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Conservation of Mechanical Energy

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Conservation of Mechanical Energy

1. 1. Conservation Of… Mechanical Energy
2. 2. Types
3. 3. Types
4. 4. Kinetic Energy
5. 5. Kinetic Energy a.k.a. KE
6. 6. Energy of Motion
7. 7. Gravitational Potential Energy
8. 8. Gravitational Potential Energy a.k.a g
9. 9. Energy object has because work was done to put an object in its present position in gravitational field
10. 10. Energy object has because work was done to put an object in its t= present position in gravitational field gh ei h th wi ct je b g O
11. 11. Elastic Potential Energy
12. 12. Elastic Potential Energy a.k.a. s
13. 13. Energy object/spring has because of work done to stretch or compress the spring
14. 14. Energy object/spring ng s ri Sp hasdbecause of se eswork done to pr s om d= C lvestretch or vo In compress the spring
15. 15. In a closed system…
16. 16. In a closed system… What's that??
17. 17. Nothing leaves…
18. 18. Nothing Enters…
19. 19. In a closed system…
20. 20. What???
21. 21. Simply… IF:
22. 22. Then: i (before) f (after)
23. 23. A Rollercoaster
24. 24. A Rollercoaster PEg KE PEg KE PEg KE PEg KE
25. 25. A Rollercoaster PEg KE PEg KE PEg KE PEg KE
26. 26. A Rollercoaster PEg KE PEg KE PEg KE PEg KE
27. 27. A Rollercoaster PEg KE PEg KE PEg KE PEg KE
28. 28. A Rollercoaster PEg KE PEg KE PEg KE PEg KE
29. 29. 1 4 2 3
30. 30. A Pendulum 1 4 2 3
31. 31. A Pendulum 1 4 PE=8J 2 3 KE=0J
32. 32. A Pendulum 1 4 PE=8J 2 3 KE=0J PE=4J KE=4J
33. 33. A Pendulum 1 4 PE=8J 2 3 KE=0J PE=4J PE=0J KE=4J KE=8J
34. 34. A Pendulum 1 4 PE=8J 2 PE=8J 3 KE=0J PE=4J KE=0J PE=0J KE=4J KE=8J
35. 35. A Pendulum 1 4 PE=8J 2 PE=8J 3 KE=0J PE=4J KE=0J PE=0J KE=4J KE=8J
36. 36. Vertical Spring With An Attached Mass
37. 37. Vertical Spring With An Attached Mass PEs
38. 38. Vertical Spring With An Attached Mass PE g+ KE PEs
39. 39. Vertical Spring With An Attached Mass PEg + PEs PEg+ KE PEs
40. 40. Vertical Spring With An Attached Mass PEg + PEs PEg+ KE PEs
41. 41. Horizontal Spring With An Attached Mass
42. 42. Horizontal Spring With An Attached Mass Equilibrium
43. 43. Horizontal Spring With An Attached Mass Equilibrium PEs
44. 44. Horizontal Spring With An Attached Mass Equilibrium PEs KE
45. 45. Horizontal Spring With An Attached Mass Equilibrium PEs KE PEs
46. 46. Horizontal Spring With An Attached Mass Equilibrium PEs KE PEs
47. 47. How To Solve…
48. 48. Example Problem: A 300 kg Hotdog cart rolls up and down a street. It passes the top of hill A. Which is 50m high at a speed of 8 meters per second. How fast is the hot dog cart going to pass the next hill (B) which is 30m high?
49. 49. Example Problem: 1: cart rolls up and ep A 300 kg Hotdog t S down a street. It passes the top of hill A. Which is 50m high at a speed of 8 meters per second. How fast is the hot dog cart going to pass the next hill (B) which is 30m high?
50. 50. Example Problem: A 300 kg Hotdog cart rolls up and down a street. It passes the top of hill A. Which is 50m high at a speed of 8 meters per second. How fast is the hot dog cart going to pass the next hill (B) which is 30m high?
51. 51. 2: ep St
52. 52. Hill A Hill B m=300kg V=8m/s V=? h=50m h=30m
53. 53. Knowns Hill A Hill B m=300kg V=8m/s V=? h=50m H=30m
54. 54. Knowns Hill A Hill B 3: M=300kg p gy te er S En h e rs y t sf e V=8m/s t if n en ra V=? Id T h=50m H=30m
55. 55. Hill A Hill B m=300kg PE i + KE i V=8m/s KEf h=50m V=? H=30m
56. 56. 4: ep St
57. 57. Ei = Ef
58. 58. Ei = Ef te i tu st l as ub u S rm Fo gy er En
59. 59. Ei = Ef mgh+.5mv2 = .5mv2
60. 60. Ei = Ef mgh+.5mv2 =e .5mv2 th t y u e o s ; th os e s rs l Cs e a anc m c
61. 61. Ei = Ef mgh+.5mv2 = .5mv2
62. 62. Ei = Ef mgh+.5mv2 = .5mv2
63. 63. Ei = Ef mgh+.5mv2 = .5mv2 (9.81m/s2)(20m)+(.5)(8m)=.5v2
64. 64. Ei = Ef mgh+.5mv^2 = .5mv^2 (9.81m/s^2)(20)+(.5)(8)=.5v^2
65. 65. Ei = Ef mgh+.5mv2 = .5mv2 (9.81m/s2)(20)+(.5)(8)=.5v2 .5 .5 V2= (9.81m/s2)(20m)+(.5)(8m/s) V=20.01m/s