Relativity rest frame Question

In summary: Thanks for trying.In summary, an armada of spaceships moving at .800c relative to a ground station takes 1.25 years to travel the same distance as an observer in frame S.
  • #1
mkkrnfoo85
50
0
Here is the question:

An armada of spaceships that is 1.00 ly long (in its rest frame) moves with speed .800c relative to a ground station in frame S. A messenger travels from the rear of the armada to the front with a speed of .950c relative to S. How long does the trip take as measured in:

(a) the messenger's rest frame?
(b) the armada's rest frame?
(c) an observer's point of view in frame S?


I am having a very hard time with relativity right now... Do I use the relativistic velocity equation?

[tex]u = \frac {u^{\prime} + v}{1+u^{\prime} v/c^2} \mbox { (relativistic velocity)}[/tex]

Or any other equations like:

[tex]\triangle t = \gamma \triangle t_0[/tex]
[tex]L = \frac {L_0}{\gamma}[/tex]

The thing that would help me most and I would be most grateful for is if someone would answer one of the questions in detail offering reasoning for each step of the problem, and offer some hints on solving the other ones. Answers to compare with might be helpful too.

Thanks in advance.

-Mark
 
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  • #2
help

would anyone please help?
 
  • #3
An armada of spaceships that is 1.00 ly long (in its rest frame) moves with speed .800c relative to a ground station in frame S. A messenger travels from the rear of the armada to the front with a speed of .950c relative to S. How long does the trip take as measured in:

(a) the messenger's rest frame?
(b) the armada's rest frame?
(c) an observer's point of view in frame S?

All the normal non-relativistic equations work provided you take all quantities in the same frame of reference.

Part (a)

In the messenger's frame, we can use s=vt to work out the trip time. But before we can do that, we need to know how far the armada moves as its front moves to the messenger (who is stationary in this frame), and how fast the armada moves in the same frame.

The speed of the armada relative to the messenger is given by the velocity addition formula.

[tex]w = \frac{v - u}{1 - uv/c^2}[/tex]

where v is the messenger's speed relative to S, u is the armada's speed relative to S, and w is the armada's speed relative to the messenger.

We get

[tex]w = \frac{0.950c - 0.800c}{1 - (0.950)(0.800)} = 0.625c[/tex]

The length of the armada L in the messenger's frame, is:

[tex]L = L_0 / \gamma[/tex]

where

[tex]\gamma = \frac{1}{\sqrt{1-(w/c)^2}} = 1.28[/tex]

So

[tex]L = 1.00 ly / 1.28 = 0.78 ly[/tex]

The time taken, in this frame, is:

[tex]t = L/w = 0.78 ly / (0.625 ly/yr) = 1.25 years[/tex]

Part (b)

We could follow the same procedure as in part (a) here. You should try that. But, there's another way to do this - use the time dilation formula between the messenger's frame and the armada's frame.

The messenger's elapsed time is 1.25 years, and the messenger is moving relative to the armada, so the armada measures a longer time, by a factor of [itex]\gamma[/itex] (given above).

The time taken is 1.60 years, in this frame.

I'll leave you to do part (c).
 

What is the relativity rest frame?

The relativity rest frame is a concept in physics that refers to the frame of reference in which an observer is at rest or moving with a constant velocity. It is a fundamental principle of Einstein's theory of relativity and states that the laws of physics are the same for all observers in inertial reference frames.

How does the relativity rest frame affect our understanding of motion?

The relativity rest frame challenges our traditional understanding of motion, which was based on Newton's laws of motion. According to the theory of relativity, the laws of physics are the same in all inertial reference frames, which means that the concept of absolute motion is no longer valid.

What is the difference between the relativity rest frame and the absolute rest frame?

The relativity rest frame is a frame of reference in which an observer is at rest or moving with a constant velocity, while the absolute rest frame is a hypothetical frame of reference in which an observer is at rest in relation to the entire universe. However, according to the theory of relativity, the concept of an absolute rest frame is not valid.

Why is the relativity rest frame important in understanding the universe?

The relativity rest frame is important because it allows us to understand the principles of motion and the laws of physics in a more accurate and comprehensive way. It also helps us to explain phenomena such as time dilation and length contraction, which are crucial in understanding the behavior of objects in the universe.

How does the relativity rest frame impact our daily lives?

The concept of the relativity rest frame has led to many technological advancements, such as the development of GPS systems and nuclear energy. It also affects our daily lives by changing our understanding of time and space, and how we perceive motion and the universe around us.

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