Spaceship length contraction problem

In summary, the "Spaceship length contraction problem" refers to the relativistic phenomenon where an object, such as a spaceship, appears to contract in length as it approaches the speed of light relative to an observer. This effect, predicted by Einstein's theory of special relativity, results from the interplay between time and space, leading to the conclusion that measurements of length differ depending on the relative motion of the observer and the object. As the spaceship moves faster, observers at rest will measure its length as shorter than when it is at rest, illustrating the non-intuitive nature of relativistic physics.
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Homework Statement
Please see below
Relevant Equations
Please see below
For this problem,
1716431584970.png

Does someone please know that won't the cabin, the person, and the clothing all shrink by the same proportion in the direction of travel so if you brought smaller cloths or a smaller cabin than you normally would then you may not be able to fit in? So you should not buy a smaller cabin or smaller cloths?

Thanks for any help.
 
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If you are on the ship, and the ship accelerates up to 0.99c relative to the Earth, what speed is the ship (and cabin and everything else inside) traveling with respect to you? What is the amount of length contraction for that speed?
 
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Drakkith said:
If you are on the ship, and the ship accelerates up to 0.99c relative to the Earth, what speed is the ship (and cabin and everything else inside) traveling with respect to you? What is the amount of length contraction for that speed?
Thank you for your reply @Drakkith !

Speed is the ship (and cabin and everything else inside) traveling with respect to you would be zero since it is in my frame of ref.

##L = \frac{L_0}{7.08}## where ##L## is length contracted spaceship.

Thanks.
 
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ChiralSuperfields said:
Speed is the ship (and cabin and everything else inside) traveling with respect to you would be zero since it is in my frame of ref.
So if the speed is zero with respect to you, would you need to buy smaller clothes or a smaller cabin?

ChiralSuperfields said:
##L = \frac{L_0}{7.08}## where ##L## is length contracted spaceship.

Where did you get 7.08?
 
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Drakkith said:
So if the speed is zero with respect to you, would you need to buy smaller clothes or a smaller cabin?



Where did you get 7.08?
Thank you for you reply @Drakkith!

Sorry I made a numerical error. Also no, you would not need to buy smaller clothes or a smaller cabin. That is actually a really neat way to look at the problem.

Thanks!
 
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FAQ: Spaceship length contraction problem

What is the spaceship length contraction problem?

The spaceship length contraction problem refers to the phenomenon predicted by the theory of relativity, where an object in motion appears shorter in the direction of its motion when observed from a stationary frame of reference. This effect becomes significant at speeds approaching the speed of light and is a direct consequence of the principles of special relativity established by Albert Einstein.

How does length contraction occur?

Length contraction occurs due to the relativistic effects of time dilation and the invariance of the speed of light. As an object moves closer to the speed of light, the space between its endpoints contracts from the perspective of a stationary observer. The formula for length contraction is given by L = L0 √(1 - v²/c²), where L0 is the proper length (the length of the object at rest), v is the velocity of the object, and c is the speed of light.

Is length contraction noticeable at everyday speeds?

No, length contraction is not noticeable at everyday speeds. The effects become significant only as an object approaches a substantial fraction of the speed of light (approximately 299,792,458 meters per second). At typical speeds encountered in daily life, such as cars or airplanes, the contraction is negligible and cannot be measured with standard instruments.

How does length contraction affect the perception of moving objects?

Length contraction alters the perception of moving objects, making them appear shorter in the direction of motion when viewed from a stationary observer's frame of reference. This means that if a spaceship is traveling at relativistic speeds, an observer on Earth would measure its length as shorter than what the crew onboard would measure. However, the crew would not notice this contraction since they are in the same frame of reference as the spaceship.

Can length contraction be experimentally verified?

Yes, length contraction can be experimentally verified through high-energy particle physics experiments. Particles such as muons, which travel close to the speed of light, exhibit behaviors consistent with length contraction and time dilation. The observed lifespan of these particles is longer than expected due to their high velocity, supporting the predictions of special relativity and demonstrating the effects of length contraction in practice.

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