Linear acceleration and speed of light and pions

In summary: I'll help you as much as I can.In summary, the beam pipe the pions see is the length of the pipe that is 0.99c from the linear accelerator.
  • #1
sappy01
3
0

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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  • #2
Please write out your work so far so we can help better. Otherwise we have no idea where you got stuck.
 
  • #3
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.
 
  • #4
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.
 
  • #5
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.
 
  • #6
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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FAQ: Linear acceleration and speed of light and pions

1. What is linear acceleration?

Linear acceleration is defined as the rate of change of an object's velocity in a straight line. It is represented by the symbol "a" and is measured in meters per second squared (m/s^2).

2. What is the speed of light?

The speed of light is a fundamental physical constant and is defined as the speed at which light travels in a vacuum. Its value is approximately 299,792,458 meters per second (m/s).

3. How are linear acceleration and speed of light related?

Linear acceleration and speed of light are not directly related. However, according to Einstein's theory of relativity, the speed of light is considered to be the maximum speed at which any object can travel. This means that no object can accelerate to or beyond the speed of light.

4. What are pions?

Pions are subatomic particles that belong to the family of mesons. They have a mass about 273 times that of an electron and are electrically neutral. Pions are unstable and decay into other particles, such as muons and neutrinos.

5. How are pions related to linear acceleration and speed of light?

Pions are not directly related to linear acceleration and speed of light. However, they are often used in experiments involving high-energy particle accelerators, where they are accelerated to close to the speed of light before decaying. The study of pions and their behavior at high speeds has contributed to our understanding of the laws of physics, including the theory of relativity and particle physics.

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