Linear acceleration and speed of light and pions

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SUMMARY

The discussion centers on calculating the maximum length of a beam pipe for pions accelerated to 0.99c in a particle physics experiment. The pion has a rest lifetime of 2.6 x 10-8 seconds, which is crucial for determining time dilation and length contraction using relativistic formulas. The relevant equations include time dilation, [delta]t = [delta]t’/√(1 - v2/c2), and length contraction, L = L’ * √(1 - v2/c2). The discussion emphasizes the importance of correctly identifying the rest lifetime as a time measurement rather than a velocity.

PREREQUISITES
  • Understanding of special relativity concepts, particularly time dilation and length contraction.
  • Familiarity with the speed of light (c) and its significance in relativistic physics.
  • Ability to manipulate and apply relativistic equations for time and length.
  • Basic knowledge of particle physics, specifically regarding pions and their properties.
NEXT STEPS
  • Study the derivation and applications of the time dilation formula in special relativity.
  • Learn about length contraction and its implications in high-speed particle physics.
  • Explore practical examples of relativistic effects in particle accelerators.
  • Review resources on the properties and behavior of pions in particle physics experiments.
USEFUL FOR

This discussion is beneficial for physics students, particle physicists, and educators seeking to deepen their understanding of relativistic effects on particles like pions in high-speed experiments.

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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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