Preview

1. Preview Section 1 Work Section 2 Energy Section 3 Conservation of Energy Section 4Power Section 5Extra questions

2. List five examples of things you have done in the last year that you would consider work. Based on these examples, how do you define work? What do you think?

3. Work • In physics, work is the magnitude of the force (F) times the magnitude of the displacement (d) in the same direction as the force. • W = Fd • What are the SI units for work? • Force units (N)  distance units (m) • N•m are also called joules (J). • How much work is 1 joule? • Lift an apple weighing about 1 N from the floor to the desk, a distance of about 1 m.

4. Work • Pushing this car is work because F and d are in the same direction. • Why aren’t the following tasks considered work? • A student holds a heavy chair at arm’s length for several minutes. • A student carries a bucket of water along a horizontal path while walking at a constant velocity.

5. Work • How would you calculate the work in this case? • What is the component of F in the direction of d? • F cos  • If the angle is 90°, what is the component of F in the direction of d? • F cos 90° = 0 • If the angle is 0°, what is the component of F in the direction of d? • F cos 0° = F

6. Work

7. Work is a Scalar • Work can be positive or negative but does not have a direction. • What is the angle between F and d in each case?

8. Classroom Practice Problem • A 20.0 kg suitcase is raised 3.0 m above a platform. How much work is done on the suitcase? • Answer: 5.9 x 102 J or 590 J

9. Based on the physics definition, list five examples of things you have done in the last year that you would consider work. Now what do you think?

10. What do you think? • You have no doubt heard the term kinetic energy. • What is it? • What factors affect the kinetic energy of an object and in what way? • You have no doubt heard the term potential energy. • What is it? • What factors affect the potential energy of an object and in what way?

11. Kinetic Energy Since then or

12. Kinetic Energy • What are the SI units for KE? • kg•m2/s2 or N•m or J

13. Work and Kinetic Energy • KE is the work an object can do if the speed changes. • Wnet is positive if the speed increases.

14. Classroom Practice Problems • A 6.00 kg cat runs after a mouse at 10.0 m/s. What is the cat’s kinetic energy? • Answer: 3.00 x 102 J or 300 J • Suppose the above cat accelerated to a speed of 12.0 m/s while chasing the mouse. How much work was done on the cat to produce this change in speed? • Answer: 1.32 x 102 J or 132 J

15. Potential Energy • Energy associated with an object’s potential to move due to an interaction with its environment • A book held above the desk • An arrow ready to be released from the bow • Some types of PE are listed below. • Gravitational • Elastic • Electromagnetic

16. Gravitational Potential Energy • What are the SI units? • kg•m2/s2 or N•m or J • The height (h) depends on the “zero level” chosen where PEg= 0.

17. Elastic Potential Energy • The energy available for use in deformed elastic objects • Rubber bands, springs in trampolines, pole-vault poles, muscles • For springs, the distance compressed or stretched = x

18. Spring Constant(k) Click below to watch the Visual Concept. Visual Concept

19. Elastic Potential Energy • The spring constant (k) depends on the stiffness of the spring. • Stiffer springs have higher k values. • Measured in N/m • Force in newtons needed to stretch a spring 1.0 meters • What are the SI Units for PEelastic?

20. Classroom Practice Problems • When a 2.00 kg mass is attached to a vertical spring, the spring is stretched 10.0 cm such that the mass is 50.0 cm above the table. • What is the gravitational potential energy associated with the mass relative to the table? • Answer: 9.81 J • What is the spring’s elastic potential energy if the spring constant is 400.0 N/m? • Answer: 2.00 J

21. Now what do you think? • What is kinetic energy? • What factors affect the kinetic energy of an object and in what way? • How are work and kinetic energy related? • What is potential energy? • What factors affect the gravitational potential energy of an object and in what way? • What factors affect the elastic potential energy of an object and in what way?

22. What do you think? • Imagine two students standing side by side at the top of a water slide. One steps off of the platform, falling directly into the water below. The other student goes down the slide. Assuming the slide is frictionless, which student strikes the water with a greater speed? • Explain your reasoning. • Would your answer change if the slide were not frictionless? If so, how?

23. What do you think? • What is meant when scientists say a quantity is conserved? • Describe examples of quantities that are conserved. • Are they always conserved? If not, why?

24. Mechanical Energy (ME) • ME = KE + PEg + PEelastic • Does not include the many other types of energy, such as thermal energy, chemical potential energy, and others • ME is not a new form of energy. • Just a combination of KE and PE

25. Classroom Practice Problems • Suppose a 1.00 kg book is dropped from a height of 2.00 m. Assume no air resistance. • Calculate the PE and the KE at the instant the book is released. • Answer: PE = 19.6 J, KE = 0 J • Calculate the KE and PE when the book has fallen 1.0 m. (Hint: you will need an equation from Chapter 2.) • Answer: PE = 9.81 J, KE = 9.81 J • Calculate the PE and the KE just as the book reaches the floor. • Answer: PE = 0 J, KE = 19.6 J

26. Table of Values for the Falling Book

27. Conservation of Mechanical Energy • The sum of KE and PE remains constant. • One type of energy changes into another type. • For the falling book, the PE of the book changed into KE as it fell. • As a ball rolls up a hill, KE is changed into PE.

