Chapter 11. Work. Copyright 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

Transcription

1 Chapter 11. Work In this chapter we explore How many kinds of energy there are; Under what conditions energy is conserved; How a system gains or loses energy. Chapter Goal: To develop a more complete understanding of energy and its conservation.

2 Chapter 11. Work Topics: The Basic Energy Model Work and Kinetic Energy Calculating and Using Work The Work Done by a Variable Force Force, Work, and Potential Energy Finding Force from Potential Energy Thermal Energy Conservation of Energy Power

3 Chapter 11. Reading Quizzes

4 The statement K = W is called the A. law of conservation of energy. B. work-kinetic energy theorem. C. kinetic energy equation. D. weight-kinetic energy theorem.

5 The statement K = W is called the A. law of conservation of energy. B. work-kinetic energy theorem. C. kinetic energy equation. D. weight-kinetic energy theorem.

6 The transfer of energy to a system by the application of a force is called A. dot product. B. power. C. work. D. watt. E. energy transformations.

7 The transfer of energy to a system by the application of a force is called A. dot product. B. power. C. work. D. watt. E. energy transformations.

8 Chapter 11. Basic Content and Examples

9 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.

10 Work and Kinetic Energy Consider a force acting on a particle as the particle moves along the s-axis from si to sf. The force component Fs parallel to the s-axis causes the particle to speed up or slow down, thus transferring energy to or from the particle. We say that the force does work on the particle. The unit of work is J. As the particle is moved by this single force, its kinetic energy changes as follows:

11 Work and Kinetic Energy

12 Work Done by a Constant Force Consider a particle which experiences a constant force which makes an angle θ with respect to the particle s displacement. The work done is Both F and θ are constant, so they can be taken outside the integral. Thus You should recognize this as the dot product of the force vector and the displacement vector:

13 EXAMPLE 11.1 Pulling a suitcase QUESTION:

14 EXAMPLE 11.1 Pulling a suitcase

15 EXAMPLE 11.1 Pulling a suitcase

16 EXAMPLE 11.1 Pulling a suitcase

17 EXAMPLE 11.1 Pulling a suitcase

18 Tactics: Calculating the work done by a constant force

19 Tactics: Calculating the work done by a constant force

20 Tactics: Calculating the work done by a constant force

21 EXAMPLE 11.6 Calculating work using the dot product QUESTION:

22 EXAMPLE 11.6 Calculating work using the dot product

23 EXAMPLE 11.6 Calculating work using the dot product

24 EXAMPLE 11.6 Calculating work using the dot product

25 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 cure, or by actually doing the integration.

26 EXAMPLE 11.7 Using work to find the speed of a car QUESTION:

27 EXAMPLE 11.7 Using work to find the speed of a car

28 EXAMPLE 11.7 Using work to find the speed of a car

29 EXAMPLE 11.7 Using work to find the speed of a car

30 The Work-Kinetic Energy Theorem when Nonconservative Forces Are Involved A force for which the work is not independent of the path is called a nonconservative force. It is not possible to define a potential energy for a nonconservative force. If Wc is the work done by all conservative forces, and Wnc is the work done by all nonconservative forces, then But the work done by the conservative forces is the negative of the change in potential energy, so the workkinetic energy theorem becomes

31 EXAMPLE 11.9 Using work and potential energy together QUESTION:

32 EXAMPLE 11.9 Using work and potential energy together

33 EXAMPLE 11.9 Using work and potential energy together

34 EXAMPLE 11.9 Using work and potential energy together

35 EXAMPLE 11.9 Using work and potential energy together

36 EXAMPLE 11.9 Using work and potential energy together

37 Conservation of Energy

38 Energy Bar Charts We may express the conservation of energy concept as an energy equation. We may also represent this equation graphically with an energy par chart.

39 EXAMPLE Energy bar chart I

40 EXAMPLE Energy bar chart I

41 EXAMPLE Energy bar chart II

42 EXAMPLE Energy bar chart II

43 Problem-Solving Strategy: Solving Energy Problems

44 Problem-Solving Strategy: Solving Energy Problems

45 Problem-Solving Strategy: Solving Energy Problems

46 Problem-Solving Strategy: Solving Energy Problems

47 Power The rate at which energy is transferred or transformed is called the power, P, and it is defined as The unit of power is the watt, which is defined as 1 watt = 1 W = 1 J/s.

