Calculating mass of particle given total energy and momentum

[Froskoy]

Homework Statement

A particle, observed in a particular reference frame, has a total energy of 10GeV and a momentum of 6GeV. What is its mass in units of GeV/c^2?

Homework Equations

I used $$p=\gamma mv$$
and
$$E=\gamma mc^2$$

The Attempt at a Solution

So I divided the above equation for P by the equation for E to get

$$\frac{P}{E} = \frac{v}{c^2} \Rightarrow v=\frac{P}{E}c^2$$

and then substituting back into the quation for E:

$$m = \frac{E}{\gamma c^2} = \frac{\sqrt{1-\frac{P^2}{E^2}}E}{c^2}$$

But this doesn't give the correct answer - any ideas?

With very, very many thanks,

Froskoy.

 

[tiny-tim]

Hi Froskoy!

(try using the X² button just above the Reply box )

A particle, observed in a particular reference frame, has a total energy of 10GeV and a momentum of 6GeV. What is its mass in units of GeV/c^2?

It's not clear what they mean by "total energy".

Maybe they mean the kinetic energy, (γ - 1)mc² …

try that ​

 

[phyzguy]

You dropped a factor of c^2, in your final equation, which should read:
$$m = \frac{E \sqrt{1-\frac{p^2 c^2}{E^2}}}{c^2}$$
which is consistent with the well-known relation E^2 = p^2 c^2 + m^2 c^4. However, this shouldn't matter, since when using units of GeV and GeV/c^2, c=1 anyway. Why doesn't this give the right answer? If E= 10Gev, and p = 6GeV/c^2, m = 8Gev/c^2, which is what your equation gives.

 

[Froskoy]

Hi!

Thanks very much for confirming what I had is correct - it turned out to be a calculation error.

With very many thanks again,

Froskoy.

 

[paranormal]

Your approach is correct, but there seems to be a mistake in your substitution. The equation for velocity should be v = P/E, not P/Ec^2. This will give you the correct answer of 2GeV/c^2 for the mass of the particle.