# Calculating rest mass and energy (in an inertial frame)

## Homework Statement

A particle is accelerated so it has a total energy of 10GeV measured in the accelerator’s rest frame. The particle's momentum is 8GeV/c in the same frame. Calculate...

a.) Rest mass of the particle
b.) Energy in an inertial frame in which its momentum is 6GeV/c
c.) The speed of the this reference frame relative to the accelerator's rest frame.

## The Attempt at a Solution

Using the stated relevant equation, I found the rest mass to be equal to 6 GeV/c^2, and then the energy in the inertial frame to be 0. I'm not sure if these are right, especially b! So I'm worried I may have over simplified things a little.

I'm not entirely sure how to do c. Could I attempt to rearrange the relativistic momentum equation using transforms?

Any guidance would be much appreciated...

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TSny
Homework Helper
Gold Member

## Homework Equations

There's a misprint in this equation. But I don't think it affected your result for (a), which I think is correct.

Using the stated relevant equation, I found the rest mass to be equal to 6 GeV/c^2, and then the energy in the inertial frame to be 0.
You must have made a mistake for part (b). Can the relativistic total energy of a free particle ever be zero?

I'm not entirely sure how to do c. Could I attempt to rearrange the relativistic momentum equation using transforms?
I'd have to see more detail of what you mean here.

You must have made a mistake for part (b). Can the relativistic total energy of a free particle ever be zero?
Yeah I was confused with b. I assumed there should always be energy as a result of mass. So I can't simply plug in my rest mass and the given momentum value for the specified inertial frame?

TSny
Homework Helper
Gold Member
Yeah I was confused with b. I assumed there should always be energy as a result of mass.
Yes, the minimum possible energy is the rest energy associated with the mass.
So I can't simply plug in my rest mass and the given momentum value for the specified inertial frame?
Yes, you can do that. But you shouldn't get zero for the total energy.

Oh I put a minus! Why?! xD Okay...

Therefore E = 8.49GeV

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For c. I was thinking of using p = γmv... But using a velocity transform