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Chapter 10 Lecture

Chapter 10 Lecture. Chapter 10 Energy. Chapter Goal: To introduce the concept of energy and the basic energy model. Slide 10-2. Chapter 10 Preview. Slide 10-3. Chapter 10 Preview. Slide 10-4. Chapter 10 Preview. Slide 10-5. Chapter 10 Preview. Slide 10-6. Chapter 10 Preview.

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Chapter 10 Lecture

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  1. Chapter 10 Lecture

  2. Chapter 10 Energy Chapter Goal: To introduce the concept of energy and the basic energy model. Slide 10-2

  3. Chapter 10 Preview Slide 10-3

  4. Chapter 10 Preview Slide 10-4

  5. Chapter 10 Preview Slide 10-5

  6. Chapter 10 Preview Slide 10-6

  7. Chapter 10 Preview Slide 10-7

  8. Chapter 10 Reading Quiz Slide 10-8

  9. Reading Question 10.1 Kinetic energy is • Mass times velocity. • ½ mass times speed-squared. • The area under the force curve in a force-versus-time graph. • Velocity per unit mass. Slide 10-9

  10. Reading Question 10.1 Kinetic energy is • Mass times velocity. • ½ Mass times speed-squared. • The area under the force curve in a force-versus-time graph. • Velocity per unit mass. Slide 10-10

  11. Reading Question 10.2 • A method for keeping track of transformations between kinetic energy and gravitational potential energy, introduced in this chapter, is • Credit-debit tables. • Kinetic energy-versus-time graphs. • Energy bar charts. • Energy conservation pools. • Energy spreadsheets. Slide 10-11

  12. Reading Question 10.2 • A method for keeping track of transformations between kinetic energy and gravitational potential energy, introduced in this chapter, is • Credit-debit tables. • Kinetic energy-versus-time graphs. • Energy bar charts. • Energy conservation pools. • Energy spreadsheets. Slide 10-12

  13. Reading Question 10.3 • Mechanical energy is • The energy due to internal moving parts. • The energy of motion. • The energy of position. • The sum of kinetic energy plus potential energy. • The sum of kinetic, potential, thermal, and elastic energy. Slide 10-13

  14. Reading Question 10.3 • Mechanical energy is • The energy due to internal moving parts. • The energy of motion. • The energy of position. • The sum of kinetic energy plus potential energy. • The sum of kinetic, potential, thermal, and elastic energy. Slide 10-14

  15. Reading Question 10.4 Hooke’s law describes the force of • Gravity. • A spring. • Collisions. • Tension. • None of the above. Slide 10-15

  16. Reading Question 10.4 Hooke’s law describes the force of • Gravity. • A spring. • Collisions. • Tension. • None of the above. Slide 10-16

  17. Reading Question 10.5 A perfectly elastic collision is a collision • Between two springs. • That conserves thermal energy. • That conserves kinetic energy. • That conserves potential energy. • That conserves mechanical energy. Slide 10-17

  18. Reading Question 10.5 A perfectly elastic collision is a collision • Between two springs. • That conserves thermal energy. • That conserves kinetic energy. • That conserves potential energy. • That conserves mechanical energy. Slide 10-18

  19. Chapter 10 Content, Examples, and QuickCheck Questions Slide 10-19

  20. Kinetic Energy K • Kinetic energy is the energy of motion. • All moving objects have kinetic energy. • The more massive an object or the faster it moves, the larger its kinetic energy. Slide 10-20

  21. Potential Energy U • Potential energy is stored energy associated with an object’s position. • The roller coaster’s gravitational potential energy depends on its height above the ground. Slide 10-21

  22. Thermal Energy Eth • Thermal energy is the sum of the microscopic kinetic and potential energies of all the atoms and bonds that make up the object. • An object has more thermal energy when hot than when cold. Slide 10-22

  23. The Basic Energy Model • Within a system, energy can be transformed from one type to another. • The total energy of the system is not changed by these transformations. • This is the law of conservation of energy. • Energy can also be transferred from one system to another. • The mechanical transfer of energy to a system via forces is called work. Slide 10-23

  24. Kinetic Energy and Gravitational Potential Energy • The figure shows a before-and-after representation of an object in free fall. • One of the kinematics equations from Chapter 2, with ay = g, is: • Rearranging: • Multiplying both sides by ½m: Slide 10-24

  25. Kinetic Energy and Gravitational Potential Energy Define kinetic energy as an energy of motion: Define gravitational potential energy as an energy of position: The sum K + Ug is not changed when an object is in free fall. Its initial and final values are equal: Slide 10-25

  26. Kinetic Energy and Gravitational Potential Energy Slide 10-26

  27. QuickCheck 10.1 A child is on a playground swing, motionless at the highest point of his arc. What energy transformation takes place as he swings back down to the lowest point of his motion? • K  Ug • Ug K • Eth K • Ug Eth • K  Eth Slide 10-27

