Relativity - Length Contraction

In summary, the observers on the space station measure the length of the spaceship as 0.30 km as it flies past at 0.75c. However, when the ship docks alongside the station and its length is measured, the observed length is 453.557m due to the effects of relativity.
  • #1
pat666
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Homework Statement


A spaceship flies past a space station at 0.75c. Observers on the station measure the length of the ship to be 0.30 km. If the ship later docks alongside the station and its length is measured, what would this measured value be?


Homework Equations



d=d0/[tex]\gamma[/tex]

The Attempt at a Solution


d0=300/[tex]\sqrt{1-.752}[/tex]
d=453.557m

I think this should be right but I need someone to check for me because relativity confuses the s*** out of me..
Thanks for any help.
 
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  • #2
Looks good to me. The observed length is the proper length contracted by gamma.
 
  • #3
Thanks for looking Doc!
 

Related to Relativity - Length Contraction

What is length contraction in relativity?

Length contraction is a phenomenon predicted by Einstein's theory of relativity, which states that objects in motion appear shorter in the direction of motion when measured by an observer at rest.

How does length contraction occur?

Length contraction occurs because of the relative motion between an observer and an object. As an object moves at high speeds, its length appears shorter to an observer at rest due to the contraction of space-time.

What is the formula for calculating length contraction?

The formula for calculating length contraction is given by L = L0 / γ, where L is the contracted length, L0 is the rest length, and γ is the Lorentz factor, which depends on the velocity of the object.

Does length contraction only occur for objects moving at near-light speeds?

Yes, length contraction is only noticeable for objects moving at near-light speeds. At everyday speeds, the effect is negligible and can only be observed with extremely precise measurements.

What are the real-life implications of length contraction?

The real-life implications of length contraction are significant in the field of particle physics and high-speed technology. It also helps explain the observed effects in experiments such as the Michelson-Morley experiment and is crucial in understanding the behavior of objects at high speeds.

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