Physics 12. Chapter 1: Vector Analysis in Two Dimensions
|
|
- Emil Houston
- 5 years ago
- Views:
Transcription
1 Physics 12 Chapter 1: Vector Analysis in Two Dimensions
2 1. Definitions When studying mechanics in Physics 11, we have realized that there are two major types of quantities that we can measure for the systems of interest. They are, respectively, scalar and vector quantities. What is the difference between them? Chapter 1: Vector Analysis in 2D 2
3 By definition: Scalar quantity is a quantity that has only magnitude. Vector quantity is a quantity that has both magnitude and direction. Chapter 1: Vector Analysis in 2D 3
4 To see more clearly the difference, let s consider the following pair of quantities: distance vs displacement Chapter 1: Vector Analysis in 2D 4
5 Problem: Which path has the largest distance? Which path has the largest displacement? Chapter 1: Vector Analysis in 2D 5
6 A vector can be represented graphically by an arrow. Its tip points toward the direction and its length represents the magnitude of the vector quantity. Vectors can be drawn on typical Cartesian plane or in cardinal orientations. Chapter 1: Vector Analysis in 2D 6
7 For example, to describe the direction of each of the following vectors: N N W 45 E W 60 E S S 45 N of E 60 S of W 45 E of N 30 W of S Chapter 1: Vector Analysis in 2D 7
8 2. Addition of vectors Vectors, like scalars, can be involved in basic arithmetic operations. They can be added, subtracted or multiplied; however, the ways they are done are different from those for real numbers. In physics 11, we have seen briefly that simple arithmetic can be used to add vectors if they are in the same direction. Chapter 1: Vector Analysis in 2D 8
9 However, same method does not work if the two vectors are not along the same line. For example: suppose a person walks 10.0 km east and then walks 5.0 km north. What is the displacement of the person? Chapter 1: Vector Analysis in 2D 9
10 To determine the resultant vector that represents the displacement, the two vectors are drawn on the grids tip-to-tail. As the two vectors are at 90 of each other, the resultant vector can be found by Pythagorean theorem: D 2 R = D D 2 D R = = 11.2 km To determine the direction, we can use trigonometry: tan θ = D 2 D 1 θ = tan = 27 Chapter 1: Vector Analysis in 2D 10
11 The resultant is actually not affected by the order in which the vectors are added. Recall the previous example; assume the man first walks 5 km north and then 10.0 km east. The Pythagorean theorem will yield exactly the same result! Chapter 1: Vector Analysis in 2D 11
12 In general, vectors can be added graphically by means of the tip-totail method which involves the following steps: Step 1: On a diagram, draw the first vector v 1 in scale. Step 2: Next, draw the second vector v 2, to scale, placing its tail at the tip of the first vector and being sure its direction is correct. Step 3: The arrow drawn from the tail of the first vector to the tip of the second vector represents the sum, or resultant, of the two vectors denoted by v = v 1 + v 2. Step 4: Measure the length of the resultant by ruler and the angle with respect to the horizontal by a protractor. They can also be deduced analytically using trigonometry. Chapter 1: Vector Analysis in 2D 12
13 The tip-to-tail method of vector addition can be extended to the cases having three or more vectors. Consider the following case: What is the resultant vector? Chapter 1: Vector Analysis in 2D 13
14 Example: A man walks 250 m due East, then 250 m 60 North of East. Using scale diagrams on graph paper, determine the magnitude and direction of the resultant displacement. Chapter 1: Vector Analysis in 2D 14
15 Another way of adding vectors together is called parallelogram method. In this method, two vectors are drawn starting from a common origin, and a parallelogram is constructed using these two vectors as adjacent sides. The resultant is the diagonal drawn from the common origin. Chapter 1: Vector Analysis in 2D 15
16 3. Subtraction and multiplication of vectors In algebra, subtracting a number is the same as adding the opposite of that number. For example: = = 5 But how about vectors? If subtracting a vector is also the same as adding the opposite of the vector, then we may have to ask what is the opposite of a vector, v? Chapter 1: Vector Analysis in 2D 16
17 Recall that each vector is associated with a magnitude and a direction. Magnitude refers to the size of the vector and is always non-negative. Therefore, the negative sign of the vector must be related to its direction. By definition, the negative of a vector is the vector with its original magnitude but in opposite direction. Chapter 1: Vector Analysis in 2D 17
18 With this definition, we would be able to perform vector subtraction. The difference between two vectors can be interpreted as: v 2 v 1 = v 2 + ( v 1 ) Graphically, using the tip-to-tail method, we can determine the resultant vector: Chapter 1: Vector Analysis in 2D 18
19 Example: Given the following vectors: A is 6.3 cm in the direction 18 N of E B is 5 cm in the direction 53 N of W Draw the diagrams and find R for: (i) R = A + B (ii) R = A B (iii) R = B A Chapter 1: Vector Analysis in 2D 19
20 When a vector is multiplied by a scalar c, the vector is either stretched (if c > 1), compressed (if 0 < c < 1), or reversed (if c < 0). The magnitude of the resultant is changed by a factor c. Chapter 1: Vector Analysis in 2D 20
21 4. Vector addition by components As shown previously, any given vector can be written as a sum of two vectors, and there exist infinite number of such pairs. Therefore, it is always possible to resolve a vector into a pair of perpendicular vectors, each of which is lying along a coordinate axis. This process is called a resolution, and the resulting two vectors are called the components of the original vector. Chapter 1: Vector Analysis in 2D 21
