1. Chapter 5 “Work and Energy” Honors Physics

2. Terms In science, certain terms have meanings that are different from common usage. Work, Energy and Power are three of them.

3. Work –Objectives: –1. Recognize the difference between the scientific and ordinary definitions of work. –2. Define work by relating it to force and displacement. –3. Identify where work is being performed in a variety of situations. –4. Calculate the net work done when many forces are applied to an object.

4. Work For the purposes of this class: Work is not where you go to after school. Work doesn’t mean sweat. Work doesn’t equal a paycheck.

5. Scientific Work Work is force x distance x cos  W = F·d·cos  Note that no Work is done by a force at 90° to the direction of motion, cos  = 0. If work is done in the direction of motion then cos  = 1. Work requires some movement.

6. Signs of Work Units are N·m or Joules, J. Force applied on the object that results in a displacement in the same direction is positive, +W. The opposite results in –W. The area under a Force vs Displacement graph = Work.

8. When is work done? –Work is not done on an object unless the object is moved through the application of a force. –If you balance your Physics book above on your head for 5 hours, not only will you not learn any Physics through osmosis, but no work will be done on the book because it does not move.

10. When is work done? –If more than one force is acting on an object, the net work can be found by first finding the net force. –W net =F net d cosθ – Work has SI units of N times meters (N▪m) or joules (J).

11. Example A 20.0 kg suitcase is raised 3.0 m above a platform by a conveyor belt. How much work is done on the suitcase?

12. Example 5.9 x 10 2 J

13. A tugboat pulls a ship with a constant net horizontal force of 5.00 x 10 3 N and causes the ship to move through a harbor. How much work is done on the ship as it moves a distance of 3.00 km?

14. Example 1.5 x 10 7 J

15. Example A weight lifter lifts a set of weights a vertical distance of 2.00 m. If a constant net force of 350 N is exerted on the weights, what is the net work done on the weights?

16. Example 7.0 x 10 2 J

17. Example A shopper in a supermarket pushes a cart with a force of 35 N directed at an angle of 25˚ downward from the horizontal. Find the work done by the shopper on the cart as the shopper moves along a 50.0 m length of aisle.

18. Example 1.6 x 10 3 J

19. Example If 2.0 J of work is done in raising a 180 g apple, how far is it lifted?

20. Example 1.1 m

21. Energy Objectives: 1. Identify several forms of energy. 2.Calculate kinetic energy for an object. 3.Apply the work-kinetic energy theorem to solve problems. 4. Distinguish between kinetic and potential energy. 5. Classify different types of potential energy. 6. Calculate the potential energy associated with an object's position.

22. Energy Energy comes in many forms. Electrical, chemical, heat, and atomic are just a few examples. A good definition of Energy is the ability to do work.

23. Categories of Energies Scientists divide energy into two basic categories: mechanical and non- mechanical. All those energies listed on the previous slide and more can be classified as mechanical or non-mechanical.

24. Kinetic Energy The kinetic energy (KE) of an object is the amount of “work” stored by that object due to its motion. The velocity of the object is the most influential component. KE = ½ mv 2

25. Example A 6.0 kg cat runs after a mouse at 10.0 m/s. What is the cat's kinetic energy?

26. Example 3.0 x 10 2 J

27. Calculate the speed of an 8.0 x 10 4 kg airliner with a kinetic energy of 1.1 x 109 J.

28. Example 1.7 x 10 2 m/s

29. Example Two bullets have masses of 3.0 g and 6.0 g, respectively. Both are fired with a speed of 40.0 m/s. Which bullet has more kinetic energy? What is the ratio of their kinetic energies?

30. Example The bullet with the greater mass; 2 to 1

31. Work-Kinetic Energy Theorem The net work done by a net force acting on an object is equal to the change in kinetic energy. W net = KE = KE f - KE i

32. Example A student wearing frictionless in-line skates on a horizontal surface is pushed by a friend with a constant force of 45 N. How far must the student be pushed, starting from rest, so that her final kinetic energy is 352 J?

33. Example 7.8 m

34. Example A 2.0 x 10 3 kg car accelerates from rest under the actions of two forces. One is a forward force of 1140 N provided by the traction between the wheels and the road. The other is a 950 N resistive force due to various frictional forces. Use the work-kinetic energy theorem to determine how far the car must travel for its speed to reach 2.0 m/s.

35. Example 21 m

36. Example –A 2.1 x 10 3 kg car starts from rest at the top of a driveway that is sloped at an angle of 20.0° with the horizontal. An average frictional force of 4.0 x 10 3 N impedes the car's motion so that the car's speed at the bottom of the driveway is 3.8 m/s. What is the length of the driveway?

