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Chapter 1 Lecture

Chapter 1 Lecture. Chapter 1 Concepts of Motion. Chapter Goal: To introduce the fundamental concepts of motion. Pickup PSE3e Photo from page 2, snowboarder jump. Slide 1-2. Chapter 1 Preview. Slide 1-3. Chapter 1 Preview. Slide 1-4. Chapter 1 Reading Quiz. Slide 1-5.

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Chapter 1 Lecture

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  1. Chapter 1 Lecture

  2. Chapter 1 Concepts ofMotion Chapter Goal: To introduce the fundamental concepts of motion. Pickup PSE3e Photo from page 2, snowboarder jump. Slide 1-2

  3. Chapter 1 Preview Slide 1-3

  4. Chapter 1 Preview Slide 1-4

  5. Chapter 1 Reading Quiz Slide 1-5

  6. Reading Question 1.1 What is a “particle?” • Any part of an atom. • An object that can be represented as a mass at a single point in space. • A part of a whole. • An object that can be represented as a single point in time. • An object that has no top or bottom, no front or back. Slide 1-6

  7. Reading Question 1.1 What is a “particle?” • Any part of an atom. • An object that can be represented as a mass at a single point in space. • A part of a whole. • An object that can be represented as a single point in time. • An object that has no top or bottom, no front or back. Slide 1-7

  8. Reading Question 1.2 What quantities are shown on a complete motion diagram? • The position of the object in each frame of the film, shown as a dot. • The average velocity vectors (found by connecting each dot in the motion diagram to the next with a vector arrow). • The average acceleration vectors (with one acceleration vector linking each two velocity vectors). • All of the above. Slide 1-8

  9. Reading Question 1.2 What quantities are shown on a complete motion diagram? • The position of the object in each frame of the film, shown as a dot. • The average velocity vectors (found by connecting each dot in the motion diagram to the next with a vector arrow). • The average acceleration vectors (with one acceleration vector linking each two velocity vectors). • All of the above. Slide 1-9

  10. Reading Question 1.3 In physics, what is the difference between “speed” and “velocity”? • Velocity is represented by an exact number, while speed is only an approximate number. • Speed can be positive or negative, while velocity is always positive. • Speed is a scalar, which is the magnitude of the velocity, which is a vector. • Velocity is a scalar and speed is a vector. • Speed and velocity mean the same thing. Slide 1-10

  11. Reading Question 1.3 In physics, what is the difference between “speed” and “velocity”? • Velocity is represented by an exact number, while speed is only an approximate number. • Speed can be positive or negative, while velocity is always positive. • Speed is a scalar, which is the magnitude of the velocity, which is a vector. • Velocity is a scalar and speed is a vector. • Speed and velocity mean the same thing. Slide 1-11

  12. Reading Question 1.4 An acceleration vector • Tells you how fast an object is going. • Is constructed from two velocity vectors. • Is the second derivative of the position. • Is parallel or opposite to the velocity vector. • Acceleration vectors weren’t discussed in this chapter. Slide 1-12

  13. Reading Question 1.4 An acceleration vector • Tells you how fast an object is going. • Is constructed from two velocity vectors. • Is the second derivative of the position. • Is parallel or opposite to the velocity vector. • Acceleration vectors weren’t discussed in this chapter. Slide 1-13

  14. Reading Question 1.5 The pictorial representation of a physics problem consists of • A sketch. • A coordinate system. • Symbols. • A table of values. • All of the above. Slide 1-14

  15. Reading Question 1.5 The pictorial representation of a physics problem consists of • A sketch. • A coordinate system. • Symbols. • A table of values. • All of the above. Slide 1-15

  16. Reading Question 1.6 The basic SI units are • Second, meter, gram. • Second, meter, kilogram. • Second, centimeter, gram. • Meter, meter/second, meter/second2. • Yard, span, cubit. Slide 1-16

  17. Reading Question 1.6 The basic SI units are • Second, meter, gram. • Second, meter, kilogram. • Second, centimeter, gram. • Meter, meter/second, meter/second2. • Yard, span, cubit. Slide 1-17

  18. Chapter 1 Content, Examples, and QuickCheck Questions Slide 1-18

  19. Four basic types of motion Slide 1-19

  20. Making a Motion Diagram • Consider a movie of a moving object. • A movie camera takes photographs at a fixed rate (i.e., 30 photographs every second). • Each separate photo is called a frame. • The car is in a different position in each frame. • Shown are four frames in a filmstrip. Slide 1-20

  21. Making a Motion Diagram • Cut individual frames of the filmstrip apart. • Stack them on top of each other. • This composite photo shows an object’s position at several equally spaced instants of time. • This is called a motion diagram. Slide 1-21

  22. Examples of Motion Diagrams • An object that has a single position in a motion diagram is at rest. • Example: A stationary ball on the ground. • An object with images that are equally spaced is moving with constant speed. • Example: A skateboarder rolling down the sidewalk. Slide 1-22

  23. Examples of Motion Diagrams • An object with images that have increasing distance between them is speeding up. • Example: A sprinter starting the 100 meter dash. • An object with images that have decreasing distance between them is slowing down. • Example: A car stopping for a red light. Slide 1-23

  24. Examples of Motion Diagrams • A motion diagram can show more complex motion in two dimensions. • Example: A jump shot from center court. • In this case the ball is slowing down as it rises, and speeding up as it falls. Slide 1-24

  25. QuickCheck 1.1 Motion diagrams are made of two cars. Both have the same time interval between photos. Which car, A or B, is going slower? Car A Car B Slide 1-25

