Calculating Relativistic Length of a Moving Spaceship

In summary, the conversation discusses the concept of proper length and relativistic length in the context of a moving spaceship passing by a planet at 0.80 c. The observer on the planet measures the length of the spaceship to be 40 m, while the astronaut measures it to be 66.66 m. The conversation also discusses the equation for finding the proper length and the speed at which the spaceship would have to travel for its relativistic length to be half its proper length.
  • #1
salsabel
17
0
“proper” length

A spaceship travels past a planet at a speed of 0.80 c as measured from the planet’s frame of reference. An observer on the planet measures the length of a moving spaceship to be 40 m.
a) How long is the spaceship, according to the astronaut?
b) At what speed would the spaceship have to travel for its relativistic length to be half its “proper” length?

a) L=L0 sqr 1-v2/c2
b) the previous equation where c=3*10^8
is that right?
 
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  • #2
Hi salsabel,

What did you get as the final answers?
 
  • #3
i just want to know if these are the correct equations because I'm little confusing about the first one does he mean the time or the distance?
 
  • #4
I'm not sure what time or distance you are referring to; in the first question, they want to know if the astronaut (moving with the spaceship) measured the length of the spaceship, what length would he find? (The observer on the planet measured 40m for the length of the spaceship, but what does the astronaut measure?)
 
  • #5


salsabel said:
A spaceship travels past a planet at a speed of 0.80 c as measured from the planet’s frame of reference. An observer on the planet measures the length of a moving spaceship to be 40 m.
a) How long is the spaceship, according to the astronaut?
b) At what speed would the spaceship have to travel for its relativistic length to be half its “proper” length?

a) L=L0 sqr 1-v2/c2
b) the previous equation where c=3*10^8
is that right?

Question (a) is asking what is the proper length of the spaceship and this is the variable L0 in your equation so the answer is

a) L0 = L/sqrt(1-v^2/c^2) = 40/0.6 = 66.66m

Question (b) is asking what the relative velocity has to be so that L/L0 = 0.5 so by simple rearrangement the answer is:

b) v/c = sqrt(1-(L/L0)^2) = sqrt(1-(0.5)^2) = 0.866c
 
  • #6


Can someone please correct me if I'm wrong but I think that kev's answer is incorrect.

L is the relativistic distance measured by an observer in the moving space ship, which is something we want to find for question A)

L0 the proper distance, is measured by an observer at rest in the same reference frame as the two points, which is given as 40 meters.

So did kev mix L and L0 up, or is it me?
 
  • #7


jwj11 said:
Can someone please correct me if I'm wrong but I think that kev's answer is incorrect.

L is the relativistic distance measured by an observer in the moving space ship, which is something we want to find for question A)

L0 the proper distance, is measured by an observer at rest in the same reference frame as the two points, which is given as 40 meters.

So did kev mix L and L0 up, or is it me?
It's you. :smile: (kev is correct.)

Reread the problem statement: "An observer on the planet measures the length of a moving spaceship to be 40 m."

That means that the 40 m represents L, the contracted length of the moving ship as observed by the planet. The length of the ship according to the astronaut, which is what you are asked to find, is the proper length L0.
 
  • #8


Ahh fudge. Keep getting proper and relativistic concepts mixed up in my head. Thanks for the correction Doc Al.
 

What is the formula for calculating relativistic length of a moving spaceship?

The formula for calculating the relativistic length of a moving spaceship is L = L0/√(1-v^2/c^2), where L0 is the rest length of the spaceship, v is its velocity, and c is the speed of light.

How does the speed of light affect the relativistic length of a moving spaceship?

The speed of light, denoted by c, is a constant in the formula for calculating relativistic length. As the speed of the spaceship approaches the speed of light, the denominator of the formula approaches 0, causing the length of the spaceship to appear to shrink.

What is the significance of calculating the relativistic length of a moving spaceship?

Calculating the relativistic length of a moving spaceship is important in understanding the effects of special relativity on objects in motion. It helps us understand the concept of time dilation and the way in which the perception of length changes for objects moving at high speeds.

Can the relativistic length of a moving spaceship be greater than its rest length?

No, according to the formula, the relativistic length of a moving spaceship can never be greater than its rest length. The value inside the square root cannot be negative, so the denominator can never be greater than 1, meaning the calculated length can never be greater than the rest length.

Are there any other factors that affect the relativistic length of a moving spaceship?

Yes, the relativistic length of a moving spaceship can also be affected by the direction of its motion and the observer's frame of reference. These factors can change the perception of length, but the formula remains the same.

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