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Special Relativity (Ch 37)

  Modern physics   special relativity   quantum mechanics

  Both were developed to explain the “few remaining puzzles” of classical physics

  Special relativity   length contraction   time dilation   simultaneity   energy-mass equivalence

Maxwell’s Equations

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Michelson & Morley experiment   Hypothesis was that the speed of light must =

c in the rest frame of “ether”   ether was material proposed to fill all space and it

allowed light to travel (waves need a medium)   M&M tried to measure shift in speed of light

due to earth’s orbital motion around sun   Did not detect any shift!!!   Michelson thought his experiment failed, but

really there was no ether.

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Postulates of Special Relativity

  The laws of physics have the same form in all inertial reference frames.   inertial frame - not accelerating

  general relativity deals with acceleration

  all reference frames are equivalent   car is at rest and earth is moving

  The speed of light in a vacuum is constant and the same for all observers.   required by Maxwell’s equations

The Galilean Transformations

The Galilean transformations of position are:

The Galilean transformations of velocity are:

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Simultaneity

  Time is not absolute   time interval between 2

events depends on observer

  Observer 2 sees lightning strikes as simultaneous

  Observer 1 does not

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Time Dilation   Moving clocks run slow

  t0 = proper time   frame where two events

occur at same place

On spaceship

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Lifetime of a moving muon

  When at rest, the lifetime of a muon is 2.2E-6 s. What will be the mean lifetime of a muon as measured in the laboratory if it is traveling at v=0.60c.

  How far does the muon travel in the laboratory, on average, before decaying?

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Twin Paradox

  One twin travels on spaceship at v=0.5c for 20 years, then turns around and returns.   Twin on earth ages 40 yrs   Twin in spaceship ages less

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Length Contraction

  The length of an object is measured to be shorter when it is moving   proper length, L0

  length of object as determined by observers at rest with respect to object

  contraction occurs only along direction of motion

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Group Problem

  A certain star is 10.6 light-years away. How long would it take a spacecraft traveling 0.960c to reach that star from Earth, as measured by observers: (a) on Earth, (b) on the spacecraft? (c) What is the distance traveled according to observers on the spacecraft? (d) What will the spacecraft occupants compute their speed to be from the results of (b) and (c)?

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Relativistic Momentum & Mass

  Relativistic Momentum   conservation of momentum in special relativity requires

  Relativistic Mass

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Relativistic KE & Total Energy   Relativistic Kinetic Energy

  Total energy

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Mass and Energy   Equivalence of mass and energy

  Pair production   electron and positron annihilate to create gamma

rays   Nuclear energy

  products have less mass than reactants   change in mass released as energy

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Group Problem

  A certain chemical reaction requires 4.82E4 J of energy input for it to go. What is the increase in mass of the products over the reactants?

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Group Problem

  Calculate the rest energy of an electron in joules and MeV (1 MeV = 1.60E-13 J).

  Calculate the velocity of an electron whose energy is equal to the rest-mass energy of a proton.

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Group Problem

  The total annual energy consumption in the United States is about 8E19 J. How much mass would have to be converted to energy to fuel this need?

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Relativistic Addition of Velocities   v = vel of 1 WRT earth   u’ = vel of 2 WRT 1   u = vel of 2 WRT earth

  can’t just add velocities!

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Group Problem

  A person on a rocket traveling at 0.50 c (WRT the Earth) observes a meteor come from behind and pass her at a speed of 0.50c. How fast is the meteor moving WRT the Earth?

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Group Problem

  Using MATLAB, plot (a) length/proper length and (b) time/proper time as a function of speed, as speed approaches the speed of light. At what speed do the special relativistic values differ classical values by 1.00%? Express velocities in terms of c.

Mastering Physics

  Start on in-class assignment for Ch 37.   Complete by Wed, 11 pm

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