\input{labpreamble}
\begin{document}


\subsubsection*{PHSX 221L\hfill Colliding Pool Balls\hfill Name:\underline{\hspace*{2in}}}


\noindent
\underline{Object:} To observe the collisions of pool balls and 
compare with theory.

\noindent
\underline{Theory:} When two objects collide the momentum of the
system is always conserved (we say this because we assume that both of
the colliding objects are part of the system so the collision forces are
internal to the system).  If conditions are such that total kinetic
energy is also conserved the collision is said to be ``totally or
perfectly elastic.''  If the two objects stick together and remain in
contact after the collision, we say that the collision is ``totally or
perfectly inelastic,'' and kinetic energy is not conserved.

\noindent
If the objects do not stick together, and there is a loss of kinetic 
energy then the collision is ``partially inelastic.''  A parameter 
known as the \underline{coefficient of restitution} has been defined 
such that it is a measure of the degree of elasticity of a collision:
\begin{equation}
\epsilon = {{\rm relative\ speed\ of\ rebound}\over{\rm relative\ speed\ of\ 
approach}}= {v_{B}' - v_{A}'\over v_{A} - v_{B}}.
\end{equation}

\begin{center}
\begin{tabular}{ll}                      
\multicolumn{2}{c}{Summary of Collision Types}  \\   \hline
Totally inelastic   & $\epsilon = 0$     \\  
Partially inelastic & $0 < \epsilon < 1$ \\  
Totally elastic     & $\epsilon = 1$     \\  
Hyperelastic       & $\epsilon > 1$     \\  
\end{tabular}       
\end{center}


\noindent
\underline{Preliminary:} 
\vspace{-.25in}
\begin{enumerate}

\item\label{elastic}Assume a pool ball moving at speed $v_{A}$ has a 
head-on collision with a stationary ball of equal mass.  If the 
collision is totally elastic ($\epsilon = 1$), show how to find the 
speed of each ball after the collision.

\item Repeat procedure \ref{elastic} for $\epsilon = 0.8$. 

\item Find the velocity of each ball after the collision if the 
collision is not head-on.  Assume an oblique impact such that the line 
of motion of the first ball is tangent to the surface of the second 
ball.  Also assume that the collision is perfectly elastic and that 
the balls are perfectly smooth.

\end{enumerate}

\noindent
\underline{Procedure:} 
Experiment with pool balls both with head-on collisions and with 
oblique collisions and compare observations with theory.  Do the 
collisions appear to be perfectly elastic?  What evidence do you have?

\newpage \ 

\end{document}
