Relativity: Solving Pion Homework Problem

[HelpPlease27]

Homework Statement

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?

Homework Equations

Δ t = Δt0 / sqrt(1-u^2/c^2)

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

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?

 

[Orodruin]

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?

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.

 

[HelpPlease27]

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.

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

 

[Orodruin]

I put p = mv

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

 

[HelpPlease27]

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

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