Length Contraction spaceship Problem

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Homework Help Overview

The problem involves a spaceship traveling at a speed of 0.750c, with its length measured at 28.2 m. The question seeks to determine the length of the spaceship when at rest, invoking concepts of length contraction from the theory of relativity.

Discussion Character

  • Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the relevant equation for length contraction and attempt to apply it to find the rest length. There are questions about variable assignments and interpretations of the equation. Some participants suggest that the original poster may have swapped variables, leading to confusion about the calculations.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the equation and calculations. Some guidance has been offered regarding the correct application of the formula, but there is no explicit consensus on the correct approach or final answer yet.

Contextual Notes

There appears to be confusion regarding the application of the length contraction formula and the assignment of variables, which may be affecting the calculations presented by participants.

hbrinn
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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.
 
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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. :-p
 
You forgot the square root.
 
Yay! Thank you very much!
 

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