Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Motion diagrams Position and time Velocity Scientific notation and units Vectors and motion Chapter 1 Concepts of Motion and Mathematical Background Topics: Sample question: As this snowboarder moves in a graceful arc through the air, the direction of his motion, and the distance between each of his positions and the next, is constantly changing. What language should we use to describe this motion? Slide 1-1

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Checking Understanding Maria is at position x = 23 m. She then undergoes a displacement ∆x = –50 m. What is her final position? A.–27 m B.–50 m C.23 m D.73 m Slide 1-16

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Maria is at position x = 23 m. She then undergoes a displacement ∆x = –50 m. What is her final position? A.–27 m Slide 1-17 Answer

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 1-20 Checking Understanding Two runners jog along a track. The times at each position are shown. Which runner is moving faster? C.They are both moving at the same speed.

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 1-21 Two runners jog along a track. The times at each position are shown. Which runner is moving faster? C.They are both moving at the same speed. Answer

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 1-7 Motion Diagram Practice

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Exercise Alice is sliding along a smooth, icy road on her sled when she suddenly runs headfirst into a large, very soft snowbank that gradually brings her to a halt. Draw a motion diagram for Alice. Show and label all displacement vectors. Slide 1-30

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Exercise Alice is sliding along a smooth, icy road on her sled when she suddenly runs headfirst into a large, very soft snowbank that gradually brings her to a halt. Draw a motion diagram for Alice. Show and label all displacement vectors. Slide 1-30

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Speed Slide 1-22 The car moves 40 m in 1 s. Its speed is = m 1 s m s The bike moves 20 m in 1 s. Its speed is = m 1 s m s

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Velocity Slide 1-23

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Vectors and Motion A quantity that requires both a magnitude (or size) and a direction can be represented by a vector. Graphically, we represent a vector by an arrow. The velocity of this car is 100 m/s (magnitude) to the left (direction). This boy pushes on his friend with a force of 25 N to the right. Slide 1-28

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Displacement Vectors A displacement vector starts at an object’s initial position and ends at its final position. It doesn’t matter what the object did in between these two positions. In motion diagrams, the displacement vectors span successive particle positions. Slide 1-29

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. Velocity Vectors Slide 1-34

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 Review Motion Models

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. 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?