Advanced Higher Physics

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Advanced Higher Physics

• Relativistic Motion

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Introduction 1

• Everyone knows that E mc2
• Proposed by Einstein in 1905 Special Theory of
  Relativity
• Important consequence of theory is that
  measurements depend on speed

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Introduction 2

• Two people taking the same measurement may get
  different results if travelling relative to each
  other Demonstration
• The greater their relative speed the greater the
  discrepancy in the measurement
• At speeds close to the speed of light, classical,
  Newtonian physics is no longer valid

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Relativistic Dynamics

• For an object of mass, m, travelling at a
  velocity, v, we could use Newtonian Mechanics to
  find
• Distance travelled in a given time
• Momentum
• Kinetic energy
• If v is approaching the speed of light,
  Relativistic Mechanics must be used.

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Relativistic Mass

• The relativistic mass of an object travelling at
  velocity, v, is given by the equation
• where m0 rest mass (mass whilst stationary)
• c - speed of light (3.0 x 108 ms-1)
• A stationary observer would observe the mass to
  be equal to the relativistic mass, m.

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Relativistic Energy 1

• Mass energy equivalence equation
• E mc2
• where E - total energy of object
• m - relativistic mass
• For a stationary object
• E0 m0c2
• where E0 - rest energy

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Kinetic Energy 1

• A moving object has kinetic energy, EK, in
  addition to its rest energy, so its total energy
  
• E EK E0
• ? EK E - E0
• If we substitute our equations, E mc2 and E0
  m0c2 , we can find the relativistic kinetic
  energy.

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Kinetic Energy 2
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Kinetic Energy 3

• This looks very different to EK ½mv2
• For vltltc, it can be shown that the relativistic
  effects are negligible, and we get values as we
  would expect

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Other relativistic Effects

• The following effects are also predicted
• Time Dilation
• time passes more slowly for an object travelling
  at high speed
• Demonstration1 Demonstration2
• Length Contraction
• shortening of the length of an object observed
  by a stationary observer of an object Demonst
  ration