Special Relativity: Object Motion and Time Dilation

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Homework Help Overview

The discussion revolves around a problem in special relativity involving an object moving at a significant fraction of the speed of light (v=0.94c) and its implications on time dilation and length contraction. The original poster presents a series of questions related to the motion of the object and the measurements in different frames of reference.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the calculations for distance traveled in the laboratory frame and the time experienced in the object's rest frame. Questions arise regarding the application of relativistic equations and the interpretation of results in different frames.

Discussion Status

Some participants provide feedback on the original poster's calculations, with one confirming the correctness of the approach up to a certain point. There is an ongoing exploration of the implications of the equations used and how they relate to the problem's context.

Contextual Notes

Participants discuss the constraints of the problem, including the need to consider the effects of special relativity on measurements in different inertial frames. There is a focus on understanding the relationship between the laboratory's length and the time experienced by the object.

Lucille
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Homework Statement


An object moves at v=0.94c in the frame of a laboratory for 32 us, decaying as it reached the other end.
a) how far did it move in the frame of the laboratory?
b) how long did the object travel in its rest frame?
c) in the rest frame, how long is the laboratory?

Homework Equations


t' = gamma * (-v/c^2*x + t)
x' = gamma* (x-vt)

The Attempt at a Solution


for a, I did:

x=v*t = (0.94c)(32us) =90,177.6 m

b)

t' = gamma * (-v/c^2 * x + t) = 10.9us

c)

x' = gamma * (x - vt) = 0 m

thanks!
 
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Welcome to PF;
Good up to (c) well done.
Recall - inside each inertial frame the regular laws of physics work like normal.
In the rest frame of the particle the laboratory of length d' zips past at speed v, and it does that in time t' ... so how long is d'?
 
would it be x' = vt' = 30,716.7 m? if so, i was wondering why x'=gamma*(x-vt) did not apply/could not work. thanks!
 
The beginning and end of the lab happen in the same place in the rest-frame of the particle.
 
Oh, that makes sense! Thank you so much!
 

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