Relativity (lorentz contraction)

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SUMMARY

The discussion focuses on the concept of Lorentz contraction in the context of special relativity, specifically calculating the length of a spacecraft runway as perceived by a pilot traveling at 4.00 x 107 m/s. The observer on Earth measures the runway at 3.6 km, while the pilot calculates the contracted length to be 3351 m using the formula L = L0/γ, where γ is the Lorentz factor. The calculation was confirmed to be correct, with the pilot correctly identifying the runway as moving relative to him.

PREREQUISITES
  • Understanding of special relativity concepts
  • Familiarity with Lorentz contraction formula L = L0/γ
  • Knowledge of the Lorentz factor γ = 1/sqrt(1 - v2/c2)
  • Basic algebra skills for manipulating equations
NEXT STEPS
  • Study the derivation of the Lorentz factor γ in special relativity
  • Explore practical applications of Lorentz contraction in physics
  • Learn about time dilation and its relationship to length contraction
  • Investigate the implications of special relativity in high-speed travel scenarios
USEFUL FOR

Physics students, educators, and anyone interested in understanding the principles of special relativity and their applications in real-world scenarios.

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Homework Statement


As measured by an observer on earth, a spacecraft runway has a length of 3.6km. What is the length of the runway as measured by the pilot of a spacecraft flying directly over the runway at a speed 4.00 x10^7 m/s relative to the earth?

Homework Equations


L= Lnot/γ

The Attempt at a Solution


I inserted 3.6km as the Lnot and got 3351m as the answer by using the equation.
L= 3600/ (1/sqrt(1-4.0E7/3.0E8))
= 3351m
Is this true? Or i have confused the L as Lnot? I got the answer as i figure the pilot is in rest and the runway is moving relative to him.
 
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