Spaceship question: Problems with Length Contraction

Click For Summary

Homework Help Overview

The discussion revolves around a problem in special relativity, specifically focusing on length contraction and simultaneity as two spaceships pass each other at a significant fraction of the speed of light. The original poster describes a scenario where each pilot fires a flare at the back of their ship as they pass, raising questions about the perceived distances involved and the implications of length contraction.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to reconcile their calculated distance with the concept of length contraction, expressing confusion about why the distance appears to extend rather than contract. Other participants clarify that the distance described is not the length of the ship but a frame-dependent measurement, prompting further inquiry into the nature of simultaneity in different reference frames.

Discussion Status

Participants are actively engaging with the original poster's confusion, providing insights into the frame-dependent nature of simultaneity and how it affects the interpretation of distances in the problem. There is a productive exchange of ideas, with some participants offering clarifications that may help deepen understanding.

Contextual Notes

There is an emphasis on the frame-dependent nature of simultaneity, which is crucial to understanding the problem. The original poster's assumptions about the relationship between the distances involved and the lengths of the ships are being questioned, highlighting the complexities of relativistic effects.

harts
Messages
29
Reaction score
0

Homework Statement



Two spaceships having rest length 100 m pass each other traveling opposite directions with a relative speed of 0.901 c As the front of the spaceships just cross, each pilot sets off a small flare at the back of her own ship, synchronized to the same instant (t=0 in her own frame).

To each pilot, how far in front does the flare of the back of the other ship occur?

Homework Equations


x'=[itex]\gamma[/itex](x-vt)
L=Lp/[itex]\gamma[/itex]

The Attempt at a Solution



I got the correct answer (x'=291 meters) with the help of a TA, but I'm a bit confused by why this is correct. I thought lengths contracted - here the length is extending. My book says that the proper length is measured by an observer for whom the endpoints of the length remain fixed in space. Also it says that L=[itex]\gamma[/itex]Lp. If that is the case, then why is the length extending? To me, it seems like x' and L are the same thing in this problem because we are finding how far back the flare occurs.

Any help? :biggrin:
 
Physics news on Phys.org
harts said:
To me, it seems like x' and L are the same thing in this problem because we are finding how far back the flare occurs.
x' is the distance between the back of the ship at the instant that it fired the flare and the point where the fronts pass. It's not the length of any object.
 
Doc Al said:
x' is the distance between the back of the ship at the instant that it fired the flare and the point where the fronts pass. It's not the length of any object.

Thanks for the reply doc.

I guess I was confused (maybe still confused) about why that distance you just described can't be the length of the ship. Its the distance from the back of the ship to the front.. so the length of the ship.

I know I'm wrong.. I guess I just want an explanation for why my reasoning is wrong. Thanks!
 
harts said:
I guess I was confused (maybe still confused) about why that distance you just described can't be the length of the ship. Its the distance from the back of the ship to the front.. so the length of the ship.
What you need to remember is that simultaneity is frame dependent. The passing of the fronts of the rockets and the firing of the flares are simultaneous only in the frame of each rocket.

Observers in the first rocket will say that the second rocket fired its flare long before the ship noses passed. So that distance does not represent the length of the second rocket, at least according to the first rocket.
 

Similar threads

Relativistic mass/length contraction problem
  • · Replies 3 ·
Replies
3
Views
2K
Simple Special Relativity Problem of Length Contraction
  • · Replies 1 ·
Replies
1
Views
2K
Length Contraction of spaceships
  • · Replies 2 ·
Replies
2
Views
2K
Calculating Time Difference and Length Contraction in Train Overtaking Scenario
  • · Replies 11 ·
Replies
11
Views
3K
Special Relativity - Length Contraction
  • · Replies 1 ·
Replies
1
Views
2K
Length Contraction/Relativistic mass question
  • · Replies 2 ·
Replies
2
Views
2K
Angled Length Contraction (Relativity)
  • · Replies 7 ·
Replies
7
Views
3K
Special Relativity spaceship problem
  • · Replies 1 ·
Replies
1
Views
2K
Length Contraction: Sally & Sheldon's Meter Stick
  • · Replies 11 ·
Replies
11
Views
2K
Time Dilation and Length Contraction Problem
  • · Replies 1 ·
Replies
1
Views
3K