22 When a vector is resolved into two perpendicular components, their magnitudes can be found easily using the Pythagorean theorem and trigonometry. sin θ = V y V V y = V sin θ cos θ = V x V V x = V cos θ tan θ = V y V x V 2 = V x 2 + V y 2 Chapter 1: Vector Analysis in 2D 22
23 Example: A cannon is shot at a muzzle velocity of 1500 m/s at an angle of 60 to the horizontal. What are the vertical and horizontal components of the velocity? Chapter 1: Vector Analysis in 2D 23
24 Example: A boy pulls a wagon with a force of 100 N at 40 to the horizontal. Find the pulling force and the lifting force. [64 N, 77 N] Chapter 1: Vector Analysis in 2D 24
25 Note that components are not always drawn as horizontal and vertical components. Sometimes it is more convenient, when dealing with systems in mechanics, to define the two components as parallel and perpendicular to the plane on which the object of interest is perched. For example: Consider an object that rests on a slope of angle θ. Chapter 1: Vector Analysis in 2D 25
26 What are W and W, and how to determine them? The parallel component W is the pulling force down the plane due to the gravitational pull W. It is calculated by W = W sin θ The perpendicular component W is the press on the object due to the gravitational pull W. It is calculated by W = W cos θ Chapter 1: Vector Analysis in 2D 26
27 Example: A ball rests on a slope. The ball weighs 600 N and the slope is 40 to the horizontal. What is the press on the ball to the surface and what is the pulling force that drags the ball down the slope? Chapter 1: Vector Analysis in 2D 27
28 Resolving vectors into components offers an alternative way of finding the resultant in a vector addition. Consider the addition of two vectors, v 1 and v 2 in the following diagram: Chapter 1: Vector Analysis in 2D 28
29 We can obtain the resultant by using the tip-to-tail method. However, from the diagram, we see that same answer can be obtained by adding respectively the components of the two vectors. That is, v Rx = v 1x + v 2x v Ry = v 1y + v 2y The magnitude and direction can be calculated in the usual way: v R = v x 2 + v y 2 θ = tan 1 v y v x Chapter 1: Vector Analysis in 2D 29
30 Example: A rural mail carrier leaves the post office and drives 22.0 km in a northerly direction. She then drives in a direction 60.0 south of east for 47.0 km. What is her displacement from the post office? [30.0 km, 38.5 S of E] Chapter 1: Vector Analysis in 2D 30
31 Example: An airplane trip involves three legs, with two stopovers as shown. The first leg is due east for 620 km; the second leg is southeast for 440 km; and the third leg is 53 south of west, for 550 km. What is the plane s total displacement? [960 km, 51 S of E] Chapter 1: Vector Analysis in 2D 31
32 Example: What is the resultant force of the following system? Chapter 1: Vector Analysis in 2D 32
33 5. Relative velocity We have encountered the situation when learning relativity in Physics 11 that observations on an event from different frames of reference may result in different, or sometimes even apparently contradicting conclusions. Chapter 1: Vector Analysis in 2D 33
34 For example, consider two trains approaching one another, each with a speed of 80 km/h with respect to the Earth. What will an observer measure for the speed of the trains if he is on Earth or on either one of the train? 80 km/h 80 km/h Chapter 1: Vector Analysis in 2D 34
35 When the two velocity vectors are along the same direction, the relative velocity can be easily obtained by simple vector addition or subtraction. Assume that there are two objects A and B moving colinearly with the velocity v A and v B, respectively. By definition, the velocity of A relative to B is given by v AB = v A v B Pay attention on the sign when computing relative velocities; they are vectors and have directions! Chapter 1: Vector Analysis in 2D 35
36 If, however, the two velocity vectors point in different directions, then we will have to use vector addition to find the resultant. To avoid the problem of adding or subtracting wrong velocities, it is recommended that each vector be specified by two labels, the first one being the object, and the second one being the reference frame in which it has this velocity. v AB The magnitude of the velocity is v A is the object The velocity is measured in the reference frame B Chapter 1: Vector Analysis in 2D 36
37 Consider the following example: Chapter 1: Vector Analysis in 2D 37
38 Example: Consider a boat heads north at the velocity of 1.85 m/s directly across a river whose westward current is 1.20 m/s. What is the velocity of the boat relative to the shore? If the river is 110 m wide, how long will it take to cross and how far downstream will the boat be then? Chapter 1: Vector Analysis in 2D 38
39 Another common scenario we may encounter involves directing a boat in a correct direction to deal with water stream. Consider the following example: In order to make sure the boat goes straight North, at what upstream angle must it head? sin θ = v WS v BW If v BW = 1.85 m/s and v WS = 1.20 m/s, then θ = sin 1 v WS v BW = sin = 40.4 Chapter 1: Vector Analysis in 2D 39
40 Example: There is a 15.0 m/s wind blowing due East and you start riding your bike North at 9.0 m/s. What is the velocity of the wind on your face? [17.5 m/s at 59 E of S] Chapter 1: Vector Analysis in 2D 40
41 Example: A plane is capable of travelling at 120 m/s in still air. Where must the pilot head the plane in order to end up going due North when there is a 35 m/s West wind? Chapter 1: Vector Analysis in 2D 41
Definitions In physics we have two types of measurable quantities: vectors and scalars.
