1. CHAPTERS 10 & 11

6. 10.1 Energy and Work ENERGY: Energy = The property/ability to produce a change in an object or the environment Forms of Energy: Thermal, chemical, solar, nuclear, hydro, fossil fuel, …

7. Kinetic Energy “K or KE” = The energy an object has due to its motion Equation: K = ½ mv 2 Units for KE, kgm 2 /s 2 = Nm

8. Work “W” = The process of changing the energy in a system W = Fdcos  If Force and displacement are in the same direction then W = Fd Units, Nm

10. Work Energy Theorem: W = ΔK W = K 2 – K 1 Joule “J” = unit of energy 1J = 1kgm 2 /s 2 = 1Nm

11. WORK ENERGY TRANSFER If the environment does work on the system, then work “W” is positive (+) and the energy of the system increases. If the system does work on the environment, then W is negative (-) and the energy of the system decreases. System/Box example, put in/out

12. CALCULATING WORK Example with stack of books & 2 volunteers Who did more work and WHY?

13. When _______ picked up the book, she applied a force in the same direction as displacement,  work was done. When ________ carried the books throughout the room, his force on the books was perpendicular (90 o ) to his/books displacement,  NO work was done, as far as physics is concerned. Biologically, ______’s muscles did perform work and required much more energy than ________ to simply pick up one book.

14. Earth & Sun Example Mass of Earth = 5.97 x 10 24 kg Speed of Earth = 20,000 m/s Q: What is the KE of the Earth? A: 1.194 x 10 33 J Q: How much work does the sun do on the Earth while keeping it in orbit? A: zero Q: Why? A: two reasons

15. Explanation #1 W = ΔK W = K 2 – K 1 W = 1/2mv 2 2 – 1/2mv 1 2 W = 1/2(5.97 x 10 24 kg)(20,000m/s) 2 – ½(5.97 x 10 24 kg)(20,000m/s) 2 W = 1.194 x 10 33 J – 1.194 x 10 33 J W = 0

16. Explanation #2 W = Fdcos  W = Fdcos90 o W = Fd(0) W = 0  if force and displacement are perpendicular to each other (90 o ), then NO work is accomplished

17. Example Problem A 150g hockey puck is at rest on ice. A player exerts a constant 400N force over a distance of 0.15m. a) How much work does the player do to the puck? b) What is the Δ in the puck’s energy? c) What is the velocity of the puck when it leaves the stick?

18. Solution “a” W = Fdcos  W = (400N)(0.15m)(cos 0 o ) W = (400N)(0.15m)(1) W = 60Nm W = 60J

19. Solution “b” ΔK = W  ΔK = W = 60J

20. Solution “c” ΔK = K 2 – K 1 = 60J 1/2mv 2 2 – 1/2mv 1 2 = 60J ½(.15kg)(v 2 2 ) – 0 = 60J 0.075kg(v 2 2 ) = 60kgm 2 /s 2 v 2 2 = 60kgm 2 /s 2 /0.075kg v 2 2 = 800m 2 /s 2 v 2 = √800m 2 /s 2 v 2 = 28.3m/s

21. Example Problem #1 A student lifts a box of books that weigh 185N. The box is lifted 0.8m. How much work did the student do on the box? A: W = FD = (185N)(.8m) = 148Nm/J

22. Example Problem #2 Two students together exert a force of 825N in pushing a car 35m. a) How much work do they do on the car? b) If the force were doubled, how much work would they do pushing the car the same distance? A-a: W = Fd = (825N)(35m) = 28,875J A-b: W = Fd = (1650N)(35m) = 57,750J

23. Example Problem #3 A 0.18kg ball falls 2.5m. How much work does the force of gravity do on the ball? A: W = Fd = ????? What is the force????? F = weight due to gravity = mg W= mgd = (.18kg)(9.8m/s 2 )(2.5m) =4.41J

24. Example #4 A forklift raises a box 1.2m doing 7kJ of work on it. What is the mass of the box? A: W = Fd = mgd  m = W/gd m = 7000kgm 2 s 2 /(9.8m/s 2 x 1.2m) m = 595kg

25. Example #5 You and a friend each carry identical boxes to a room one floor above you and down the hall. You choose to carry it first up the stairs, then down the hall. Your friend carries it down the hall, then back, then down the hall again, then up the stairwell. Who does more work? Both do the same. The work done was only carrying the box up the stairs.

26. Lawn Mower Example (pg227) How much work is done by Hannah if she pushes a lawn mower 10m with a force of 125N at an angle of 25 o from horizontal? Draw sketch, equation, steps,… W = Fdcos  W = (125N)(10m)(cos25 o ) W = 1132.8J

27. Finding Work Done When Forces Change Sketch 3 examples of Force vs displacement graphs a) rectangle b) triangle c) ½ circle  Using a Force vs displacement graph, the work done on an object is represented by the area under the curve/line.

28. POWER Power = The rate of doing work. Power “P” = W/t W = work in joules t = time in seconds P = W/t (J/s) 1J/s = 1 W (watt)

29. A watt “W” is a small amount of power  power is usually measured in kW (kilowatts). Power plant outputs are measured in MW (MegaWatts) Shippingport Nuclear plants  900MW (2) Shippingport Bruce Mansfield, coal plants  1200MW (3)

30. Light Bulb Example How long can you leave a light on at home before your parents yell at you? Light bulb watts = _____ Time to get in trouble = _____ Cost of a kWhr  12 cents per kWhr, National Average as of 4-4-11

31. Power Example An electric motor lifts an elevator 9m in 15s by exerting an upward force of 12,000N. How much power did it take to raise the elevator? P = W/t P = Fd/t P = (12,000kgm/s 2 )(9m) ÷ 15s P = 7200kgm 2 /s 2 P = 7200W

32. 11.1 THE MANY FORMS OF ENERGY A Model of The Work-Energy Theorem Your own notes

33. Kinetic Energy KE = energy due to an object’s motion KE = ½ mv 2 A 1000kg car is traveling at 20m/s, how much KE would it have if its velocity doubled?