  28. QuickCheck 10.1 A child is on a playground swing, motionless at the highest point of his arc. What energy transformation takes place as he swings back down to the lowest point of his motion? • K  Ug • Ug K • Eth K • Ug Eth • K  Eth Slide 10-27

  29. QuickCheck 10.2 A skier is gliding down a gentle slope at a constant speed. What energy transformation is taking place? K  Ug Ug K Eth K Ug Eth K  Eth Slide 10-29

  30. QuickCheck 10.2 A skier is gliding down a gentle slope at a constant speed. What energy transformation is taking place? K  Ug Ug K Eth K Ug Eth K  Eth Slide 10-30

  31. Example 10.1 Launching a Pebble Slide 10-31

  32. Example 10.1 Launching a Pebble Slide 10-32

  33. Example 10.1 Launching a Pebble Slide 10-33

  34. Energy Bar Charts • A pebble is tossed up into the air. • The simple bar charts below show how the sum of K + Ug remains constant as the pebble rises and then falls. Slide 10-34

  35. Energy Bar Charts • The figure below shows how to make an energy bar chart suitable for problem solving. • The chart is a graphical representation of the energy equation Kf + Ugf = Ki + Ugi. Slide 10-35

  36. QuickCheck 10.3 Ball A has half the mass and eight times the kinetic energy of ball B. What is the speed ratio vA/vB? 16 4 2 1/4 1/16 Slide 10-36

  37. QuickCheck 10.3 Ball A has half the mass and eight times the kinetic energy of ball B. What is the speed ratio vA/vB? 16 4 2 1/4 1/16 Slide 10-37

  38. QuickCheck 10.4 Rank in order, from largest to smallest, the gravitational potential energies of the balls. 1 > 2 = 4 > 3 1 > 2 > 3 > 4 3 > 2 > 4 > 1 3 > 2 = 4 > 1 Slide 10-38

  39. QuickCheck 10.4 Rank in order, from largest to smallest, the gravitational potential energies of the balls. 1 > 2 = 4 > 3 1 > 2 > 3 > 4 3 > 2 > 4 > 1 3 > 2 = 4 > 1 Slide 10-39

  40. The Zero of Potential Energy • Amber and Bill use coordinate systems with different origins to determine the potential energy of a rock. • No matter where the rock is, Amber’s value of Ug will be equal to Bill’s value plus 9.8 J. • If the rock moves, both will calculate exactly the same value for Ug. • In problems, only Ug has physical significance, not the value of Ug itself. Slide 10-40

  41. Example 10.2 The Speed of a Falling Rock Slide 10-41

  42. Example 10.2 The Speed of a Falling Rock Slide 10-42

  43. Example 10.2 The Speed of a Falling Rock Slide 10-43

  44. Example 10.2 The Speed of a Falling Rock ASSESS The figure below shows energy bar charts for Amber and Bill. despite their disagreement over the value of Ug, Amber and Bill arrive at the same value for vf and their Kf bars are the same height. You can place the origin of your coordinate system, and thus the “zero of potential energy,” wherever you choose and be assured of getting the correct answer to a problem. Slide 10-44

  45. Gravitational Potential Energy on a Frictionless Surface – Slide 1 of 4 • Figure (a) shows an object of mass m sliding along a frictionless surface. • Figure (b) shows a magnified segment of the surface that, over some small distance, is a straight line. • Define an s-axis parallel to the direction of motion • Newton’s second law along the axis is: Slide 10-45

  46. Gravitational Potential Energy on a Frictionless Surface – Slide 2 of 4 • Using the chain rule, we can write Newton’s second law as: • It is clear from the diagram that the net force along s is: • So Newton’s second law is: Slide 10-46

  47. Gravitational Potential Energy on a Frictionless Surface – Slide 3 of 4 • Rearranging, we obtain: • Note from the diagram that sinds = dy, so: • Integrating this from “before” to “after”: Slide 10-47

  48. Gravitational Potential Energy on a Frictionless Surface – Slide 4 of 4 • With K = ½ mv2 and Ug =mgy, we find that: • The total mechanical energy for a particle moving along any frictionless smooth surface is conserved, regardless of the shape of the surface. Slide 10-48

  49. QuickCheck 10.5 Starting from rest, a marble first rolls down a steeper hill, then down a less steep hill of the same height. For which is it going faster at the bottom? Faster at the bottom of the steeper hill. Faster at the bottom of the less steep hill. Same speed at the bottom of both hills. Can’t say without knowing the mass of the marble. Slide 10-49

  50. QuickCheck 10.5 Starting from rest, a marble first rolls down a steeper hill, then down a less steep hill of the same height. For which is it going faster at the bottom? Faster at the bottom of the steeper hill. Faster at the bottom of the less steep hill. Same speed at the bottom of both hills. Can’t say without knowing the mass of the marble. Slide 10-50

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