1 Definitions In physics we have two types of measurable quantities: vectors and scalars. Scalars: have magnitude (magnitude means size) only Examples of scalar quantities include time, mass, volume, area,
More informationKinematics in Two Dimensions; Vectors
Kinematics in Two Dimensions; Vectors Vectors & Scalars!! Scalars They are specified only by a number and units and have no direction associated with them, such as time, mass, and temperature.!! Vectors
More informationLecture PowerPoints. Chapter 3 Physics for Scientists & Engineers, with Modern Physics, 4 th edition Giancoli
Lecture PowerPoints Chapter 3 Physics for Scientists & Engineers, with Modern Physics, 4 th edition Giancoli 2009 Pearson Education, Inc. This work is protected by United States copyright laws and is provided
More informationCHAPTER 3 KINEMATICS IN TWO DIMENSIONS; VECTORS
CHAPTER 3 KINEMATICS IN TWO DIMENSIONS; VECTORS OBJECTIVES After studying the material of this chapter, the student should be able to: represent the magnitude and direction of a vector using a protractor
More information4/13/2015. I. Vectors and Scalars. II. Addition of Vectors Graphical Methods. a. Addition of Vectors Graphical Methods
I. Vectors and Scalars A vector has magnitude as well as direction. Some vector quantities: displacement, velocity, force, momentum A scalar has only a magnitude. Some scalar quantities: mass, time, temperature
More informationAP* PHYSICS B DESCRIBING MOTION: KINEMATICS IN TWO DIMENSIONS &VECTORS
AP* PHYSICS B DESCRIBING MOTION: KINEMATICS IN TWO DIMENSIONS &VECTORS The moment of truth has arrived! To discuss objects that move in something other than a straight line we need vectors. VECTORS Vectors
More informationChapter 3. Vectors. θ that the vector forms with i ˆ is 15. I. Vectors and Scalars
Chapter 3. Vectors I. Vectors and Scalars 1. What type of quantity does the odometer of a car measure? a) vector; b) scalar; c) neither scalar nor vector; d) both scalar and vector. 2. What type of quantity
More informationKinematics in Two Dimensions; 2D- Vectors
Kinematics in Two Dimensions; 2D- Vectors Addition of Vectors Graphical Methods Below are two example vector additions of 1-D displacement vectors. For vectors in one dimension, simple addition and subtraction
More informationVectors. AP/Honors Physics Mr. Velazquez
Vectors AP/Honors Physics Mr. Velazquez The Basics Any quantity that refers to a magnitude and a direction is known as a vector quantity. Velocity, acceleration, force, momentum, displacement Other quantities
More informationNewton 3 & Vectors. Action/Reaction. You Can OnlyTouch as Hard as You Are Touched 9/7/2009
Newton 3 & Vectors Action/Reaction When you lean against a wall, you exert a force on the wall. The wall simultaneously exerts an equal and opposite force on you. You Can OnlyTouch as Hard as You Are Touched
More informationChapter 3 Kinematics in Two Dimensions; Vectors
Chapter 3 Kinematics in Two Dimensions; Vectors Vectors and Scalars Units of Chapter 3 Addition of Vectors Graphical Methods Subtraction of Vectors, and Multiplication of a Vector by a Scalar Adding Vectors
More informationObjectives and Essential Questions
VECTORS Objectives and Essential Questions Objectives Distinguish between basic trigonometric functions (SOH CAH TOA) Distinguish between vector and scalar quantities Add vectors using graphical and analytical
More informationChapter 3. Table of Contents. Section 1 Introduction to Vectors. Section 2 Vector Operations. Section 3 Projectile Motion. Section 4 Relative Motion
Two-Dimensional Motion and Vectors Table of Contents Section 1 Introduction to Vectors Section 2 Vector Operations Section 3 Projectile Motion Section 4 Relative Motion Section 1 Introduction to Vectors
More informationVector Addition and Subtraction: Graphical Methods
Vector Addition and Subtraction: Graphical Methods Bởi: OpenStaxCollege Displacement can be determined graphically using a scale map, such as this one of the Hawaiian Islands. A journey from Hawai i to
More informationVectors. Introduction. Prof Dr Ahmet ATAÇ
Chapter 3 Vectors Vectors Vector quantities Physical quantities that have both n u m e r i c a l a n d d i r e c t i o n a l properties Mathematical operations of vectors in this chapter A d d i t i o
More informationA SCALAR is ANY quantity in physics that has MAGNITUDE, but NOT a direction associated with it. Magnitude A numerical value with units.
