Energy-Mass Equivalence Principle

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Energy-Mass Equivalence Principle

• By Albert Einstein

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E mc2

• E total energy of a system
• M total mass of the system
• C speed of light
• If an object is not moving then
• Eo moc2
• Eo is the rest energy and mo is the rest mass

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• Example I put my sisters 200g pet gerbil into
  a thermonuclear flux capacitor which converts the
  gerbil into pure energy. How much energy do I
  get out?
• Eo moc2
• Eo 0.200(3.0x108 )2
• Eo 1.8x1016 J
• One gerbil is enough energy to power the entire
  country for a little while

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Relativistic Considerations

• If the object is moving at relativistic speeds,
  then mass dilates
• m ?mo
• So
• E mc2 becomes
• E ?moc2

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Relativisitic Considerations

• Total E is the rest E plus Ek
• E Eo Ek
• mc2 moc2 Ek
• Ek mc2 - moc2
• Ek ?moc2 - moc2
• Ek moc2 (? 1)

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• Newtons formula for Ek works well
• Ek ½ mv2
• But it breaks down at very high speeds. In that
  case, use Einsteins version.
• Einsteins formula is the same as Newtons
  formula but it is harder to work with.

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Sample Problem

• A 400kg car is traveling at 30m/s. Find the
  kinetic energy of the car using Newtons formula
  and Einsteins formula.
• Newton
• Ek ½ mv2
• Ek ½ (400)(30)2
• Ek 1.80x105 J

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• Einstein
• Ek moc2 (? 1)
• At v 30m/s, ? 1.000000000000005
• Ek 400(3.0x108)2 (5x10-15)
• Ek 1.80x105 J
• Same as Newton, but a lot more tricky.

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Nuclear Fusion

• Helium-3 is made of 2 protons and 1 neutron.
• proton mass 1.0072764668 amu 1.6726 x
  10-27 kg 
• neutron mass 1.0086649156 amu 1.6749 x
  10-27 kg
• electron mass 0.0005446623 amu 9.1093
  10-31 kg 
• Total mass 3.0243071738 amu

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Nuclear Fusion

• Sum of parts of He-3 is 3.0243071738 amu
• Actual mass of He-3 is 3.0160293191 amu
• The Helium has less mass than its component
  parts! Where does the extra mass go?

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Nuclear Fusion

• All elements are made of protons and neutrons etc
  that are bound together.
• Once they are bound together, they lose mass
  really they lose energy. The energy lost is
  called the binding energy.
• To split the atoms apart, youll need to inject
  this energy back into the atom.

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• The binding energy of He-3 is
• 3.0243071738 amu - 3.0160293191 amu
• 0.0082778547 amu
• This energy is given off as a gamma ray.
• 2P 1N ? He3 ?
• The fusion of hydrogen to make helium produces
  energy. This is the process that makes the sun
  hot and bright.

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Nuclear Fission

• Fission is the reverse process of fusion.
• Splitting Helium takes energy, so it is not a
  useful process.
• As elements get heavier, it takes more and more
  energy to keep them together. Some elements are
  too massive to stay in one piece, so they
  naturally fall apart. These are radioactive
  elements.

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• Uranium is one of these heavy elements. It has
  235 nucleons (protons and neutrons) and readily
  falls apart.
• Unlike Helium, Uranium takes energy to keep it
  together.
• When uranium 235 fissions, it splits into
  Krypton, Barium and 3 neutrons. It also releases
  mass in the form of a gamma ray.
• U ? Kr Ba 3n ?
• This process is called nuclear fission.