34. KE = ½ mv 2 KE = ½ (1000kg)(20m/s) 2 KE = ½ (1000kg)(400m 2 /s 2 ) KE = 200,000J KE = ½ (1000kg)(40m/s) 2 KE = ½ (1000kg)(1600m 2 /s 2 ) KE = 800,000J

35. Example A 555kg car is traveling at 15m/s, a force is applied increasing its velocity to 40m/s. a) What is the initial and final KE? b) How much work was done to the car?

36. STORED ENERGY Example with chair, book, meter stick & eraser/…..???? Stored Energy = Potential Energy = … The energy stored in an object that has the “potential” to do work. Examples: Stretched springs, chemical, batteries, …

37. GRAVITATIONAL POTENTIAL ENERGY Gravitational potential energy “U g ” = The stored energy in an object by virtue of its position above some reference level and the force of gravity acting on it. Ug = mgh W = Fdcos  → when  = 0 → W = Fd  W = mad W = ΔU g = Δmgh

38. Example Tossing Ball How does gravity affect the work done on the ball? When is the work positive, Negative, zero? When is the acceleration Positive, negative, zero?

39. Sketch diagrams of Force & d How does gravity affect work? On the way up, the work done by gravity is negative. Why? Because F & d are in opposite directions, the force (force of gravity) is in the negative direction (pulling down), but the displacement is positive (upward). W = ∆Ug = Δmgh = m(-g)(h)

40. At the top. Work is zero Why? B/c ball is not moving. W = m(-g)(0) = 0 On the way down. Work is positive. Why? Because W = ∆mgh = m(-g)(-h) W = Fd

41. Using W = ∆K = K 2 - K 1 On the way up the ball looses KE, therefore K 2 is less than K 1 making W = a negative value. On the way down the ball increases its KE, therefore K 2 is greater than K 1 making W = a positive value.

42. Refer to book on a stool example again Does the book have any PE (Ug) when its on the stool? Does the book have any Ug (PE) when its laying on the desk? Does the book have any Ug when its laying on the floor? Answer ??????????????????????? We cannot say. WHY?

43. ANSWER Because a “REFERENCE LEVEL” was not established, therefore a determination if the book has Ug cannot be made. REFERENCE LEVEL = Some arbitrary point where the gravitational potential energy (Ug) is = 0 The reference level must established before an object’s Ug can be determined.

44. Return to Book-Chair-Eraser Example Does the book have any PE (Ug) when its laying on the desk? No/Yes?? Does the book have any PE when its laying on the floor? No/Yes?? Answer = We cannot say for sure.

45. WHY??????? Because we did not establish a REFERENCE LEVEL. Reference Level = some arbitrary point where the gravitational potential energy (Ug-PE) is equal to ZERO  the reference level would have to be established before we could determine if the book has any PE or not.

46. Elastic Potential Energy Elastic Potential Energy = The potential energy stored in an object that is released as KE when the object undergoes Δ form or shape. Examples: Rubber band, trampoline, springs, bow & arrow, pole vault pole

47. 11.2 CONSERVATION OF ENERGY CHOOSING A SYSTEM Drop a ball, roll a ball, slide a book, …etc Q: Why do they stop? Newton’s First Law, AKA Law of Inertia, says “An object at rest remains at rest and an object in motion remains at a constant velocity unless an outside net force acts on it”

48. The Law of Conservation of Energy is a description of nature. As long as the “system” under investigation is closed so that the objects do not move in and out, and as long as the system is isolated from external forces, then the energy can only change form. The total amount of energy remains constant. In other words, energy can neither be created nor destroyed, in a closed, isolated system, energy can only change form, ENERGY IS CONSERVED.

49. Mechanical Energy E = KE + Ug for this chapter, there are other forms of mechanical energy  Conservation of mechanical energy E 1 = E 2 KE before + Ug before = KE after + Ug after K = 1/2mv 2 U g = mgh

50. Ball thrown off cliff example Draw on board. Q: Where does the ball have the greatest amount of energy? Point A,B,C,D,E…??? A: Same amount everywhere If the ball has a mass of 0.5kg, what is the velocity of the ball a) just before it hits the ground and b) when it leaves the hand???

51. Choosing A system Continued Q: What weighs more a)Cold potato or hot potato b)Straight or bent pole vault pole Answers: a)Hot potato b)Bent pole vault pole Q: WHY?????

52. Energy is transferred to the hot potato and bent pole, this energy has mass, however the added mass is in the form of energy, in this case the mass is insignificant but the added energy does add small amounts of weight to objects. This can be compared to adding a bucket of water to the oceans or dropping a ball and having the Earth accelerate upwards during free fall.

53. Albert Einstein What was Albert Einstein’s most famous equation? E = mc 2 E = energy m = mass c = speed of light in a vacuum  if E is added and the speed of light is a constant, then the mass must increase

54. When forces holding atoms together in the nucleus are considered, huge amounts of energy can be released when mass changes/decreases. This happens when atoms are split (fission), enourmous amounts of energy is released due to nuclear fission. Hence; nuclear power and nuclear weapons.

55. ANALYZING COLLISIONS Examples of Elastic, Inelastic and Super-elastic collisions on board.