Vectors and Scalars A SCALAR is ANY quantity in physics that has MAGNITUDE, but NOT a direction associated with it. Magnitude A numerical value with units. Scalar Example Speed Distance Age Heat Number
More informationHomework due Nov 28 Physics
Homework due Nov 28 Physics Name Base your answers to questions 1 through 4 on the information and vector diagram below and on your knowledge of physics. A hiker starts at point P and walks 2.0 kilometers
More informationScalar Quantities - express only magnitude ie. time, distance, speed
Chapter 6 - Vectors Scalar Quantities - express only magnitude ie. time, distance, speed Vector Quantities - express magnitude and direction. ie. velocity 80 km/h, 58 displacement 10 km (E) acceleration
More informationMathematical review trigonometry vectors Motion in one dimension
Mathematical review trigonometry vectors Motion in one dimension Used to describe the position of a point in space Coordinate system (frame) consists of a fixed reference point called the origin specific
More informationChapter 2 Mechanical Equilibrium
Chapter 2 Mechanical Equilibrium I. Force (2.1) A. force is a push or pull 1. A force is needed to change an object s state of motion 2. State of motion may be one of two things a. At rest b. Moving uniformly
More informationCHAPTER 2: VECTOR COMPONENTS DESCRIBE MOTION IN TWO DIMENSIONS
CHAPTER 2: VECTOR COMPOETS DESCRIBE MOTIO I TWO DIMESIOS 2.1 Vector Methods in One Dimension Vectors may be pictured with sketches in which arrows represent quantities such as displacement, force and velocity.
More informationSection 1.4: Adding and Subtracting Linear and Perpendicular Vectors
Section 1.4: Adding and Subtracting Linear and Perpendicular Vectors Motion in two dimensions must use vectors and vector diagrams. Vector Representation: tail head magnitude (size): given by the length
More informationVectors in Physics. Topics to review:
Vectors in Physics Topics to review: Scalars Versus Vectors The Components of a Vector Adding and Subtracting Vectors Unit Vectors Position, Displacement, Velocity, and Acceleration Vectors Relative Motion
More informationVectors and Kinematics Notes 1 Review
Velocity is defined as the change in displacement with respect to time. Vectors and Kinematics Notes 1 Review Note that this formula is only valid for finding constant velocity or average velocity. Also,
More informationChapter 2 One-Dimensional Kinematics
Review: Chapter 2 One-Dimensional Kinematics Description of motion in one dimension Copyright 2010 Pearson Education, Inc. Review: Motion with Constant Acceleration Free fall: constant acceleration g =
More informationStudent Exploration: Vectors
Name: Date: Student Exploration: Vectors Vocabulary: component, dot product, magnitude, resultant, scalar, unit vector notation, vector Prior Knowledge Question (Do this BEFORE using the Gizmo.) An airplane
More informationVectors. An Introduction
Vectors An Introduction There are two kinds of quantities Scalars are quantities that have magnitude only, such as position speed time mass Vectors are quantities that have both magnitude and direction,
More information2- Scalars and Vectors
2- Scalars and Vectors Scalars : have magnitude only : Length, time, mass, speed and volume is example of scalar. v Vectors : have magnitude and direction. v The magnitude of is written v v Position, displacement,
More informationWhat is Relative Motion
RELATIVE MOTION What is Relative Motion Strictly speaking all motion is relative to something. Usually that something is a reference point that is assumed to be at rest (i.e. the earth). Motion can be
More informationTrigonometry Basics. Which side is opposite? It depends on the angle. θ 2. Y is opposite to θ 1 ; Y is adjacent to θ 2.
Trigonometry Basics Basic Terms θ (theta) variable for any angle. Hypotenuse longest side of a triangle. Opposite side opposite the angle (θ). Adjacent side next to the angle (θ). Which side is opposite?
