Calculating the Distance Traveled by a Charged Pimeson in Relativistic Mechanics

[eri3an]

I have problems with some excercises before my exam on friday. please help me

1) A charged pimeson has a lifetime of t=2,6*10^-8 s in its resting system.

a) How far distance L does it travel in Inrelastvistic mechanics?If its kinetic energy is 700 MeV?

b) How far distance L0 (seen by observator in laboratoriesystem) does it go by relativistik mechaniks?

Pimesons mass is140 MeV/c^2.

I get a to be 20 m using 700 = 1/2*mv^2 but i don't get b. Anyone that can solve it?

 

[Doc Al]

What the expression for relativistic kinetic energy? (Either look it up or derive it.)

 

[borisleprof]

You have to remember the famous equation of Einstein: E = mc^2.
Where m is the mass of the particle when it moves.

the kinetic energie is the difference between the energy of the particle when it is movin and the rest energy (the energy that the particle has when it is at rest).
You must know how to calculate the value of m when the particle moves.
bye

 

[Daverz]

Write down the square of the 4-momentum in the lab frame and the pi meson rest frame, then set them equal. From this, knowing the rest mass and kinetic energy, you can get the velocity and then the time and length contraction factors. You can also use the square of the proper time to get the lab frame travel distance from the lab frame lifetime, or vice versa.

 

[eri3an]

Solved

Thanks I solved it tnhe answer was just ight ifront of me but i made an awful mistake during my way Thnx guys and (girls?)