# Relativity - Pion

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1. Feb 22, 2017

### HelpPlease27

1. The problem statement, all variables and given/known data
After being produced in a collision between elementary particles, a positive pion (π+) must travel down a 1.00 km -long tube to reach an experimental area. A π+ particle has an average lifetime (measured in its rest frame) of 2.60×10−8s; the π+ we are considering has this lifetime.
How fast must the π+ travel if it is not to decay before it reaches the end of the tube? (Since u will be very close to c, write u=(1−Δ)c and give your answer in terms of Δ rather than u.)
The π+ has a rest energy of 139.6 MeV. What is the total energy of the π+ at the speed calculated in part A?

2. Relevant equations
Δ t = Δt0 / sqrt(1-u^2/c^2)

E^2 = (mc^2)^2 + (pc)^2

3. The attempt at a solution
I got the correct answer for speed, the first part of the question. It's the second part I can't get to work. I used the total energy equation and my speed, which worked out to give me E = 197.4 MeV but this wasn't right. I'm not sure where I'm going wrong?

2. Feb 22, 2017

### Orodruin

Staff Emeritus
We will not be able to tell you this unless you actually show us what you did, not just try to describe it in words.

3. Feb 23, 2017

### HelpPlease27

E^2 = (mc^2)^2 + (pc)^2
I used mc^2 = 139.6 MeV
I put p = mv so the pc = mvc but m = 139.6/c^2 and v = (1-Δ)c = (1-(3.04*10-5))c so pc = 139.6 MeV
So then E = sqrt(139.6^2 + 139.6^2) = 197.4 MeV

4. Feb 23, 2017

### Orodruin

Staff Emeritus
This is not the relativistic momentum. This relation is only valid at non-relativistic speeds.

5. Feb 23, 2017

### HelpPlease27

Yes, that makes sense. I forgot to include gamma. I got the correct answer now, thanks.

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