Calculating Invariant Mass Using Momentum and Rest Mass

[iloveflickr]

Hello,

I'm working on this problem and I'd like to know how to find the invariant mass using just the lab-frame momentum and rest mass.

I've found a lot of equations that deal with E, and I'm not completely sure what that is either.

Thanks

 

[pam]

You have to tell us "this problem".

 

[iloveflickr]

I have a proton with momentum = 1GeV hitting a neutron at rest, and I'd like to find the CM-momentum before collision.

Thanks

 

[robphy]

I have a proton with momentum = 1GeV hitting a neutron at rest, and I'd like to find the CM-momentum before collision.

Thanks

This really belongs in one of the Homework forums:
https://www.physicsforums.com/forumdisplay.php?f=152

 

[iloveflickr]

More work...

So here's what I have so far...

E* = (Ep* + En*),

where
Ep* = Mp + Pe
En* = Mn

Pe = momentum of electron in lab frame
Ep* = energy of proton in CM frame
En* = energy of neutron in CM frame
Mn/Mp = mass of neutron/proton

Is E* = Invariant mass? If so, I've got this problem done.

 

[pmb_phy]

Hello,

I'm working on this problem and I'd like to know how to find the invariant mass using just the lab-frame momentum and rest mass.

I've found a lot of equations that deal with E, and I'm not completely sure what that is either.

Thanks

As measured in an inertial frame of reference - If m₀ = invariant mass of system, p = total momentum of system and E = total inertial energy of the system then


E^2 = m₀²c⁴+(pc)². Simply solve for the invariant mass m₀ of the system and you have you're answer.

Pete

 

[iloveflickr]

As measured in an inertial frame of reference - If m₀ = invariant mass of system, p = total momentum of system and E = total inertial energy of the system then


E^2 = m₀²c⁴+(pc)². Simply solve for the invariant mass m₀ of the system and you have you're answer.

Pete

Thanks for your response. I found that exact equation in many texts and I haven't a clue what the total inertial energy of the system is.

In my particular problem, would it be E = KE(proton) + Mass(proton) + Mass(neutron)?

 

[pmb_phy]

Thanks for your response. I found that exact equation in many texts and I haven't a clue what the total inertial energy of the system is.

In my particular problem, would it be E = KE(proton) + Mass(proton) + Mass(neutron)?

The total inertial energy, E, of a particle is the sum of the particle's rest mass and its kinetic energy. The total energy, W, of a particle is the inertial energy + potential energy. That is to say that

E = K + E₀

W = E + V

Best wishes

Pete

 

[iloveflickr]

Thanks much.