37. Example 5.0 m

38. Potential Energy The potential energy (PE) of an object is the amount of “work” stored by that object due to its position. The “height” of the object is the most influential component.

40. Types of Potential Energy For gravitational potential energy: PE g = mgh For elastic potential energy: PE elastic = ½ kx 2 k is the spring constant and x is the distance the spring is compressed or stretched.

41. Elastic Potential Energy Elastic potential energy is the energy stored in any compressed or stretched object. The kinetic energy of an object moved by a spring comes from the potential energy stored in the spring. The length of the spring when no external forces are acting on it is called the relaxed length. When an external force compresses or stretches the spring, elastic potential energy is stored.

43. Example 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. a. What is the gravitational potential energy associated with this mass relative to the table? b. What is the spring's elastic potential energy if the spring constant is 400.0 N/m? c. What is the total potential energy?

44. Example –a. 9.81 J –b. 2.00 J –c. 11.81 J

45. Example A spring with a force constant of 5.2 N/m has a relaxed length of 2.45 m. When a mass is attached to the end of the spring and allowed to come to rest, the vertical length of the spring is 3.57 m. Calculate the elastic potential energy stored in the spring.

46. Example 3.3 J

47. Example –A 40.0 kg child is in a swing that is attached to ropes 2.00 m long. Find the gravitational potential energy associated with the child relative to the child's lowest position under the following conditions: –a. when the ropes are horizontal. –b. when the ropes make a 30.0° angle with the vertical. –c. at the bottom of the circular arc.

48. Example –a. 785 J –b. 106 J –c. 0.00 J

49. Conservation of Energy –Objectives: –1. Identify situations in which conservation of mechanical energy is valid. –2. Recognize the forms that conserved energy can take. –3. Solve problems using conservation of mechanical energy.

50. The Law of Conservation of Energy Energy can’t be created or destroyed, however, it can be transferred. When you burn gasoline in your car the chemical energy is transferred to heat energy, etc.. Total energy is always conserved.

51. Mechanical Energy Mechanical energy is the sum of the kinetic energy and all forms of potential energy that are assoicated with an object or system. ME = KE + PE

52. Conservation of Mechanical Energy In the absence of friction, mechanical energy is conserved. Remember that friction produces heat and heat is not a mechanical energy. ME i = ME f

53. Conservation of Mechanical Energy –In the absence of friction, the total mechanical energy remains the same. –Conservation of mechanical energy –Me i =ME f –If the only force acting on an object is the force due to gravity, then –½ mv i 2 + mgh i = ½ mv f 2 + mgh f –If other forces (besides friction) are acting on an object, add the appropriate potential energy formulae.

54. Example –A small 10.0 g ball is held to a slingshot that is stretched 6.0 cm. The spring constant is 2.0 x 10 2 N/m. –a. What is the elastic potential energy of the slingshot before it is released? –b. What is the kinetic energy of the ball just after the slingshot is released? –c. What is the ball's speed at that instant? –d. How high does the ball rise if it is shot directly upward?

55. Example –a. 0.36 J –b. 0.36 J –c. 8.5 m/s –d. 3.7 m

56. Example A bird is flying with a speed of 18.0 m/s over water when it accidentally drops a 2.00 kg fish. If the altitude of the bird is 5.40 m and friction is disregarded, what is the speed of the fish when it hits the water?

57. Example 20.7 m/s

58. Example A 755 N diver drops from a board 10.0 m above the water's surface. Find the diver's speed 5.00 m above the water's surface. Then find the diver's speed just before striking the water.

59. Example 9.9 m/s; 14.0 m/s

60. Example –An Olympic runner leaps over a hurdle. If the runner's initial vertical speed is 2.2 m/s, how much will the runner's center of mass be raised during the jump?

61. Example 0.25 m

62. Power –Objectives: –1. Relate the concepts of energy, time, and power. –2. Calculate power in two different ways. –3. Explain the effects of machines on work and power.

63. Simple Machines Simple machines change the direction or magnitude of the exerted force but do not change the work done. The usually trade distance for effort.

64. POWER Power is the rate at which work is done. It also describes the rate of energy transfer. P = W / t or F d / t or F (speed) The unit is Watt (W) 1 horsepower = 746 W

65. Example –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. –a. Calculate the power delivered by the horses. –b. How much work is done by the two horses?

66. Example –a. 1.0 x 10 3 W –b. 6.0 x 10 5 J

67. Mechanical Advantage Mechanical Advantage (MA) is the ratio of the effort force compared to the resistance force. MA = F r /F e or W out = W in F r d r = F e d e F r /F e = d e /d r

68. Ideal Mechanical Advantage IMA = d e /d r Efficiency = W o /W i x 100% = MA/IMA x 100% = MA/IMA x 100%