More informationFind graphically, using scaled diagram, following vectors (both magnitude and direction):
1 HOMEWORK 1 on VECTORS: use ruler and protractor, please!!! 1. v 1 = 3m/s, E and v = 4m/s, 3 Find graphically, using scaled diagram, following vectors (both magnitude and direction): a. v = v 1 + v b.
More informationGeneral Physics I, Spring Vectors
General Physics I, Spring 2011 Vectors 1 Vectors: Introduction A vector quantity in physics is one that has a magnitude (absolute value) and a direction. We have seen three already: displacement, velocity,
More informationUNIT-05 VECTORS. 3. Utilize the characteristics of two or more vectors that are concurrent, or collinear, or coplanar.
UNIT-05 VECTORS Introduction: physical quantity that can be specified by just a number the magnitude is known as a scalar. In everyday life you deal mostly with scalars such as time, temperature, length
More informationName: Class: Date: Solution x 1 = units y 1 = 0. x 2 = d 2 cos = = tan 1 y
Assessment Chapter Test B Teacher Notes and Answers Two-Dimensional Motion and Vectors CHAPTER TEST B (ADVANCED) 1. b 2. d 3. d x 1 = 3.0 10 1 cm east y 1 = 25 cm north x 2 = 15 cm west x tot = x 1 + x
More informationVectors A Guideline For Motion
AP Physics-1 Vectors A Guideline For Motion Introduction: You deal with scalar quantities in many aspects of your everyday activities. For example, you know that 2 liters plus 2 liters is 4 liters. The
More informationUnit 1: Math Toolbox Math Review Guiding Light #1
Unit 1: Math Toolbox Math Review Guiding Light #1 Academic Physics Unit 1: Math Toolbox Math Review Guiding Light #1 Table of Contents Topic Slides Algebra Review 2 8 Trigonometry Review 9 16 Scalar &
More informationBELLWORK feet
BELLWORK 1 A hot air balloon is being held in place by two people holding ropes and standing 35 feet apart. The angle formed between the ground and the rope held by each person is 40. Determine the length
More informationUNCORRECTED PAGE PROOFS
TOPIC 3 Motion in two dimensions 3.1 Overview 3.1.1 Module 1: Kinematics Motion on a Plane Inquiry question: How is the motion of an object that changes its direction of movement on a plane described?
More informationStudent Content Brief Advanced Level
Student Content Brief Advanced Level Vectors Background Information Physics and Engineering deal with quantities that have both size and direction. These physical quantities have a special math language
More informationExperiment 3: Vector Addition
Experiment 3: Vector Addition EQUIPMENT Force Table (4) Pulleys (4) Mass Hangers Masses Level (TA s Table) (2) Protractors (2) Rulers (4) Colored Pencils (bold colors) Figure 3.1: Force Table 15 16 Experiment
More informationVectors. Chapter 3. Arithmetic. Resultant. Drawing Vectors. Sometimes objects have two velocities! Sometimes direction matters!
Vectors Chapter 3 Vector and Vector Addition Sometimes direction matters! (vector) Force Velocity Momentum Sometimes it doesn t! (scalar) Mass Speed Time Arithmetic Arithmetic works for scalars. 2 apples
More informationVector components and motion
Vector components and motion Objectives Distinguish between vectors and scalars and give examples of each. Use vector diagrams to interpret the relationships among vector quantities such as force and acceleration.
More informationPhysics 20 Lesson 10 Vector Addition
Physics 20 Lesson 10 Vector Addition I. Vector Addition in One Dimension (It is strongly recommended that you read pages 70 to 75 in Pearson for a good discussion on vector addition in one dimension.)
More information9/29/2014. Chapter 3 Kinematics in Two Dimensions; Vectors. 3-1 Vectors and Scalars. Contents of Chapter Addition of Vectors Graphical Methods
Lecture PowerPoints Chapter 3 Physics: Principles with Applications, 7 th edition Giancoli Chapter 3 Kinematics in Two Dimensions; Vectors This work is protected by United States copyright laws and is
More information2 Dimensional Vectors
2 Dimensional Vectors Vectors that are not collinear must be added using trigonometry or graphically (with scale diagrams) Vector quantities are drawn as arrows, the length of the arrow indicates the magnitude
More informationChapter 3. Vectors. 3.1 Coordinate Systems 3.2 Vector and Scalar Quantities 3.3 Some Properties of Vectors 3.4 Components of a Vector and Unit Vectors
Chapter 3 Vectors 3.1 Coordinate Systems 3.2 Vector and Scalar Quantities 3.3 Some Properties of Vectors 3.4 Components of a Vector and Unit Vectors 1 Vectors Vector quantities Physical quantities that
More information10.1 Vectors. c Kun Wang. Math 150, Fall 2017
10.1 Vectors Definition. A vector is a quantity that has both magnitude and direction. A vector is often represented graphically as an arrow where the direction is the direction of the arrow, and the magnitude
More informationPreliminary Physics. Moving About. DUXCollege. Week 2. Student name:. Class code:.. Teacher name:.
