Relativistic Length Contraction in Three-Spacecraft Chase Scenario

In summary, the asteroid colonists plan to trap three enemy spacecraft by having one of their fastest ships chase one of the enemy spacecraft into an asteroid with a large hole in it. Once the enemy spacecraft is inside, the colonists will close two giant trapdoors on each side of the asteroid to catch them.
  • #1
vachan
23
0
Three enemy spacecraft have been causing trouble in the asteroid belt. They always travel in a line, evenly spaced apart, attempting to chase down local spacecraft to steal their goods. The local asteroid colonists have decided to set a trap to capture these three spacecraft . They'll get them to chase one of their fastest ships into an asteroid with a large hole in it and, once the three enemy ships are inside, close two giant trapdoors on each side of the asteroid to catch them. These spacecraft all travel close to the speed of light so the locals will have to take relativity into account. Intelligence about the enemy spacecraft reveals that, in their reference frame, they always travel 90 m behind their teammate, each spacecraft is 10 m in length, and their maximum velocity is 90% the speed of light (relative to the asteroids). The asteroid tunnel is only 215 m in length. In this problem we will analyze whether the locals will be able to capture the enemy spacecraft after taking into account relativity.

If the spacecraft are traveling at 90% the speed of light, what is the total length of the three- spacecraft team as observed from the asteroid?


My attempt was putting the number in the L=Lo( 1/[tex]\sqrt{}1-v2/c2[/tex]

Then i add them up... but wasnt right... anyone has idea?!? please!
 
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  • #2
What do you mean by "the number" and "add them up"? Are you calculating contraction in the length of each spaceship separately? Are you calculating the contraction in the space between the ships? There are a total of 5 length numbers here: three ships and two distances between them. But it would be simpler to take the total distance, from the head of the first ship to the tail of the last ship and calculate the contraction of that.

Oh, and notice that I am talking about contraction. Since v< c, 1- v^2/c^2< 1 and dividing by it makes L larger than Lo. Is that what you want?
 
  • #3
im not so sure how you do that... could you please show me?!
 

What is "A Breakdown in Simultaneity"?

"A Breakdown in Simultaneity" is a concept in physics that refers to the idea that events that appear to occur simultaneously to one observer may not appear simultaneous to another observer. This phenomenon is a result of the relativity of time and space in the theory of special relativity.

What is the theory of special relativity?

The theory of special relativity is a cornerstone of modern physics that was developed by Albert Einstein in 1905. It describes how time and space are relative and how they can be affected by the speed and motion of an observer. The theory has been extensively tested and is widely accepted by the scientific community.

How does "A Breakdown in Simultaneity" occur?

"A Breakdown in Simultaneity" occurs when two events that appear to occur simultaneously to one observer are observed as happening at different times by another observer, due to differences in their relative motion. This is because the speed of light is constant and the perception of time and space is relative to the observer's frame of reference.

What are some real-world examples of "A Breakdown in Simultaneity"?

One example of "A Breakdown in Simultaneity" is the famous "twin paradox" in which one twin travels at high speeds in space while the other remains on Earth. When the traveling twin returns, they have aged less than their twin on Earth due to the effects of time dilation. Another example is the observation of a supernova, which may appear to occur at different times to observers on Earth and in a spacecraft traveling at high speeds.

Why is understanding "A Breakdown in Simultaneity" important?

Understanding "A Breakdown in Simultaneity" is important because it challenges our intuitive understanding of time and space and provides a deeper understanding of the fundamental laws of the universe. It also has practical implications for technologies such as GPS, which rely on precise timing and the principles of relativity to function accurately.

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