- #1
squelch
Gold Member
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Homework Statement
A proton of mass "m" is accelerated up to a kinetic energy "K" and then collides with a stationary proton at rest. All that is left after the collision is a new particle of mass "M".
(a) Write out the momentum and energy equations for the collision.
(b) What is the maximum mass M that can be created in this collision?
Homework Equations
I'm not quite sure what to use here. I have:
[tex]\begin{array}{l}
{E^2} = {p^2}{c^2} + {m^2}{c^4}\\
p = \gamma mv
\end{array}[/tex]
The Attempt at a Solution
It seems like what I'm supposed to do is use the energy-momentum relationship and the formula for kinetic energy in this way:
[tex]\begin{array}{l}
{(K - m{c^2})^2} = {p^2}{c^2} + {m^2}{c^4}\\
K - m{c^2} = \sqrt {{p^2}{c^2} + {m^2}{c^4}}
\end{array}[/tex]
From here, do I use [itex]K = \frac{1}{2}m{v^2}[/itex] to put together the [itex]p=mv[/itex] relationship?
edit: I'm supposing that what I'm supposed to do here is solve for [itex]v[/itex] somehow.
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