Week 2 Student name:. Class code:.. Teacher name:. DUXCollege Week 2 Theory 1 Present information graphically of: o Displacement vs time o Velocity vs time for objects with uniform and non-uniform linear
More informationTeacher Content Brief
Teacher Content Brief Vectors Introduction Your students will need to be able to maneuver their Sea Perch during the competition, so it will be important for them to understand how forces combine to create
More informationNew concepts: scalars, vectors, unit vectors, vector components, vector equations, scalar product. reading assignment read chap 3
New concepts: scalars, vectors, unit vectors, vector components, vector equations, scalar product reading assignment read chap 3 Most physical quantities are described by a single number or variable examples:
More informationIntroduction to vectors
Lecture 4 Introduction to vectors Course website: http://facult.uml.edu/andri_danlov/teaching/phsicsi Lecture Capture: http://echo360.uml.edu/danlov2013/phsics1fall.html 95.141, Fall 2013, Lecture 3 Outline
More informationPre-Calculus Vectors
Slide 1 / 159 Slide 2 / 159 Pre-Calculus Vectors 2015-03-24 www.njctl.org Slide 3 / 159 Table of Contents Intro to Vectors Converting Rectangular and Polar Forms Operations with Vectors Scalar Multiples
More informationCoordinate Systems. Chapter 3. Cartesian Coordinate System. Polar Coordinate System
Chapter 3 Vectors Coordinate Systems Used to describe the position of a point in space Coordinate system consists of a fixed reference point called the origin specific axes with scales and labels instructions
More informationVector and Relative motion discussion/ in class notes. Projectile Motion discussion and launch angle problem. Finish 2 d motion and review for test
AP Physics 1 Unit 2: 2 Dimensional Kinematics Name: Date In Class Homework to completed that evening (before coming to next class period) 9/6 Tue (B) 9/7 Wed (C) 1D Kinematics Test Unit 2 Video 1: Vectors
More informationNotes: Vectors and Scalars
A particle moving along a straight line can move in only two directions and we can specify which directions with a plus or negative sign. For a particle moving in three dimensions; however, a plus sign
More informationSECTION 6.3: VECTORS IN THE PLANE
(Section 6.3: Vectors in the Plane) 6.18 SECTION 6.3: VECTORS IN THE PLANE Assume a, b, c, and d are real numbers. PART A: INTRO A scalar has magnitude but not direction. We think of real numbers as scalars,
More informationChapter 3. Vectors and. Two-Dimensional Motion Vector vs. Scalar Review
Chapter 3 Vectors and Two-Dimensional Motion Vector vs. Scalar Review All physical quantities encountered in this text will be either a scalar or a vector A vector quantity has both magnitude (size) and
More informationFORCE TABLE INTRODUCTION
FORCE TABLE INTRODUCTION All measurable quantities can be classified as either a scalar 1 or a vector 2. A scalar has only magnitude while a vector has both magnitude and direction. Examples of scalar
More informationChapter 7.4: Vectors
Chapter 7.4: Vectors In many mathematical applications, quantities are determined entirely by their magnitude. When calculating the perimeter of a rectangular field, determining the weight of a box, or
More informationPhysics 12 Unit 1: Kinematics Notes. Name: What you will be able to do by the end of this unit:
Physics 12 Unit 1: Kinematics Notes. Name: What you will be able to do by the end of this unit: B1. Perform vector analysis in one or two dimensions identify scalars and vectors resolve a vector into two
More informationPhysics 1-2 Mr. Chumbley
Physics 1-2 Mr. Chumbley Physical quantities can be categorized into one of two types of quantities A scalar is a physical quantity that has magnitude, but no direction A vector is a physical quantity
More informationMotion in Two Dimensions An Algebraic Approach
. Motion in Two Dimensions An Algebraic Approach In ection.1 you learned how to solve motion problems in two dimensions by using vector scale diagrams. This method has some limitations. First, the method
More informationSignificant Figures & Vectors
You have to complete this reading Booklet before you attempt the Substantive Assignment. Significant Figures Significant Figures & Vectors There are two kinds of numbers in the world Exact: o Example:
More informationLesson 7. Chapter 3: Two-Dimensional Kinematics COLLEGE PHYSICS VECTORS. Video Narrated by Jason Harlow, Physics Department, University of Toronto
COLLEGE PHYSICS Chapter 3: Two-Dimensional Kinematics Lesson 7 Video Narrated by Jason Harlow, Physics Department, University of Toronto VECTORS A quantity having both a magnitude and a direction is called
More informationVectors & scalars: Force as vector Review
Vectors & scalars: Force as vector Review Name 1. Two forces act concurrently on an object on a horizontal, frictionless surface, as shown in the diagram below. What additional force, when applied to the
More informationChapter 2 A Mathematical Toolbox
Chapter 2 Mathematical Toolbox Vectors and Scalars 1) Scalars have only a magnitude (numerical value) Denoted by a symbol, a 2) Vectors have a magnitude and direction Denoted by a bold symbol (), or symbol
More informationVectors and 2D Kinematics. AIT AP Physics C
Vectors and 2D Kinematics Coordinate Systems Used to describe the position of a point in space Coordinate system consists of a fixed reference point called the origin specific axes with scales and labels
More informationPhysics 3214 Unit 1 Motion. Vectors and Frames of Reference
