General Physics - Special Relativity

• Special Relativity


  Resolved the conflict between Newtonian Mechanics and Maxwell's Electromagnetic Theory

  
• Newtonian Mechanics


  • Laws of Motion
  • Law of Universal Gravitation
• James Clerk Maxwell


  Proposed the Electromagnetic Theory

  
• Maxwell's Equations


  • Like charges repel; unlike charges attract
  • Magnetic monopoles do not exist
  • A changing electric field produces magnetic field
  • A changing magnetic field produces an electric field

  
• Maxwell's Equations

  • Explain why electromagnetic waves can propagate in a vacuum
  • Calculated the exact value of the speed of light (symbol: c)

  
• Speed of light from the headlight of a moving vehicle

  • Newtonian Mechanics: The speed of light is the sum of its speed plus the speed of the vehicle
  • Maxwell's EMT: The speed of light is constant and is not affected by the speed of its source
• Special Relativity


  Proposed by Albert Einstein and solved the conflict
• Postulates of Special Relativity

  • The laws of Physics are the same in all inertial frame of reference moving with constant velocity relative to one another
  • The speed of light is the same in all inertial frame of reference
• Inertial Frame of Reference

  A frame where the observed object that is either at rest or moving with a constant velocity relative to the observer

  
• Newtonian mechanics is only valid when the velocity of the objects involved are much less than the speed of light plus the inertial frame of reference is considered
• Consequences of Special Relativity

  • Time Dilation
  • Length Contraction
  • Relativistic Mass
• Time Dilation


  Difference of the time interval between two events measured by an observer in a stationary frame and by another observer in a moving frame
• • Proper Time Interval is the time interval measured by the astronaut and always the shortest
  • Dilated Time Interval is the time interval measured by the observed on Earth and always the longest
• Time Dilation Equation

  Δt = Δto / √(1 - (v/c)^2)
• Length Contraction


  A phenomenon that is experienced by a moving object near the speed of light where its length is observed to be contracting
• • An observer at rest relative to the moving object will observe that the moving object is shorter than its original length
  • The faster the speed of the moving objects, the more it gets contracted to the observer
• Length Contraction Equation

  L = Lo / √(1 - (v/c)^2)
• Relativistic Mass


  • The mass of a moving object as it approaches the speed of light in vacuum is greater than its mass at rest relative to the observer
  • The faster the speed of the moving object, the greater its mass as compared with its original mass
• Relativistic Mass Equations


  m = mo / √(1 - (v/c)^2)

  p = m*v
• Sample Problem #1


  Given: Initial Age = 30 y/o, v = 0.95c, Δto = 20 years

  Step 1: Compute the dilated time

  Step 2: Add the dilated time to Christian's initial age. While for Leo, simply add the time recorded in the shipboard clock

  
• Sample Problem #2


  Given: v = 0.75c, Δt = 25 years

  The astronaut aged by 16.54 years during the trip
• Sample Problem #3


  Given: v = 0.50c, Lo = 45 m

  The spaceship as measured by the mission control in Texas is 38.97 m
• Sample Problem #4


  Given: v = 0.70c, Lo = 76 m

  The dimension measured by an observer on Earth is 54.27 m
• Sample Problem #5


  Given: m = 9.11x10^-31 kg, v = 0.50c

  (a) Classical Mechanics: pCM = 1.37x10^22 kg.m/s

  (b) Special Relativity: pSR = 1.58x10^22 kg.m/s