Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Vectors, coordinate systems, and components Motion Models Problem Solving Strategy Chapters 2 & 3 Vectors, Problem Solving, and Motion Models Topics: Slide 3-1

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. 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 3-17 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? 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 Motion Models General Motion Model Constant Velocity Model

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 1-7 Problem Solving Strategy (PSS) On problems, it is important to show how you reasoned from the information given in the problem and key physics ideas to your final answer. The correct final answer with units is only worth 1-3 points. The remainder of the points are given for the quality of your solution.†You are expected to include the following to receive full credit: Prepare Identify the Physics: State explicitly which physics principle apply to the problem situation and that you will use to solve the problem Drawing a Picture: Draw at least one picture to visualize the physics of the problem and define your variables and constants. For motion problems this could be a motion diagram, motion graph, or pictorial diagram (Friday) Collecting Necessary Information: State all the information given in the problem with correct units. Include preliminary calculations such as unit conversions Solve Start with key equation(s) in symbol form Solve for the unknown quantity in symbols explicitly before numeric calculations Then substitute numbers with units and calculate the numeric answer Assess Check to see if your answer is reasonable Does it answer the question that was asked Does it have the right units? Be prepared to make reasonable estimations and state your assumptions when solving problems. Be aware of significant digits in your answers. (Keep lots of digits until the final calculation, then round to the appropriate precision. For intermediate steps, remember to keep one extra siginificant digit