Chapter 11 Work

1. Chapter 11 Work Chapter Goal: To develop a more complete understanding of energy and its conservation. Slide 11-2

2. Chapter 11 Preview Slide 11-3

3. Chapter 11 Preview Slide 11-3

4. Chapter 11 Preview Slide 11-5

5. Chapter 11 Preview Slide 11-6

6. Chapter 11 Preview Slide 11-7

7. Chapter 11 Preview Slide 11-8

8. The Basic Energy Model W > 0: The environment does work on the system and the system’s energy increases. W < 0: The system does work on the environment and the system’s energy decreases. Slide 11-21

9. The Basic Energy Model • The energy of a system is a sum of its kinetic energy K, its potential energy U, and its thermal energy Eth. • The change in system energy is: Energy can be transferred to or from a system by doing work Won the system. This process changes the energy of the system: Esys = W. Energy can be transformed within the system among K,U, and Eth. These processes don’t change the energy of the system: Esys = 0. Slide 11-22

10. Work and Kinetic Energy • The word “work” has a very specific meaning in physics. • Work is energy transferred to or from a body or system by the application of force. • This pitcher is increasing the ball’s kinetic energy by doing work on it. Slide 11-25

11. Work and Kinetic Energy • Consider a force acting on a particle which moves along the s-axis. • The force component Fs causes the particle to speed up or slow down, transferring energy to or from the particle. • The force does work on the particle: • The units of work are N m, where 1 N m = 1 kg m2/s2 = 1 J. Slide 11-26

12. The Work-Kinetic Energy Theorem • The net force is the vector sum of all the forces acting on a particle . • The net work is the sum Wnet = Wi, where Wi is the work done by each force . • The net work done on a particle causes the particle’s kinetic energy to change. Slide 11-27

13. An Analogy with the Impulse-Momentum Theorem • The impulse-momentum theorem is: • The work-kinetic energy theorem is: • Impulse and work are both the area under a force graph, but it’s very important to know what the horizontal axis is! Slide 11-28

14. Work Done by a Constant Force • A force acts with a constant strength and in a constant direction as a particle moves along a straight line through a displacement . • The work done by this force is: • Here is the angle makes relative to . Slide 11-31

15. Example 11.1 Pulling a Suitcase Slide 11-32

16. Example 11.1 Pulling a Suitcase Slide 11-33

17. Tactics: Calculating the Work Done by a Constant Force Slide 11-36

18. Tactics: Calculating the Work Done by a Constant Force Slide 11-37

19. Tactics: Calculating the Work Done by a Constant Force Slide 11-38

20. Example 11.2 Work During a Rocket Launch Slide 11-43

21. Example 11.2 Work During a Rocket Launch Slide 11-44

22. Example 11.2 Work During a Rocket Launch Slide 11-45

23. Example 11.2 Work During a Rocket Launch Slide 11-46

24. QuickCheck 11.6 Which force below does the most work? All three displacements are the same. The 10 N force. The 8 N force The 6 N force. They all do the same work. sin60 = 0.87 cos60 = 0.50 Slide 11-47

25. QuickCheck 11.6 Which force below does the most work? All three displacements are the same. The 10 N force. The 8 N force The 6 N force. They all do the same work. sin60 = 0.87 cos60 = 0.50 Slide 11-48

26. QuickCheck 11.7 A light plastic cart and a heavy steel cart are both pushed with the same force for a distance of 1.0 m, starting from rest. After the force is removed, the kinetic energy of the light plastic cart is ________ that of the heavy steel cart. greater than equal to less than Can’t say. It depends on how big the force is. Slide 11-49

27. QuickCheck 11.7 A light plastic cart and a heavy steel cart are both pushed with the same force for a distance of 1.0 m, starting from rest. After the force is removed, the kinetic energy of the light plastic cart is ________ that of the heavy steel cart. greater than equal to less than Can’t say. It depends on how big the force is. Same force, same distance  same work done Same work  change of kinetic energy Slide 11-50

28. Force Perpendicular to the Direction of Motion • The figure shows a particle moving in uniform circular motion. • At every point in the motion, Fs, the component of the force parallel to the instantaneous displacement, is zero. • The particle’s speed, and hence its kinetic energy, doesn’t change, so W = K = 0. • A force everywhere perpendicular to the motion does no work. Slide 11-51

29. QuickCheck 11.8 A car on a level road turns a quarter circle ccw. You learned in Chapter 8 that static friction causes the centripetal acceleration. The work done by static friction is _____. positive negative zero Slide 11-52

30. QuickCheck 11.8 A car on a level road turns a quarter circle ccw. You learned in Chapter 8 that static friction causes the centripetal acceleration. The work done by static friction is _____. positive negative zero Slide 11-53

31. The Dot Product of Two Vectors • The figure shows two vectors, and , with angle  between them. • The dot product of and is defined as: • The dot product is also called the scalar product, because the value is a scalar. Slide 11-54

32. The Dot Product of Two Vectors • The dot product as  ranges from 0 to 180. Slide 11-55

33. Example 11.3 Calculating a Dot Product Slide 11-56

34. The Dot Product Using Components If and , the dot product is the sum of the products of the components: Slide 11-57

35. Example 11.4 Calculating a Dot Product Using Components Slide 11-58

36. Work Done by a Constant Force • A force acts with a constant strength and in a constant direction as a particle moves along a straight line through a displacement . • The work done by this force is: Slide 11-59

37. Example 11.5 Calculating Work Using the Dot Product Slide 11-60

38. Example 11.5 Calculating Work Using the Dot Product Slide 11-61

39. The Work Done by a Variable Force To calculate the work done on an object by a force that either changes in magnitude or direction as the object moves, we use the following: We must evaluate the integral either geometrically, by finding the area under the curve, or by actually doing the integration. Slide 11-62

40. Example 11.6 Using Work to Find the Speed of a Car Slide 11-63

41. Example 11.6 Using Work to Find the Speed of a Car Slide 11-64

42. Example 11.6 Using Work to Find the Speed of a Car Slide 11-65

43. Example 11.6 Using Work to Find the Speed of a Car Slide 11-66

44. Conservative Forces • The figure shows a particle that can move from A to B along either path 1 or path 2 while a force is exerted on it. • If there is a potential energy associated with the force, this is a conservative force. • The work done by as the particle moves from A to B is independent of the path followed. Slide 11-67

45. Nonconservative Forces • The figure is a bird’s-eye view of two particles sliding across a surface. • The friction does negative work: Wfric = kmgs. • The work done by friction depends on s, the distance traveled. • This is not independent of the path followed. • A force for which the work is not independent of the path is called a nonconservative force. Slide 11-68

46. Mechanical Energy • Consider a system of objects interacting via both conservative forces and nonconservative forces. • The change in mechanical energy of the system is equal to the work done by the nonconservative forces: • Mechanical energy isn’t always conserved. • As the space shuttle lands, mechanical energy is being transformed into thermal energy. Slide 11-69

47. Example 11.8 Using Work and Potential Energy Slide 11-70

48. Example 11.8 Using Work and Potential Energy Slide 11-71

49. Example 11.8 Using Work and Potential Energy Slide 11-72

50. Finding Force from Potential Energy • The figure shows an object moving through a small displacement s while being acted on by a conservative force . • The work done over this displacement is: • Because is a conservative force, the object’s potential energy changes by U = −W = −FsΔs over this displacement, so that: Slide 11-73