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Special Relativity (Ch 37)
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Modern physics
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special relativity
quantum mechanics
Both were developed to explain the “few
remaining puzzles” of classical physics
Special relativity
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length contraction
time dilation
simultaneity
energy-mass equivalence
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Maxwell’s Equations
Michelson & Morley experiment
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Hypothesis was that the speed of light must =
c in the rest frame of “ether”
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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
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The laws of physics have the same form in all
inertial reference frames.
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inertial frame - not accelerating
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all reference frames are equivalent
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general relativity deals with acceleration
car is at rest and earth is moving
The speed of light in a vacuum is constant
and the same for all observers.
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required by Maxwell’s equations
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The Galilean Transformations
The Galilean transformations of position are:
The Galilean transformations of velocity are:
Simultaneity
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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
On
spaceship
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Moving clocks run slow
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t0 = proper time
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frame where two events
occur at same place
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Lifetime of a moving muon
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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
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One twin travels on spaceship at v=0.5c for
20 years, then turns around and returns.
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Twin on earth ages 40 yrs
Twin in spaceship ages less
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Length Contraction
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The length of an object is measured to be
shorter when it is moving
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proper length, L0
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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
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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
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Relativistic Momentum
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conservation of momentum in special relativity requires
Relativistic Mass
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Relativistic KE & Total Energy
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Relativistic Kinetic Energy
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Total energy
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Mass and Energy
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Equivalence of mass and energy
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Pair production
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electron and positron annihilate to create gamma
rays
Nuclear energy
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products have less mass than reactants
change in mass released as energy
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Group Problem
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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
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Calculate the rest energy of an electron in
joules and MeV (1 MeV = 1.60E-13 J).
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Calculate the velocity of an electron whose
energy is equal to the rest-mass energy of a
proton.
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Group Problem
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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
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v = vel of 1 WRT earth
u’ = vel of 2 WRT 1
u = vel of 2 WRT earth
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can’t just add velocities!
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Group Problem
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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
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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.
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Mastering Physics
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Start on in-class assignment for Ch 37.
Complete by Wed, 11 pm
Physics 140
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