General Physics - Special Relativity

Cards (24)

  • 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