\batchmode
%***** homework set 11 ***********
\documentstyle[12pt]{report}
\makeatletter
\pagestyle{empty}







 











                          



  








\textheight=9.5in
\textwidth=6.5in
\hoffset=-0.75in
\voffset=-1.0in

\def\Bskip{\vskip 1cm}

\def\bskip{\vskip 0.75cm}

\def\Mskip{\vskip 0.5cm}

\def\ssk{\vskip 0.2cm}

\def\hb{\hfill\break }

\def\ul#1{$\underline{\hbox{#1}}$}

\def\rr{\hbox{\vrule height 3pt depth-2pt width.5cm}}

\def\ie{{\it i.e.}, }

\def\viz{ {\it viz. }}

\def\eg{{\it e.g.},}

\def\DZ{D\O ~}

\def\dz{D\O }

\def\DN{D\O Note~}

\def\DG{D\O GEANT~}

\def\Lum{{\cal L}}

\def\Bul{~~$\bullet $~}

\def\pbarp{$\overline{\rm p} {\rm p}$}

\def\ppbar{${\rm p}\overline{\rm p} $}

\def\squark{$\widetilde q$}

\def\gluino{$\widetilde g$}

\def\MEt{/\kern-.75em\hbox{$E_t$}}

\def\Deg{$^{\circ} $}

\def\Lsim{$ \sim$\llap {$^<$}}

\def\Gsim{$ \sim$\llap {$^>$}}

\def\ang{$^{\circ }$\llap A }

\def\Ang{
\setbox0=\hbox{h}\dimen1=\ht0 \advance\dimen1 by-1ex
\rlap{\raise.67\dimen1\hbox{{}\hskip2pt\char'27}}A}

\def\Bul{\ifmmode {\bullet }\else {$\bullet $\enskip}\fi}

\def\Ebul{\ifmmode {\circ }\else {$\circ $\enskip}\fi}

\def\imply{\ifmmode {\Rightarrow }\else {$\Rightarrow $}\fi}

\def\lt{<}

\def\gt{>}

\makeatother
\newenvironment{tex2html_wrap}{}{}
\newwrite\lthtmlwrite
\def\lthtmltypeout#1{{\let\protect\string\immediate\write\lthtmlwrite{#1}}}%
\newbox\sizebox
\begin{document}
\pagestyle{empty}
{\newpage
\clearpage
\samepage \begin{displaymath}L = {L_{\circ} \over  \gamma },~~~
\gamma ~=~{1 \over {\sqrt{1 - \beta ^2}}}, ~~~
\beta = {v\over c}\end{displaymath}
}

{\newpage
\clearpage
\samepage \setbox\sizebox=\hbox{$L_{\circ}$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline136: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
}

{\newpage
\clearpage
\samepage \setbox\sizebox=\hbox{$\beta $}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline138: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
}

{\newpage
\clearpage
\samepage \setbox\sizebox=\hbox{$\gamma = 2.$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline140: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
}

{\newpage
\clearpage
\samepage \setbox\sizebox=\hbox{$\gamma $}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline142: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
}

{\newpage
\clearpage
\samepage \setbox\sizebox=\hbox{$\beta $}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline144: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
}

{\newpage
\clearpage
\samepage \setbox\sizebox=\hbox{$\beta $}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline146: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
}

{\newpage
\clearpage
\samepage \begin{displaymath}\beta =  {\sqrt {1- {1\over {\gamma ^2}}}}\end{displaymath}
}

{\newpage
\clearpage
\samepage \begin{displaymath}\beta = {\sqrt {1- {1\over {2^2}}}} = {\sqrt{3}\over 2}~~\approx 0.866\end{displaymath}
}

{\newpage
\clearpage
\samepage \setbox\sizebox=\hbox{$0.866 c.$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline152: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
}

{\newpage
\clearpage
\samepage \begin{displaymath}\gamma = {1\over \sqrt {{1 - \beta ^2}}}~=~ 
{1\over \sqrt {{1 - 0.6 ^2}}}~=~ {10\over 8}.\end{displaymath}
}

{\newpage
\clearpage
\samepage \setbox\sizebox=\hbox{$0.8 \times 20$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline156: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
}

{\newpage
\clearpage
\samepage \setbox\sizebox=\hbox{$= (0.25 + 0.5)c = 0.75 c$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline158: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
}

{\newpage
\clearpage
\samepage \begin{displaymath}\beta = {{\beta_1 + \beta_2}\over {1 + \beta_1 \beta_2}}.\end{displaymath}
}

{\newpage
\clearpage
\samepage \begin{displaymath}\beta = {{0.25 + 0.5}\over {1 + 0.25\times 0.5}} = {0.75\over 1.125}
\approx 0.667.\end{displaymath}
}

{\newpage
\clearpage
\samepage \setbox\sizebox=\hbox{$\gamma  $}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline164: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
}

{\newpage
\clearpage
\samepage \begin{displaymath}\gamma ~= ~{1\over \sqrt {{1 - \beta ^2}}}~=~ {1\over \sqrt {{1 - 0.8^2}}}
~=~{1\over 0.6} = {10\over 6}\end{displaymath}
}

{\newpage
\clearpage
\samepage \setbox\sizebox=\hbox{$\gamma $}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline168: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
}

{\newpage
\clearpage
\samepage \setbox\sizebox=\hbox{${1\over \gamma }$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline170: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
}

{\newpage
\clearpage
\samepage \begin{displaymath}0.01 {\rm kg \times (3 \times 10^8  m)^2 = 9\times 10^{14}~J}\end{displaymath}
}

{\newpage
\clearpage
\samepage \setbox\sizebox=\hbox{$100{\rm kcal} \approx  4.2\times 10^5{\rm J}$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline174: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
}

{\newpage
\clearpage
\samepage \setbox\sizebox=\hbox{$9\times 10^{14}$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline176: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
}

{\newpage
\clearpage
\samepage \begin{displaymath}{9\times 10^{14}\over 4.2\times 10^5}~ {\rm kg} = 2.14\times 10^9 {\rm kg},\end{displaymath}
}

{\newpage
\clearpage
\samepage \setbox\sizebox=\hbox{$0.5 g$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline182: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
}

{\newpage
\clearpage
\samepage \setbox\sizebox=\hbox{$0.5 g$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline188: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
}

{\newpage
\clearpage
\samepage \setbox\sizebox=\hbox{$0.5 g$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline190: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
}


\end{document}
