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E=mc 2

E=mc 2. Physics 100 Chapt 19. Einstein’s hypotheses:. 1. The laws of nature are equally valid in every inertial reference frame. 2. The speed of light in empty space is same for all inertial observers, regard- less of their velocity or the velocity of the source of light.

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E=mc 2

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  1. E=mc2 Physics 100 Chapt 19

  2. Einstein’s hypotheses: 1. The laws of nature are equally valid in every inertial reference frame. 2. The speed of light in empty space is same for all inertial observers, regard- less of their velocity or the velocity of the source of light.

  3. Summary (so far) • Moving clocks run slow • Moving objects appear shorter • Moving object’s mass increases By a factor of g

  4. GPS system 3 m precision requires corrections for relativity

  5. Summer 1905 What is the significance of the increase mass of a moving object?? m=gm0 increase in mass=m– m0 increase in m=gm0-m0 =(g-1)m0

  6. Increase in m=(g-1)m0 g-1 =?? 1 1 – v2/c2 g = v/c

  7. Mathematicians tell us: 1 1 – v2/c2 v2 c2 g = = 1+½+other stuff 1 1 – v2/c2 The “other stuff” is pretty huge near v=c What about here? v2 c2 1+½ v/c

  8. Below v/c = 0.5, “other stuff” is not so large 1 1 – v2/c2 v2 c2 g = = 1+½+other stuff 1 1 – v2/c2 At v=0.5c the “other stuff”is about 10% v2 c2 1+½ How about down here? 0.5 v/c

  9. Below v/c = 0.1, “other stuff” is negligible 1 1 – v2/c2 v2 c2 g = = 1+½+other stuff 1 1 – v2/c2 v2 c2 1+½ v=0.1c

  10. v2 c2 Below v/c = 0.1, g = 1+½ v2 c2 g – 1 = ½ This covers all velocities ever encountered by mankind in 1905

  11. Increase in mass = (g-1)m0 v2 c2 for v<0.1c = g-1 = ½ v2 c2 increase in mass = ½ m0 Multiply both sides by c2 (increase in mass)c2 = ½ m0 v2 Kinetic energy

  12. For v < 0.1c m = m0 + increase in m Multiply both sides by c2 mc2= m0c2+ (increase in m)c2 mc2= m0c2+ kinetic energy

  13. Einstein’s hypothesis: mc2= m0c2+ kinetic energy holds for all velocities (not only for v<0.1c) “other stuff” Kinetic energy=(m-m0)c2 =½m0v2+ Since this is only significant for huge speeds, Newton, etc had no way of knowing about it

  14. E = mc2 This must be the total energy mc2= m0c2+ kinetic energy This must also be a form of energy: ”rest mass energy”

  15. Mass is a form of energy The conversion factor from mass to energy is c2, a huge number! E = mc2 Energy (Joules) = Mass (kg) x (3x108)2 =9x1016 E(Joules) = 90,000,000,000,000,000 x m(kg)

  16. Mass contains an enormous amount of energy

  17. Electric power usage on Oahu Power =1,300 MegaWatts = 1,300 x 106 Watts Power = 1.3 x 109 J/s Energy usage = Power x time # of secs in 1 yr Energy usage/yr=1.3x109 J/s x (3.2 x 107 s/yr) =1.3 x 3.2 x 109+7 J/yr =4.2 x 1016 J/yr

  18. How much mass would be needed to produce 4.2 x 1016 J ? E c2 E = mc2  m = 4.2x1016 J 9x1016 m2/s2  m = 4.2 9 m = kg About the mass of an apple m = 0.47 kg

  19. Nuclear Power Plant Converts about 1kg of massenergy/yr

  20. Another nuclear power plant Sun’s power output=4x1026Watts

  21. Sun converts mass to energy Power = energy generated in one sec: =m1secC2 E1sec= 4x1026J E1sec C2 4x1026J 9x1016m2/s2 m1sec= = m1sec= 4/9x1026-16 kg = 0.44x1010 kg over 4 million tons each second!! m1sec= 4.4x109 kg

  22. Another nuclear power plant 4.4x109 kg  energy / sec

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