Calculating rest mass and energy (in an inertial frame)

[CricK0es]

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.

Homework Equations

http://www.sciweavers.org/upload/Tex2Img_1486938602/render.png

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...

 

[TSny]

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.

 

[CricK0es]

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]

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.

 

[CricK0es]

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

http://www.sciweavers.org/upload/Tex2Img_1486942686/render.png

Therefore E = 8.49GeV

 

[CricK0es]

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

http://www.sciweavers.org/upload/Tex2Img_1486943107/render.png

I'm not entirely sure how applicable it would be. But I'll have a play and come back in the morning. Come to think of it I don't think it would work with the available info, without some serious playing around. But I'll come back in the morning and see what I've got. Thank you so far