Physics 3214 Unit 1 Motion Vectors and Frames of Reference Review Significant Digits 1D Vector Addition BUT First. Diagnostic QuizTime Rules for Significant DigitsRule #1 All non zero digits are ALWAYS
More informationScalars and Vectors I
Scalars and Vectors I Learning Outcome When you complete this module you will be able to: Define and identify scalar and vector quantities and solve simple vector problems graphically. Learning Objectives
More informationUnit 1, Lessons 2-5: Vectors in Two Dimensions
Unit 1, Lessons 2-5: Vectors in Two Dimensions Textbook Sign-Out Put your name in it and let s go! Check-In Any questions from last day s homework? Vector Addition 1. Find the resultant displacement
More informationb) (6) How far down the road did the car travel during the acceleration?
General Physics I Quiz 2 - Ch. 2-1D Kinematics June 17, 2009 Name: For full credit, make your work clear to the grader. Show the formulas you use, all the essential steps, and results with correct units
More informationIntroduction to Vectors
Introduction to Vectors Why Vectors? Say you wanted to tell your friend that you re running late and will be there in five minutes. That s precisely enough information for your friend to know when you
More informationVector x-component (N) y-component (N)
Name AP Physics C Summer Assignment 2014 Where calculations are required, show your work. Be smart about significant figures. Print these sheets and hand them in (neatly done) on the first day of class.
More informationChapter 3 Vectors Prof. Raymond Lee, revised
Chapter 3 Vectors Prof. Raymond Lee, revised 9-2-2010 1 Coordinate systems Used to describe a point s position in space Coordinate system consists of fixed reference point called origin specific axes with
More information9.4 Polar Coordinates
9.4 Polar Coordinates Polar coordinates uses distance and direction to specify a location in a plane. The origin in a polar system is a fixed point from which a ray, O, is drawn and we call the ray the
More informationChapter 3 Vectors in Physics. Copyright 2010 Pearson Education, Inc.
Chapter 3 Vectors in Physics Units of Chapter 3 Scalars Versus Vectors The Components of a Vector Adding and Subtracting Vectors Unit Vectors Position, Displacement, Velocity, and Acceleration Vectors
More informationFebruary 26, Algebraic Method (filled).notebook PHYSICS 11 TEACHER'S NOTES LESSON
PHYSICS 11 TEACHER'S NOTES LESSON 1 Adding Two Vectors Algebraically Going the Other Way: Making Component Vectors 2 3 4 Adding Vectors Algebraically Section 2.2 Drag and drop the following steps to the
More informationCONDITIONS OF EQUILIBRIUM
CONDITIONS OF EQUILIBRIUM Introduction Aim: To investigate the conditions required for an object to be in equilibrium This exercise looks at a rigid object which is in both translational and rotational
More informationPhysics 40 Chapter 3: Vectors
Physics 40 Chapter 3: Vectors Cartesian Coordinate System Also called rectangular coordinate system x-and y- axes intersect at the origin Points are labeled (x,y) Polar Coordinate System Origin and reference
More information10.2 Introduction to Vectors
Arkansas Tech University MATH 2934: Calculus III Dr. Marcel B Finan 10.2 Introduction to Vectors In the previous calculus classes we have seen that the study of motion involved the introduction of a variety
More informationOtterbein University Department of Physics Physics Laboratory Partner s Name: EXPERIMENT D FORCE VECTORS
Name: Partner s Name: EXPERIMENT 1500-7 2D FORCE VECTORS INTRODUCTION A vector is represented by an arrow: it has a direction and a magnitude (or length). Vectors can be moved around the page without changing
More informationVectors. Introduction
Chapter 3 Vectors Vectors Vector quantities Physical quantities that have both numerical and directional properties Mathematical operations of vectors in this chapter Addition Subtraction Introduction
More informationNorth by Northwest - An Introduction to Vectors
HPP A9 North by Northwest - An Introduction to Vectors Exploration GE 1. Let's suppose you and a friend are standing in the parking lot near the Science Building. Your friend says, "I am going to run at
More informationMain Ideas in Class Today
Main Ideas in Class Today After today, you should be able to: Understand vector notation Use basic trigonometry in order to find the x and y components of a vector (only right triangles) Add and subtract
More informationReview of Coordinate Systems
Vector in 2 R and 3 R Review of Coordinate Systems Used to describe the position of a point in space Common coordinate systems are: Cartesian Polar Cartesian Coordinate System Also called rectangular coordinate
More informationReview. Projectile motion is a vector. - Has magnitude and direction. When solving projectile motion problems, draw it out
Projectile Motion Review Projectile motion is a vector - Has magnitude and direction When solving projectile motion problems, draw it out Two methods to drawing out vectors: 1. Tail-to-tip method 2. Parallelogram
More informationOpenStax-CNX module: m Vectors. OpenStax College. Abstract
OpenStax-CNX module: m49412 1 Vectors OpenStax College This work is produced by OpenStax-CNX and licensed under the Creative Commons Attribution License 4.0 In this section you will: Abstract View vectors
More informationPhysics Chapter 3 Notes. Section 3-1: Introduction to Vectors (pages 80-83)
Physics Chapter 3 Notes Section 3-1: Introduction to Vectors (pages 80-83) We can use vectors to indicate both the magnitude of a quantity, and the direction. Vectors are often used in 2- dimensional problems.
