GENERAL-PHYSICS-1-LESSON-2-ON-PHYSICAL-QUANTITIES.pdf

G E N E R A L P H Y S I C S Lesson 2 in General Physics 1 STEM-Specialized 1 Learning Competency General At the end of the lesson, you should be able to d...

G E N E R A L P H Y S I C S Lesson 2 in General Physics 1 STEM-Specialized 1 Learning Competency General At the end of the lesson, you should be able to do the following: Physics 1 Differentiate vector and scalar quantities (STEM_GP12V-Ia-8) Perform addition of vectors (STEM_GP12V-Ia-9) Rewrite a vector in component form (STEM_GP12V-Ia10) 2 Learning Objectives General At the end of the lesson, you should be able to do the following: Physics 1 Differentiate vector from scalar quantities. Identify examples of scalar and vector quantities. Represent vector quantities using arrows in a Cartesian plane. Explain the rules of vector addition and subtraction. Use the graphical method to add vectors. Apply the analytical method to calculate the components of a vector. Calculate the magnitude and the direction of the resultant vector using its components. 3 Lesson Outline General This shows the overall scheme of things for this lesson Physics 1 Physical Vector Vector Quantities Addition Component through Graphical Method 4 G E N E R A L P H Y S I C S Lesson 2.1 Physical Quantities General Physics 1 STEM-Specialized 5 Physical Quantities General Overview and definition Physics 1 Quantities can be classified based on how they are presented. Two types of physical quantities: scalar quantities vector quantities 6 Scalar Quantities General Overview and definition Physics 1 A scalar quantity is a physical quantity that has magnitude (size or quantity) but no direction. single number 25 C 0 unit 7 Scalar Quantities General Overview and definition Physics 1 Other examples of scalar quantities are mass, time, distance, speed, density, and volume. 15 kg single number unit 8 Operations on Scalar Quantities General Overview and definition Physics 1 Scalar quantities can be added or subtracted using the rules of ordinary arithmetic. 136 grams + 262 grams 398 grams 9 Vector Quantities General Overview and definition Physics 1 A vector quantity is a physical quantity with both magnitude and direction. Magnitude describes the quantity or the size of the physical quantity while direction describes how the vector is oriented relative to a reference point. 10 Vector Quantities General Overview and definition Physics 1 The car is moving at a speed of 30 m/s. Eastward. Speed is a scalar quantity. Adding direction turns it into velocity, a vector quantity 11 Vector Quantities General Overview and definition Physics 1 Vectors are represented by a single letter with an arrow above them. speed velocity scalar quantity vector quantity The magnitude of a scalar quantity is either zero or always positive. 12 Physical Quantities General Scalar and Vector Quantities Physics 1 13 Representing vector quantities General Overview and definition Physics 1 There are many ways to go from P1 to P2. All of them are different distances. 14 Representing vector quantities General Overview and definition Physics 1 But the shortest distance is defined as displacement. longer distance shorter distance (the shortest, actually) 15 Representing vector quantities General Overview and definition Physics 1 Displacement is a vector quantity, and it is represented by an arrow. longer distance shorter distance (the shortest, actually) 16 Representing vector quantities General Overview and definition Physics 1 The length of the arrow represents the vector’s magnitude. shorter arrow, smaller magnitude longer arrow, bigger magnitude 17 Rules in Representing Vectors General Overview and definition Physics 1 1. Begin by deciding on the scale that you want to use. Scale: 1 cm = 1 km This 5-cm arrow is 5 km in reality. 18 Rules in Representing Vectors General Overview and definition Physics 1 Rules in Representing Vectors 2. Identify where to place the vector based on its direction. 19 Rules in Representing Vectors General Overview and definition Physics 1 The direction of the vector is expressed as an angle of rotation either from the north, south, east, or west. 20 Rules in Representing Vectors General Overview and definition Physics 1 By default, angle covered are measured from the east direction. 21 Plotting Vectors General Sample exercise A Physics 1 Vehicle A covered 500km, 185 ° Meanwhile vehicle B traveled 250 km, 40° south of west. 22 Plotting Vectors General Sample exercise B Physics 1 Student A moved to 8.5 meters, 50° north of West meanwhile Student B moved 5 meters, 60 ° south of East. 23 Plotting Vectors General Sample exercise C Physics 1 Yae and Sara are training for a marathon in two different locations. Yae covered 54 km, 110° while Sara covered a displacement of 60 km, 78° south of east. Illustrate the displacements in one cartesian plane. 24 G E N E R A L P H Y S I C S Lesson 2.2 Vector Addition through Graphical Method General Physics 1 STEM-Specialized 25 Distance vs. Displacement General Physical Quantities Physics 1 Distance Displacement covers a non- covers a straight path straight path from an origin between the to the origin to the destination. destination. 26 Concept of Vectors in One Dimension General Concept & Preview Physics 1 Two vectors are considered equal if their magnitudes and direction are the same. If two or more vectors are pointing in the same direction, it means that they are parallel to each other. 27 Concept of Vectors in One Dimension General Concept & Preview Physics 1 When two vectors have opposite directions but have the same magnitude, they are called antiparallel. 