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

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