Linear acceleration and speed of light and pions

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Homework Help Overview

The problem involves a particle physics experiment using pions, which are accelerated to a speed of 0.99c. The original poster seeks to determine the maximum length of a beam pipe for transporting the pions and the length of the beam pipe as perceived by the pions, while considering relativistic effects such as time dilation and length contraction.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to apply relativistic formulas but expresses uncertainty about the correct application of the given values. Some participants clarify that the rest lifetime of the pion is not a velocity and emphasize the importance of using the correct speed (0.99c) in calculations.

Discussion Status

The discussion is ongoing, with participants providing clarifications and suggesting resources for further understanding. There is a recognition of confusion regarding the application of the formulas, and some guidance has been offered, though no consensus or resolution has been reached.

Contextual Notes

One participant notes a lack of understanding due to missing a week of class, which may contribute to the confusion regarding the problem setup and the application of relativistic concepts.

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Homework Statement



In a particle physics experiment a particle called pion is used to hit a target. The particle pion has a (rest) lifetime of 2.6x 10-8 second and is accelerated to a speed 0.99c with respect to the linear accelerator. A straight beam pipe is used to transport the pions to the target. What would be the maximum length of the beam pipe? What is the length of the beam pipe the pions see?

Homework Equations



Relativistic formulas..
To an observer at rest, the clock in a moving system appears to have slowed down, so that time intervals seem longer than his own clock intervals (time dilation).

[delta]t = [delta]t’/√ (1 - v^2 / c^2 )


Similarly, to an observer at rest the meter stick of the moving system appears shorter than his own meter stick (length contraction)

L = L’ *√ (1 - v^2 / c^2 )


The Attempt at a Solution



I tried to put in the numbers given and put them in the formulas but I'm not completely sure what I should do. Any help is appreciated.
 
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Please write out your work so far so we can help better. Otherwise we have no idea where you got stuck.
 
Well I put in 2.6x 10-8 for velocity. But I have no idea what I am supposed to do. I missed the last week of class and need help with this problem. I don't think that is the right thing to do.
 
2.6E-8 sec is the time that it takes for the pion to decay in its rest frame. It is not a velocity. The velocity would be 0.99c where 'c' is the speed of light.
 
nickjer said:
2.6E-8 sec is the time that it takes for the pion to decay in its rest frame. It is not a velocity. The velocity would be 0.99c where 'c' is the speed of light.

So I put .99c in for the v's. I still don't know how to get the answer still I'm lost, but thanks for your help.
 
Unfortunately this isn't the best place to teach the whole subject. Here are some good sources:

http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/tdil.html" (Check the Time Dilation section)

http://www2.slac.stanford.edu/vvc/theory/relativity.html" (Read time dilation for particles section and the rest of it)

If you have more questions then just ask.
 
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