\input{labpreamble}
\begin{document}


\subsubsection*{PHSX 221L\hfill Measurement and Density\hfill Name:\underline{\hspace*{2in}}}


% \noindent
% \underline{Title:} A Study of Radius-Circumference, and Radius-Mass 
% for Several Masonite Disks

\noindent
\underline{Object:} (a) To practice measuring skills.  (b) To 
determine the relationship between the circumference and the radius 
for six masonite disks.  (c) To determine the relationship between 
mass and radius for six masonite disks.  (d) To determine the density 
of the masonite from which the disks are made as well as the density 
of some other substances.

\noindent
\underline{Theory:} From geometry we know that the radius and 
the circumference of a circle are related by:
\begin{equation}
C = 2 \pi r.
\end{equation}
Thus, if $C$ were plotted against $r$ the graph should be linear with 
a slope equal to $2\pi$.

\noindent
Density, $\rho$, is defined as 
\begin{equation}
\rho = {m\over V}
\end{equation} 
which becomes for a disk 
\begin{equation}
\rho  = {m\over \pi r^2 t} 
\end{equation}
where $t$ is the thickness of the disk.

\noindent
Solving these equations for mass we obtain:
\begin{equation}
m= \rho V = \rho\pi r^2 t.
\end{equation}

\noindent
Consequently, a plot of mass $m$ versus radius $r$ should be a 
parabolic curve.  But, if $m$ were plotted versus $r^2$ the graph 
should be a straight line with slope equal to $\rho\pi t$.


\noindent
\underline{Procedure:} 

\vspace{-.1in}
\begin{enumerate}

\item Measure and record the radius and circumference of each 
masonite disk.

\item Plot a graph of circumference versus radius from this data.

\item Measure the mass of each disk. 

\item Plot a graph of mass versus the square of the radius.

\item\label{density} Compute the density for each disk by formula.

\item Measure the mass and volume of a pine block, an aluminum rod (or 
a copper wire) and compute the densities of these solids.

\item Measure the mass and volume (a graduated cylinder would be 
useful) of various amounts of water.  Make a plot of mass vs.~volume 
and compute the slope of the line.

\end{enumerate}

\noindent
\underline{Results:}

\vspace{-.1in}
\begin{enumerate}

\item What is the slope of your circumference-radius graph?  How does 
this value compare with the theoretical prediction?

\item Does your mass-radius squared graph appear linear?  If so, what 
is the slope?

\item Use the slope of your mass-radius squared graph to compute the 
density of masonite.

\item Compute the average density of all the disks found in step 
\ref{density} of the procedure.

\item How does this average density compare with the density as 
computed from the slope of the mass-radius squared graph?

\item How do your measured densities for pine, aluminum (or copper), 
and water compare with accepted values?

\end{enumerate}

\noindent
\underline{Questions:}
\vspace{-.1in}
\begin{enumerate}

\item What could affect or change the density of a substance?
\vspace{.3in}

\item How could you measure the density of irregularly shaped objects?
\vspace{.3in}

\end{enumerate}

\noindent
\underline{Conclusions:}  What was the main purpose of this lab?  What did 
you learn from this lab?  How big were the errors?  What were the 
various sources of error?  What clever things did you do to reduce 
error as much as possible?  Did you like the lab?  What will you 
remember in 3 months about this lab?

\end{document}