28 Operations on Vectors General Concept & Preview Physics 1 Suppose a person has a displacement of A eastward. And an additional displacement B eastward The initial point of the total displacement is the starting point of A while the endpoint is the endpoint of B. 29 Addition of Vectors General Concept & Preview Physics 1 The total displacement is called the resultant, R. 30 Addition of Vectors General Head to tail method Physics 1 The addition (and subtraction) of vectors can be done using the head to tail method. tail head tail head 31 Addition of Vectors General Concept & Preview Physics 1 Suppose a person has a displacement of A eastward. Suppose he covers another displacement of B westward. The resultant R can be measured using head to tail method. 32 Graphical Method of Adding Vectors General Overview and discussion Physics 1 Suppose a person covered two different displacements: A = 30 m, 30° north of east and B = 55 m, 70° south of east. What is her total displacement? 1. Draw vector A on a graphing or bond paper. Make sure that the magnitude is represented by a proper scale. 33 Graphical Method of Adding Vectors General Overview and discussion Physics 1 Suppose a person covered two different displacements: A = 30 m, 30° north of east and B = 55 m, 70° south of east. What is her total displacement? 2. Draw vector B using the same scale that you used. Its tail should start from the tip of A. 34 Graphical Method of Adding Vectors General Overview and discussion Physics 1 Suppose a person covered two different displacements: A = 30 m, 30° north of east and B = 55 m, 70° south of east. What is her total displacement? 3. Draw an arrow connecting the tail of A and the tip of B. This is the resultant vector R. 35 Graphical Method of Adding Vectors General Sample exercise Physics 1 A car initially traveled 35 km due south and then traveled 65 km to the west. What is the car’s resultant displacement? 36 Graphical Method of Adding Vectors General Sample exercise Physics 1 A hiker walks from the drop-off and initially covers 3000 m, 35° north of west. He then traveled another 5500 m heading to 10° north of west. Finally, he reached his destination by walking 1500 m due north. What is his total displacement? 37 Graphical Method of Adding Vectors General Sample exercise Physics 1 A speed boat leaves the beach and has an initial displacement of 650 m 45° north of west, then again travels 400 m 10° north of east. After stopping for a while, it traveled 550 m, 130°. Finally, it covered 350 m, 168° to reach a small island. What is the total displacement of the speed boat? 38 G E N E R A L P H Y S I C S Lesson 2.3 Components of Vectors General Physics 1 STEM-Specialized 39 Components of Vectors General Overview and discussion Physics 1 A truss bridge is composed of interconnected beams arranged in a repeated triangular pattern. 40 Components of Vectors General Overview and discussion Physics 1 Each component of the bridge adds to its ability to hold its own weight as well as the weight of everything that uses it. 41 Components of Vectors General Overview and discussion Physics 1 Some of its parts can accommodate compression forces while some handle tension forces. 42 Components of Vectors General Overview and discussion Physics 1 A force, which is a vector quantity, being experienced by a diagonal beam in the bridge can be resolved into its two components. Determination of these force components is important in calculating and determining its maximum strength. 43 Components of Vectors General Concept & Preview Physics 1 Consider a displacement vector pointing northeast. It also has a component along the north (vertical axis). It has a component along the east (horizontal axis). 44 Components of Vectors General Concept & Preview Physics 1 A vector can be resolved into its components. 45 Components of Vectors General Concept & Preview Physics 1 The sides of the triangle can be defined from the angle. Legend: h = hypotenuse (hyp) o = opposite (opp) a = adjacent (adj) 46 Components of Vectors General Concept & Preview Physics 1 Suppose we have the following displacement vector. 47 Components of Vectors General Concept & Preview Physics 1 It has a component in the vertical axis. 48 Components of Vectors General Concept & Preview Physics 1 It has a component in the horizontal axis. 49 Components of Vectors General Concept & Preview Physics 1 The relationships between its components and its angle can be expressed as the given equations: 50 Components of Vectors General Concept & Preview Physics 1 Hence, trigonometrically, we can define the components as the following equations. 51 Components of Vectors General Concept & Preview Physics 1 The resultant vector can be calculated using Pythagorean theorem. 52 Components of Vectors General Concept & Preview Physics 1 The angle or direction of the vector is determined using the inverse tangent function of the ratio of the x- and y- components. 53 Calculating Components of Vectors General Sample exercise Physics 1 What are the x- and y-components of a displacement vector with a magnitude of 50 m and an angle of 30°? 54 Calculating Components of Vectors General Sample exercise Physics 1 A car has a displacement of 750 m, 45° north of west. What are the components of the displacement vector? 55 Calculating Components of Vectors General Sample exercise Physics 1 A vector located in the second quadrant has an x- component of ‒80 m at an angle of 20°, as shown in the figure below. Find the magnitude of the vector and its y- component. 56 Calculating Components of Vectors General Sample exercise Physics 1 What is the magnitude and direction of a displacement vector if its components are as follows: Ax = 10 m, Ay = 5m? 57 Calculating Components of Vectors General Sample exercise Physics 1 An airplane covered a displacement vector with components of Dx= ‒2500 km and Dy= 1800 km. What is the magnitude and direction of the displacement vector? 58 Calculating Components of Vectors General Sample exercise Physics 1 A displacement vector located in the first quadrant has a magnitude of 50 km and has an x-component of 44 km. Find the (a) y-component of the vector and (b) its direction from the +x-axis. 59