More informationChapter 5. Forces in Two Dimensions
Chapter 5 Forces in Two Dimensions Chapter 5 Forces in Two Dimensions In this chapter you will: Represent vector quantities both graphically and algebraically. Use Newton s laws to analyze motion when
More information3 TWO-DIMENSIONAL KINEMATICS
Chapter 3 Two-Dimensional Kinematics 95 3 TWO-DIMENSIONAL KINEMATICS Figure 3.1 Everyday motion that we experience is, thankfully, rarely as tortuous as a rollercoaster ride like this the Dragon Khan in
More informationVectors (Trigonometry Explanation)
Vectors (Trigonometry Explanation) CK12 Editor Say Thanks to the Authors Click http://www.ck12.org/saythanks (No sign in required) To access a customizable version of this book, as well as other interactive
More informationChapter 5: Forces in Two Dimensions. Click the mouse or press the spacebar to continue.
Chapter 5: Forces in Two Dimensions Click the mouse or press the spacebar to continue. Chapter 5 Forces in Two Dimensions In this chapter you will: Represent vector quantities both graphically and algebraically.
More informationGround Rules. PC1221 Fundamentals of Physics I. Coordinate Systems. Cartesian Coordinate System. Lectures 5 and 6 Vectors.
PC1221 Fundamentals of Phsics I Lectures 5 and 6 Vectors Dr Ta Seng Chuan 1 Ground ules Switch off our handphone and pager Switch off our laptop computer and keep it No talking while lecture is going on
More informationDISPLACEMENT AND FORCE IN TWO DIMENSIONS
DISPLACEMENT AND FORCE IN TWO DIMENSIONS Vocabulary Review Write the term that correctly completes the statement. Use each term once. coefficient of kinetic friction equilibrant static friction coefficient
More informationAdding Vectors in Two Dimensions
Slide 37 / 125 Adding Vectors in Two Dimensions Return to Table of Contents Last year, we learned how to add vectors along a single axis. The example we used was for adding two displacements. Slide 38
More informationProjectile Motion and 2-D Dynamics
Projectile Motion and 2-D Dynamics Vector Notation Vectors vs. Scalars In Physics 11, you learned the difference between vectors and scalars. A vector is a quantity that includes both direction and magnitude
More informationVectors. Example: Example: 2 cm. Parts of a vector: 3 cm. Body / Line Segment. Tail / Toe. Tip / Head
Vectors The study of motion involves the introduction of a variety of quantities which are used to describe the physical world. Examples of such quantities include distance, displacement, speed, velocity,
More informationGENERAL PHYSICS (101 PHYS)
INAYA MEDICAL COLLEGE (IMC) PHYS 101- LECTURE 1 GENERAL PHYSICS (101 PHYS) DR. MOHAMMED MOSTAFA EMAM LECTURES & CLASS ACTIVITIES https://inayacollegedrmohammedemam.wordpress.com/ Password: drmohammedemam
More informationSCIENTIFIC MEASUREMENTS
SCIENTIFIC MEASUREMENTS Textbook References: Textbook 4 th, Appendix A-1 & C-1 Textbook 5 th, Appendix B Lesson Objectives: By Studying this chapter, you will learn 1. What the fundamental quantities of
More informationChapter 3 Kinematics in Two Dimensions; Vectors
Chapter 3 Kinematics in Two Dimensions; Vectors Vectors and Scalars Addition of Vectors Graphical Methods (One and Two- Dimension) Multiplication of a Vector by a Scalar Subtraction of Vectors Graphical
More information