28. Conservation of Mechanical Energy Click below to watch the Visual Concept. Visual Concept

29. Conservation of Energy • Acceleration does not have to be constant. • ME is not conserved if friction is present. • If friction is negligible, conservation of ME is reasonably accurate. • A pendulum as it swings back and forth a few times • Consider a child going down a slide with friction. • What happens to the ME as he slides down? • Answer: It is not conserved but, instead, becomes less and less. • What happens to the “lost” energy? • Answer: It is converted into nonmechanical energy (thermal energy).

30. Classroom Practice Problems • A small 10.0 g ball is held to a slingshot that is stretched 6.0 cm. The spring constant is 2.0  102 N/m. • What is the elastic potential energy of the slingshot before release? • What is the kinetic energy of the ball right after the slingshot is released? • What is the ball’s speed at the instant it leaves the slingshot? • How high does the ball rise if it is shot directly upward?

31. Now what do you think? • Imagine two students standing side by side at the top of a water slide. One steps off of the platform, falling directly into the water below. The other student goes down the slide. Assuming the slide is frictionless, which student strikes the water with a greater speed? • Explain your reasoning. • Would your answer change if the slide were not frictionless? If so, how?

32. Now what do you think? • What is meant when scientists say a quantity is “conserved”? • Describe examples of quantities that are conserved. • Are they always conserved? If not, why?

33. What do you think? • Two cars are identical with one exception. One of the cars has a more powerful engine. How does having more power make the car behave differently? • What does power mean? • What units are used to measure power?

34. Power • The rate of energy transfer • Energy used or work done per second

35. Power • SI units for power are J/s. • Called watts (W) • Equivalent to kg•m2/s3 • Horsepower (hp) is a unit used in the Avoirdupois system. • 1.00 hp = 746 W

36. Watts • These bulbs all consume different amounts of power. • A 100 watt bulb consumes 100 joules of energy every second.

37. Classroom Practice Problems • Two horses pull a cart. Each exerts a force of 250.0 N at a speed of 2.0 m/s for 10.0 min. • Calculate the power delivered by the horses. • How much work is done by the two horses? • Answers: 1.0 x 103 W and 6.0 x 105 J

38. Now what do you think? • Two cars are identical with one exception. One of the cars has a more powerful engine. How does having more power make the car behave differently? • What does power mean? • What units are used to measure power?

39. Preview • Multiple Choice • Short Response • Extended Response

40. Multiple Choice 1. In which of the following situations is work not being done? A. A chair is lifted vertically with respect to the floor. B. A bookcase is slid across carpeting. C. A table is dropped onto the ground. D. A stack of books is carried at waist level across a room.

41. Multiple Choice, continued Use the graph below to answer questions 3–5. The graph shows the energy of a 75 g yo-yo at different times as the yo-yo moves up and down on its string.

42. Multiple Choice, continued 3. By what amount does the mechanical energy of the yo-yo change after 6.0 s? A. 500 mJ B. 0 mJ C. –100 mJ D. –600 mJ

43. Multiple Choice, continued 4. What is the speed of the yo-yo after 4.5 s? F. 3.1 m/s G. 2.3 m/s H. 3.6 m/s J. 1.6 m/s

44. Multiple Choice, continued 5. What is the maximum height of the yo-yo? A. 0.27 m B. 0.54 m C. 0.75 m D. 0.82 m

45. Multiple Choice, continued 6. A car with mass m requires 5.0 kJ of work to move from rest to a final speed v. If this same amount of work is performed during the same amount of time on a car with a mass of 2m, what is the final speed of the second car?

46. Multiple Choice, continued Use the passage below to answer questions 7–8. A 70.0 kg base runner moving at a speed of 4.0 m/s begins his slide into second base. The coefficient of friction between his clothes and Earth is 0.70. His slide lowers his speed to zero just as he reaches the base. 7. How much mechanical energy is lost because of friction acting on the runner? A. 1100 J B. 560 J C. 140 J D. 0 J

47. Multiple Choice, continued Use the passage below to answer questions 7–8. A 70.0 kg base runner moving at a speed of 4.0 m/s begins his slide into second base. The coefficient of friction between his clothes and Earth is 0.70. His slide lowers his speed to zero just as he reaches the base. 8. How far does the runner slide? F. 0.29 m G. 0.57 m H. 0.86 m J. 1.2 m

48. Multiple Choice, continued Use the passage below to answer questions 9–10. A spring scale has a spring with a force constant of 250 N/m and a weighing pan with a mass of 0.075 kg. During one weighing, the spring is stretched a distance of 12 cm from equilibrium. During a second weighing, the spring is stretched a distance of 18 cm.

49. Extended Response Base your answers to questions 14–16 on the information below. A projectile with a mass of 5.0 kg is shot horizontally from a height of 25.0 m above a flat desert surface. The projectile’s initial speed is 17 m/s. Calculate the following for the instant before the projectile hits the surface: 14. The work done on the projectile by gravity.

50. Extended Response, continued Base your answers to questions 14–16 on the information below. A projectile with a mass of 5.0 kg is shot horizontally from a height of 25.0 m above a flat desert surface. The projectile’s initial speed is 17 m/s. Calculate the following for the instant before the projectile hits the surface: 15. The change in kinetic energy since the projectile was fired.