Calculating the Distance Traveled by a Charged Pimeson in Relativistic Mechanics

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The discussion focuses on calculating the distance traveled by a charged pimeson in relativistic mechanics, specifically under conditions of kinetic energy of 700 MeV and a rest mass of 140 MeV/c². The user successfully calculated the distance traveled in the rest frame to be 20 meters using classical mechanics but struggled with the relativistic calculations. Key concepts include the use of Einstein's equation E = mc² and the relationship between kinetic energy and relativistic mass. The solution involves equating the square of the 4-momentum in both the lab frame and the pimeson rest frame to derive velocity and distance.

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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?
 
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What the expression for relativistic kinetic energy? (Either look it up or derive it.)
 
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
 
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.
 
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Thanks I solved it tnhe answer was just ight ifront of me but i made an awful mistake during my way :confused: Thnx guys and (girls?)
 

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