics1_SLKWeek1_v2 26  REFERENCES College Physics Labs Mechanics, The University of North Carolina at Chapel Hill, accessed July 16, 2020, https://www.webassign.net/question_assets/unccolphysmechl1/measur ements/manual.html Component Method of Vector Addition. Retrieved from https://www.physicsclassroom.com/class/vectors/Lesson-1/Component- Addition Lawrence Kok, “IB Chemistry on Uncertainty, Error Analysis, Random and Systematic Error”, accessed July 16, 2020, https://lawrencekok.blogspot.com/2014/03/ib-chemistry-on-uncertainty- error.html Padua, A., and Crisostomo, R. (2003). Practical and Explorational Physics. Vibal Publishing House Inc.: Quezon City. Scalars and Vectors. Retrieved from https://courses.lumenlearning.com/suny-osuniversityphysics/chapter/2-1- scalars-and-vectors/ NegOr_Q1_GenPhysics1_SLKWeek1_v2 27  DEPARTMENT OF EDUCATION Division of Negros Oriental SENEN PRISCILLO P. PAULIN, CESO V Schools Division Superintendent JOELYZA M. ARCILLA EdD OIC - Assistant Schools Division Superintendent MARCELO K. PALISPIS EdD JD OIC - Assistant Schools Division Superintendent NILITA L. RAGAY EdD OIC - Assistant Schools Division Superintendent/CID Chief ROSELA R. ABIERA Education Program Supervisor – (LRMDS) ARNOLD R. JUNGCO PSDS-Division Science Coordinator MARICEL S. RASID Librarian II (LRMDS) ELMAR L. CABRERA PDO II (LRMDS) ROSEWIN P. ROCERO THOMAS JOGIE U. TOLEDO ANDRE ARIEL B. CADIVIDA Writers ROSEWIN P. ROCERO Illustrator/Lay-out Artist _________________________________ ALPHA QA TEAM LIEZEL A. AGOR EUFRATES G. ANSOK JR. JOAN Y. BUBULI MA. OFELIA I. BUSCATO DEXTER D. PAIRA LIELIN A. DE LA ZERNA BETA QA TEAM ZENAIDA A. ACADEMIA RANJEL D. ESTIMAR ALLAN Z. ALBERTO MARIA SALOME B. GOMEZ EUFRATES G. ANSOK JR. JUSTIN PAUL ARSENIO C. KINAMOT DORIN FAYE D. CADAYDAY LESTER C. PABALINAS MERCY G. DAGOY ARJIE T. PALUMPA ROWENA R. DINOKOT DISCLAIMER The information, activities and assessments used in this material are designed to provide accessible learning modality to the teachers and learners of the Division of Negros Oriental. The contents of this module are carefully researched, chosen, and evaluated to comply with the set learning competencies. The writers and evaluator were clearly instructed to give credits to information and illustrations used to substantiate this material. All content is subject to copyright and may not be reproduced in any form without expressed written consent from the division. NegOr_Q1_GenPhysics1_SLKWeek1_v2 28 SYNOPSIS ANSWER KEY This self-learning kit discusses the following topics: estimating errors from multiple measurements of a physical quantity using variance, differentiating accuracy from precision, and systematic from random errors, vector from scalar quantities. Further, learners are expected to develop their scientific abilities and critical thinking skills as they perform various problem-solving activities involving conversion of units and scientific notation and addition of vectors. This Self-Learning Kit is developed to help learners on their self-study habit. The discussions herein are contextualized and thus meet the standards of the K to 12 Curriculum. Hence, this learning kit serves as their way of expanding their knowledge of the things in nature and apply these in daily lives. Come and let us make learning fun. THE AUTHORS ROSEWIN P. ROCERO is a Senior High School teacher of Sta. Catalina Science High School. She is a part-time instructor of NORSU- Bayawan-Sta. Catalina Campus. She earned her Bachelor of Science in Biology from NORSU Main Campus and she is currently finishing her post- graduate studies in Master of Arts in Science Teaching. THOMAS JOGIE U. TOLEDO finish his course at Negros Oriental State University with a degree of Bachelor of Secondary Education major in Biological Science last 2015. A Senior High Teacher II at Sumaliring High School and District Planning Coordinator of Siaton 1 District. Currently, he is finishing his master’s degree, Masters of Art in Science Teaching at Negros Oriental State University. ANDRE ARIEL B. CADIVIDA finished Bachelor of Science in Biology at Negros Oriental State University Main Campus in 2013. He is currently teaching at Cansal-ing Provincial Community High School as a senior high teacher, library designate and the focal person of the senior high department. He is currently completing Master of Arts in Science Teaching at Negros Oriental State University. NegOr_Q1_GenPhysics1_SLKWeek1_v2 29