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\centerline{\bf PH 429: Reference Frames}
\centerline{\bf Relativistic Particles I}

\bigskip
\bigskip
\centerline{\emph{Solve the following problem on a large whiteboard}}

\medskip
\textbf{COSMIC RAYS}
% Taylor \& Wheeler, 1st edition, Ex.\ 42, p.\ 89.

The collision of cosmic rays with gas nuclei in the atmosphere 60 km above the surface of the earth produces $\mu$-mesons, which then
move vertically downward at close to the speed of light.  The halflife before
$\mu$-mesons decay into other particles is 1.5 $\mu$s ($1.5\times10^{-6}$ s).

{\it Assume all the mesons are traveling straight down at the same speed.}
\begin{enumerate}
\item Assuming it doesn't decay, what is the minimum time it would take a $\mu$-meson to reach the
surface of the earth?
\vfill
\item Assuming there were no time dilation, what is the maximum fraction of the
mesons that would reach the earth without decaying?
\vfill
\item In actual fact, roughly $1\over8$ of the mesons reach the earth!  How fast are
they going?
\vfill
\end{enumerate}


\vfill
\leftline{\it by Tevian Dray}
\leftline{Revised 2013 by Mary Bridget Kustusch}
\newpage

\centerline{\bf PH 429: Reference Frames}
\centerline{\bf Relativistic Particles II}

\bigskip
\bigskip
\centerline{\emph{Choose one of the following problems to work on a large whiteboard.}}

\medskip
\textbf{MASS ISN'T CONSERVED}
% Example 7 on pp.\ 480--481 of Griffiths.

Two identical lumps of clay of (rest) mass $m$ collide head on, with each
moving at ${3\over5}c$.  What is the mass of the resulting lump of clay?\\
\vfill

\textbf{IDENTICAL PARTICLES}
% Problem 10.32 on pp.\ 483--484 of Griffiths.
% Problem 29 of Griffiths. % 1st edition!

Consider the head on collision of 2 identical particles each of mass $m$ and
energy $E$.
\begin{enumerate}
\item In Newtonian mechanics, what multiple of $E$ is the energy $E'$ of one
particle as observed in the reference frame of the other?
\vfill
\item In special relativity, what is the energy $E'$ of one particle as observed in
the reference frame of the other?
\vfill
\item
Suppose we collide 2 protons ($mc^2=1 \hbox{ GeV}$) with energy $E=30
\hbox{ GeV}$.  Roughly what multiple of $E$ is $E'$ in this case?
\vfill
\end{enumerate}

\vfill
\leftline{\it by Tevian Dray}
\leftline{Revised 2013 by Mary Bridget Kustusch}
\end{document}