# Length Contraction spaceship Problem

• hbrinn
In summary, when a spaceship passes you at a speed of 0.750c and you measure its length to be 28.2 m, the length would be 42.6 m when at rest. The relevant equation is L = L_0 {\sqrt{1 - \frac{v^2}{c^2}} and by solving for L_0, the length when the relative velocity is 0, the answer is 42.6 m. This was found by taking the square root of 28.2=L(1-.75^2).

## Homework Statement

A spaceship passes you at a speed of .750c. You measure its length to be 28.2 m. How long would it be when at rest?

## Homework Equations

I think the equation that is relevant is L=L(sub0)xsqrt(1-v^2/c^2)

## The Attempt at a Solution

L=28.2xsqrt(1-(.75^2))=18.65m
Apparently, the answer is 42.6 m. I can't even imagine how to get 42.6 from that.

hbrinn said:

## Homework Statement

A spaceship passes you at a speed of .750c. You measure its length to be 28.2 m. How long would it be when at rest?

## Homework Equations

I think the equation that is relevant is L=L(sub0)xsqrt(1-v^2/c^2)

## The Attempt at a Solution

L=28.2xsqrt(1-(.75^2))=18.65m
Apparently, the answer is 42.6 m. I can't even imagine how to get 42.6 from that.

I think you just got your variables swapped. If you are using

$$L = L_0 {\sqrt{1 - \frac{v^2}{c^2}}$$

then $$L$$ is 28.2 m, and you need to solve for $$L_0$$, the length when the relative velocity is 0. $$L$$ is the length when traveling at speed $$v$$.

Then by that logic isn't the answer 64.457?

I did 28.2=L(1-.75^2). Is that wrong?

hbrinn said:
Then by that logic isn't the answer 64.457?

I did 28.2=L(1-.75^2). Is that wrong?

You forgot to take the square root. :tongue2:

You forgot the square root.

Yay! Thank you very much!

## 1. What is the "Length Contraction spaceship Problem"?

The "Length Contraction spaceship Problem" is a thought experiment commonly used in the theory of relativity to explain the concept of length contraction. It involves a hypothetical spaceship traveling at extremely high speeds and the observed difference in length of the spaceship by an observer on Earth compared to an observer on the spaceship.

## 2. How does length contraction occur on a spaceship?

According to the theory of relativity, as an object approaches the speed of light, its length in the direction of motion appears to contract from the perspective of an observer at rest. This means that the spaceship would appear shorter to an observer on Earth compared to an observer on the spaceship itself.

## 3. What is the significance of the "Length Contraction spaceship Problem"?

The "Length Contraction spaceship Problem" helps to illustrate the principles of relativity and the effects of high speeds on the perception of length. It also has practical applications in fields such as aeronautics and space travel, where understanding the effects of relativity is crucial.

## 4. Is length contraction a real physical phenomenon or just a mathematical concept?

Length contraction is a real physical phenomenon that has been observed and confirmed in experiments. It is a consequence of the principles of relativity and plays a crucial role in our understanding of the universe.

## 5. Can length contraction be applied to objects other than spaceships?

Yes, the concept of length contraction can be applied to any object that is moving at high speeds relative to an observer. This includes objects on Earth, such as bullets or particles in accelerators, as well as objects in space, like planets and stars.