  26. QuickCheck 1.1 Motion diagrams are made of two cars. Both have the same time interval between photos. Which car, A or B, is going slower? Car A Car B Slide 1-26

  27. The Particle Model • Often motion of the object as a whole is not influenced by details of the object’s size and shape. • We only need to keep track of a single point on the object. • So we can treat the object as if all its mass were concentrated into a single point. • A mass at a single point in space is called a particle. • Particles have no size, no shape and no top, bottom, front or back. • Below is a motion diagram of a car stopping, using the particle model. Slide 1-27

  28. The Particle Model Motion Diagram in which the object is represented as a particle Motion diagram of a rocket launch Slide 1-26

  29. QuickCheck 1.2 Three motion diagrams are shown. Which is a dust particle settling to the floor at constant speed, which is a ball dropped from the roof of a building, and which is a descending rocket slowing to make a soft landing on Mars? • (a) is dust, (b) is ball, (c) is rocket. • (a) is ball, (b) is dust, (c) is rocket. • (a) is rocket, (b) is dust, (c) is ball. • (a) is rocket, (b) is ball, (c) is dust. • (a) is ball, (b) is rocket, (c) is dust. Slide 1-29

  30. QuickCheck 1.2 Three motion diagrams are shown. Which is a dust particle settling to the floor at constant speed, which is a ball dropped from the roof of a building, and which is a descending rocket slowing to make a soft landing on Mars? • (a) is dust, (b) is ball, (c) is rocket. • (a) is ball, (b) is dust, (c) is rocket. • (a) is rocket, (b) is dust, (c) is ball. • (a) is rocket, (b) is ball, (c) is dust. • (a) is ball, (b) is rocket, (c) is dust. Slide 1-30

  31. Position and Time • In a motion diagram it is useful to add numbers to specify where the object is and when the object was at that position. • Shown is the motion diagram of a basketball, with 0.5 s intervals between frames. • A coordinate system has been added to show (x, y). • The frame at t 0 is frame 0, when the ball is at the origin. • The ball’s position in frame 4 can be specified with coordinates (x4, y4)  (12 m, 9 m) at time t4 2.0 s. Slide 1-31

  32. Position as a Vector • Another way to locate the ball is to draw an arrow from the origin to the point representing the ball. • You can then specify the length and direction of the arrow. • This arrow is called the position vector of the object. • The position vector is an alternative form of specifying position. • It does not tell us anything different than the coordinates (x, y). Slide 1-32

  33. Tactics: Vector Addition Slide 1-33

  34. Vector Addition Example: Displacement Sam is standing 50 ft east of the corner of 12th Street and Vine. He then walks northeast for 100 ft to a second point. What is Sam’s change of position? • Sam’s initial position is the vector . • Vector is his position after he finishes walking. • Sam has changed position, and a change in position is called a displacement. • His displacement is the vector labeled . Slide 1-34

  35. The negative of a vector. Definition of Displacement • The displacement of an object as it moves from an initial position to a final position is • The definition of involves vector subtraction. • With numbers, subtraction is the same as the addition of a negative number. • Similarly, with vectors Slide 1-35

  36. Tactics: Vector Subtraction Slide 1-36

  37. QuickCheck 1.3 Given vectors and , what is ? Slide 1-37

  38. Given vectors and , what is ? QuickCheck 1.3 Slide 1-38

  39. QuickCheck 1.4 Given vectors and , what is ? Slide 1-39

  40. Given vectors and , what is ? QuickCheck 1.4 Slide 1-40

  41. Time Interval • It’s useful to consider a change in time. • An object may move from an initial position at timeti to a final position at time tf. • Different observers may choose different coordinate systems and different clocks, however, all observers find the same values for the displacement  and the time interval t. A stopwatch is used to measure a time interval. Slide 1-41

  42. Average Speed, Average Velocity To quantify an object’s fastness or slowness, we define a ratio: • Average speed does not include information about direction of motion. • The average velocity of an object during a time interval t, in which the object undergoes a displacement  , is the vector: The victory goes to the runner with the highest average speed. Slide 1-42

  43. Motion Diagrams with Velocity Vectors • The velocity vector is in the same direction as the displacement  . • The length of is directly proportional to the length of  . • Consequently, we may label the vectors connecting the dots on a motion diagram as velocity vectors . • Below is a motion diagram for a tortoise racing a hare. • The arrows are average velocity vectors. • The length of each arrow represents the average speed. Slide 1-43

  44. EXAMPLE 1.2 Accelerating Up a Hill Motion diagram of a car accelerating up a hill. Slide 1-44

  45. Acceleration • Sometimes an object’s velocity is constant as it moves. • More often, an object’s velocity changes as it moves. • Acceleration describes a change in velocity. • Consider an object whose velocity changes from to during the time interval ∆t. • The quantity is the change in velocity. • The rate of change of velocity is called the average acceleration: The Audi TT accelerates from 0 to 60 mph in 6 s. Slide 1-45

  46. Tactics: Finding the Acceleration Vector Slide 1-46

  47. Tactics: Finding the Acceleration Vector • Notice that the acceleration vectors goes beside the dots, not beside the velocity vectors. • That is because each acceleration vector is the difference between two velocity vectors on either side of a dot. Slide 1-47

  48. QuickCheck 1.5 A particle has velocity as it accelerates from 1 to 2. What is its velocity vector as it moves away from point 2 on its way to point 3? Slide 1-48

  49. QuickCheck 1.5 A particle has velocity as it accelerates from 1 to 2. What is its velocity vector as it moves away from point 2 on its way to point 3? Slide 1-49

  50. The Complete Motion Diagram Slide 1-50

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