Physics question? proton/antiproton collision find velocity

[asdf12312]

physics question?? proton/antiproton collision find velocity

Homework Statement

A proton and antiproton collide with equal and opposite momentum at the SPS collider in Geneva to form a single massive particle which is 10 times more massive than a proton. What is the velocity (as a fraction of c) of the proton beam?

The Attempt at a Solution

http://openstudy.com/updates/529bde51e4b0e39d4e82bfe3

^this is something like what the answer would be. except its not right (its telling me its not -_-)
I got v=0.9992c as my answer

 

[collinsmark]

Homework Statement

A proton and antiproton collide with equal and opposite momentum at the SPS collider in Geneva to form a single massive particle which is 10 times more massive than a proton. What is the velocity (as a fraction of c) of the proton beam?

The Attempt at a Solution

http://openstudy.com/updates/529bde51e4b0e39d4e82bfe3

^this is something like what the answer would be. except its not right (its telling me its not -_-)
I got v=0.9992c as my answer

I think the attempted solution link makes the problem a little more difficult than necessary. Also, I think there might be something wrong with the final couple of steps.

Suffice it to say, there is a very useful result in there which you can use to solve this problem. The total energy for an object with mass (unlike a photon) -- which describes both its rest mass energy plus its kinetic energy, is
$$E = \gamma m c^2$$
That's the total energy for just for a single particle though. The problem statement says that there are two particles, a proton and an anti-proton, with equal and opposite momentum. Since the proton and antiproton have the same mass, we can assume that the total energy before the collision is twice that of the equation above (there are two particles involved, each with the same energy, $\gamma m_p c^2$).

The rest mass energy of a proton is simply $m_p c^2$. The resulting, massive particle has 10 times that energy. (And it's all rest mass energy, since the total momentum of that massive particle is zero, due to conservation of momentum).

So, given that information, solve for gamma. Once you have gamma, you can easily find the original speed before the collision.

 

[asdf12312]

Thanks! that's so much easier.