Length contraction of two spaceships

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SUMMARY

The discussion focuses on calculating the relative velocity of two spaceships, each 100 meters long at rest, traveling towards each other at 0.85c relative to Earth. The participant initially misapplies Newtonian mechanics, suggesting a relative velocity of 1.5c, which is incorrect. The correct approach involves using Einstein's relativistic velocity addition formula, specifically vBA = (vB - vA) / (1 - (vAvB/c2)). The relevant equations for length contraction and time dilation are also provided, including λ = 1 / √(1 - (v2/c2)), x' = λ(x - vt), and L' = L / λ.

PREREQUISITES
  • Understanding of special relativity concepts, including time dilation and length contraction.
  • Familiarity with the relativistic velocity addition formula.
  • Knowledge of the Lorentz factor, λ = 1 / √(1 - (v2/c2)).
  • Basic algebra skills for manipulating equations.
NEXT STEPS
  • Study the derivation and application of the relativistic velocity addition formula.
  • Learn about the implications of length contraction in special relativity.
  • Explore examples of time dilation and its effects on moving observers.
  • Investigate practical applications of special relativity in modern physics.
USEFUL FOR

Students of physics, particularly those studying special relativity, as well as educators and anyone interested in understanding the effects of high-speed travel on length and time measurements.

Saxby
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Homework Statement


Two space ships, each a hundred metres long when measured at rest, travel toward each other with a speed of 0.85c relative to the Earth.


Homework Equations


λ = 1 / √1 - (v2/c2)
x' = λ(x - vt)
L' = L / λ

The Attempt at a Solution


Well to be honest i may be missing an equation or something but that's what i was given.

I find that the relative velocity of one spaceship to another (according to Newton) would be 1.5c. This doesn't work using the equations above. I know i have to find the relative velocity according to Einstein's theory but i don't know how.
 
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Saxby said:

Homework Statement


Two space ships, each a hundred metres long when measured at rest, travel toward each other with a speed of 0.85c relative to the Earth.


Homework Equations


λ = 1 / √1 - (v2/c2)
x' = λ(x - vt)
L' = L / λ

The Attempt at a Solution


Well to be honest i may be missing an equation or something but that's what i was given.

I find that the relative velocity of one spaceship to another (according to Newton) would be 1.5c. This doesn't work using the equations above. I know i have to find the relative velocity according to Einstein's theory but i don't know how.
So, you are trying to find the relative velocity of one to the other?

Let the first spaceship be spaceship A and the second be spaceship B.

Consider ##v_{BA}=\frac{v_B-v_A}{1-\frac{v_Av_B}{c^2}}##.
 

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