48 EXAMPLE Choosing a motor QUESTION:

49 EXAMPLE Choosing a motor

50 Chapter 11. Summary Slides

51 General Principles

52 General Principles

53 General Principles

54 Important Concepts

55 Important Concepts

56 Important Concepts

57 Important Concepts

58 Applications

59 Applications

60 Chapter 11. Clicker Questions

61 A child slides down a playground slide at constant speed. The energy transformation is A. B. C. D. E. There is no transformation because energy is conserved.

62 A child slides down a playground slide at constant speed. The energy transformation is A. B. C. D. E. There is no transformation because energy is conserved.

63 A particle moving along the x-axis experiences the force shown in the graph. If the particle has 2.0 J of kinetic energy as it passes x = 0 m, what is its kinetic energy when it reaches x = 4 m? A. 0.0 J B. 2.0 J C. 6.0 J D. 4.0 J E. 2.0 J

64 A particle moving along the x-axis experiences the force shown in the graph. If the particle has 2.0 J of kinetic energy as it passes x = 0 m, what is its kinetic energy when it reaches x = 4 m? A. 0.0 J B. 2.0 J C. 6.0 J D. 4.0 J E. 2.0 J

65 A crane lowers a steel girder into place at a construction site. The girder moves with constant speed. Consider the work Wg done by gravity and the work WT done by the tension in the cable. Which of the following is correct? A. Wg and WT are both zero. B. Wg is negative and WT is negative. C. Wg is negative and WT is positive. D. Wg is positive and WT is positive. E. Wg is positive and WT is negative.

66 A crane lowers a steel girder into place at a construction site. The girder moves with constant speed. Consider the work Wg done by gravity and the work WT done by the tension in the cable. Which of the following is correct? A. Wg and WT are both zero. B. Wg is negative and WT is negative. C. Wg is negative and WT is positive. D. Wg is positive and WT is positive. E. Wg is positive and WT is negative.

67 Which force does the most work? A. the 10 N force B. the 8 N force C. the 6 N force D. They all do the same amount of work.

68 Which force does the most work? A. the 10 N force B. the 8 N force C. the 6 N force D. They all do the same amount of work.

69 A particle moves along the x-axis with the potential energy shown. The force on the particle when it is at x = 4 m is A. 1 N. B. 2 N. C. 1 N. D. 2 N. E. 4 N.

70 A particle moves along the x-axis with the potential energy shown. The force on the particle when it is at x = 4 m is A. 1 N. B. 2 N. C. 1 N. D. 2 N. E. 4 N.

71 A child at the playground slides down a pole at constant speed. This is a situation in which A. U Eth. Emech is conserved. B. U Eth. Emech is not conserved but Esys is. C. U Wext. Neither Emech nor Esys is conserved. D. U K. Emech is not conserved but Esys is. E. K Eth. Emech is not conserved but Esys is.

72 A child at the playground slides down a pole at constant speed. This is a situation in which A. U Eth. Emech is conserved. B. U Eth. Emech is not conserved but Esys is. C. U Wext. Neither Emech nor Esys is conserved. D. U K. Emech is not conserved but Esys is. E. K Eth. Emech is not conserved but Esys is.

73 Four students run up the stairs in the time shown. Rank in order, from largest to smallest, their power outputs Pa to Pd. A. Pd > Pb > Pa > Pc B. Pd > Pa = Pb > Pc C. Pb > Pa = Pc > Pd D. Pc > Pb = Pa > Pd E. Pb > Pa > Pc > Pd

74 Four students run up the stairs in the time shown. Rank in order, from largest to smallest, their power outputs Pa to Pd. A. Pd > Pb > Pa > Pc B. Pd > Pa = Pb > Pc C. Pb > Pa = Pc > Pd D. Pc > Pb = Pa > Pd E. Pb > Pa > Pc > Pd