Length Contraction

• What happens to objects traveling close to the speed of light?

  They appear shorter to a moving observer
• How is length contraction best demonstrated?

  Using rulers
• What length does observer H measure for their pencil?

  14 cm
• How does observer G perceive the length of the pencil?

  As shorter than 14 cm
• What is the length observer G might see for the pencil?

  10 cm
• What happens from observer H's perspective regarding observer G?

  Observer G's pencil appears shorter
• What is the definition of proper length?

  The length measured in the object's rest frame
• How do observers G and H measure the length of the pencil?

  By measuring the position of its ends simultaneously
• What is the equation for the proper length measured by observer H?

  ∆x' = L0
• What does observer G measure for the length of the pencil?

  ∆x = L
• What does the length contraction equation relate?

  It relates lengths in different reference frames
• What is the length contraction equation?

  L = L0 / γ
• What does γ represent in the length contraction equation?

  The Lorentz factor
• What does it mean if γ > 1?

  Lengths measured are shorter than proper lengths
• Why does length contraction occur according to observer G?

  Because observer H's time runs slower
• What must be true for both observers regarding the speed of light?

  Both must measure it as c
• What is crucial when measuring length in relativity?

  Both ends must be measured at the same time
• What is the proper length of the space station?

  482 m
• What speed does the spacecraft travel at relative to Earth?

  0.75c

  
• How far is the planet from Earth according to observer G?

  15 light-years
• How do you calculate the length of the space station in the spacecraft's reference frame?

  Using the length contraction equation
• What is the calculated length of the space station according to the observer in the spacecraft?

  319 m
• Why does the length of the space station make sense?

  It is shorter than the proper length
• What are the key concepts of length contraction?

  • Objects appear shorter when moving close to light speed
  • Proper length is measured in the object's rest frame
  • Length contraction depends on the observer's reference frame
  • Both ends of an object must be measured simultaneously

  
• What steps are involved in calculating length contraction?

  1. Identify known quantities (speed, proper length)
  2. Determine the reference frame
  3. Use the length contraction equation
  4. Verify the result makes sense