Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Vectors, coordinate systems, and components Chapter 3 Vectors Topics: Slide 3-1

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Reading Quiz 1. A x is the __________ of the vector A. A. magnitude B. x-component C. direction D. size E. displacement Slide 3-3 

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Answer 1. A x is the __________ of the vector A. C.direction Slide 3-4 

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Vectors Slide 3-9

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Adding Vectors Graphically Slide 1-33

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Adding Displacement Vectors Slide 1-31

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Example: Adding Displacement Vectors Jenny runs 1 mi to the northeast, then 1 mi south. Graphically find her net displacement. Slide 1-32

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Example: Velocity Vectors Jake throws a ball at a 60° angle, measured from the horizontal. The ball is caught by Jim. Draw a motion diagram of the ball with velocity vectors. Slide 1-35

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 1-7 Adding Vectors Find the resultants graphically (letters in bold are vectors)

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Vector Subtraction Slide 3-10

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 3-11 Acceleration Vectors

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Component Vectors and Components Slide 3-12

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Checking Understanding Slide 3-13 Which of the vectors below best represents the vector sum P + Q ? 

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 3-14 Which of the vectors below best represents the vector sum P + Q ?  Answer

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Checking Understanding Slide 3-15 Which of the vectors below best represents the difference P – Q ? 

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 3-16 Which of the vectors below best represents the difference P – Q ?  Answer

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Checking Understanding Slide 3-17 Which of the vectors below best represents the difference Q – P ? 

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 3-18 Which of the vectors below best represents the difference Q – P ?  Answer

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. What are the x- and y-components of these vectors? A.3, 2 B.2, 3 C.-3, 2 D.2, -3 E.-3, -2 Slide 3-19

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. What are the x- and y-components of these vectors? B.2, 3 Slide 3-20

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. What are the x- and y-components of these vectors? A.3, 4 B.4, 3 C.-3, 4 D.4, -3 E.-3, -4 Slide 3-21

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. What are the x- and y-components of these vectors? B.4, 3 Slide 3-22

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. The following vectors have length 4.0 units. What are the x- and y-components of these vectors? A.3.5, 2.0 B.-2.0, 3.5 C.-3.5, 2.0 D.2.0, -3.5 E.-3.5, -2.0 Slide 3-23

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. The following vectors have length 4.0 units. What are the x- and y-components of these vectors? B. -2.0, 3.5 Slide 3-24

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. The following vectors have length 4.0 units. What are the x- and y-components of these vectors? A.3.5, 2.0 B.2.0, 3.5 C.-3.5, 2.0 D.2.0, -3.5 E.-3.5, -2.0 Slide 3-25

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. The following vectors have length 4.0 units. What are the x- and y-components of these vectors? E.-3.5, -2.0 Slide 3-26

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Examples Slide 3-27 The labeled vectors each have length 4 units. For each vector, what is the component parallel to the ramp? The labeled vectors each have length 4 units. For each vector, what is the component perpendicular to the ramp?

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 3-28 The diagram below shows two successive positions of a particle; it’s a segment of a full motion diagram. Which of the acceleration vectors best represents the acceleration between v i and v f ?  

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 3-29 The diagram below shows two successive positions of a particle; it’s a segment of a full motion diagram. Which of the acceleration vectors best represents the acceleration between v i and v f ?  Answer 

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 1-7 Can you move? Fill in the tables for these motion events by indicating whether or not a motion event is possible. If it is, give an example. If not, explain why not. DisplacementFinal PositionPossible?Example/Explanation 00 0Not 0 0 Average SpeedAverage Velocity Possible?Example/Explanation 00 0Not 0 0

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 1-7 There and Back You and a friend decide to drive to Las Vegas, Nevada on Saturday over Labor Day weekend to go to a concert with some friends who live there. You figure you have to reach the vicinity of Las Vegas by 6 PM in order to meet your friends for dinner before the concert. 1.It's 574 miles from UNM to the Las Vegas strip. You'd like to stop for lunch and gas bout noon. What does your average velocity need to be? 2.It's almost all highway driving from here to Las Vegas. If you keep your speed approximately constant, what speed should your speedometer read while you are driving? 3.After you return to UNM, what is your displacement from the time you left to go to Las Vegas? What is the total distance traveled? What is your average speed and velocity?

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 1-7 Penny = Dollar? A student makes the following argument: "I can prove a dollar equals a penny. Since a dime (10 cents) is one-tenth of a dollar, I can write: 10¢ = 0.1 $ Square both sides of this equation. Since the squares of equals are equal, 100 ¢ = 0.01 $. Since 100 ¢ = 1 $ and 0.01 $ = 1 ¢ it follows that 1$ = 1 ¢.” What's wrong with the argument?

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Looking Back: What You Already Know From this class: In Chapter 1 you learned what a vector is and learned how to add vectors. In Chapter 2 you learned about motion in one dimension. Motion in two dimensions will build naturally on this foundation. From previous classes: You probably know that any two objects in free fall will undergo similar motions; if you drop two objects from the same height at the same time, they will hit the ground simultaneously. You might well have learned a bit about vectors in another course. Slide 3-2