Calculating Mean Distance Traveled by Pi-Mesons at Speed v=0.3c

[EIRE2003]

A beam of charged pi-mesons is traveling with a speed of v=0.3c.
The mean life of a pi-meson is 2.6 x 10^-8s. What is the mean distance traveled by a pi meson before it decays?

How do u do this?

 

[chroot]

Do you understand how to calculate time dilation?

- Warren

 

[EIRE2003]

No

 

[chroot]

Have you not been paying attention in class or something?

- Warren

 

[EIRE2003]

Im not in school i finished last yr. I am repeating cause our teacher was never into teach us the stuff. So I am trying to learn this stuff myself from the past examination papers. My leaving cert is in june.

 

[chroot]

Well, in special relativity theory, when an object is moving at velocity v with respect to a stationary observer, the object will appear to suffer a time dilation of

$$T = \frac{T_0}{\sqrt{1 - v^2/c^2}}$$

where $T$ is the time measured by the observer and $T_0$ is the time as measured in the rest frame of the pion.

In other words, the pion will seem to live longer when moving than it would when at rest by a factor of $1/\sqrt{1 - v^2/c^2}$.

Does this make sense?

- Warren

 

[EIRE2003]

not really. I've seen this in hawkings book universe in a nutshell but never understood it.

I don't understand what T_o is?

Maybe if u cud actually do the sum and i will go through it and try to get my head around it. Then it won't be as confusing. I just need an example of how its done.

 

[chroot]

$T_0$ is the proper time, the time experienced by the pion itself. Plug in its lifetime here.

We don't generally just give answers to homework questions here. I've given you plenty to start with. Consider reading more here:

http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/tdil.html

- Warren