Homework Help: Special Relativity Question

1. Feb 23, 2013

bmb2009

1. The problem statement, all variables and given/known data

A particle has a rest energy of 1672MeV and a lifetime of 8.2x10^-11 s. It creates a .024m long track in a lab detector. What is the total energy of the particle

2. Relevant equations

3. The attempt at a solution

Total Energy = mc^2 + mc^2(1 - A) where A is defined as the Gamma Factor...basically i need to calculate the velocity of the particle and I realize that the lifetime give is the proper time (life of the particle in its frame) and the distance is in the lab frame. So I need to distance/time and I want to convert the proper time to the time interval in the lab frame but how do i do time dilation without the velocity? Thanks

2. Feb 23, 2013

Simon Bridge

You'll have to find a bunch of relations that have to hold simultaniously - so that you can cancel out v.

3. Feb 23, 2013

bmb2009

soo...what relations? I'm still stuck

4. Feb 23, 2013

Simon Bridge

1. total energy
2. time dilation
3. length contraction (related to 2)
4. relationship between distance and time in one reference frame

5. Feb 23, 2013

bmb2009

got it..thanks

6. Feb 23, 2013

Simon Bridge

No worries :)

7. Feb 24, 2013

bmb2009

Ugh nevermind lol I don't have it.... and it's driving me crazy.

V= L/T = L'/T' and I know L and T'.

Time dilation says T=T'sqrt(1-A^2) where A is V/c

so i plug in V=L/(T'sqrt(1-A^2)) and solve for V but I get (V^2)(T')^2 - ((V^4)(T')^2)/c^2 = c^2

ahhhhhh

8. Feb 24, 2013

Simon Bridge

 didn't read all the way ...

Well done.
Sometimes explaining why you have a problem produces the solution.

The particle travels distance L in the lab, in the particle's proper time T, then $L=v\gamma T$
Since the total energy is $E=\gamma E_0$ I have two equations and two unknowns.

When I saw your problem, actually did it via length contraction ... to put everything in the particle's frame.
In that frame, the detector moves a distance $L/\gamma$ in time T - and you get the same equation out.

Notice how I constructed the relations from the physics rather than trying to find the "right" equation to manipulate?

Last edited: Feb 24, 2013