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\subsubsection*{PHSX 221L\hfill Acceleration Due to Gravity\hfill Name:\underline{\hspace*{2in}}}

% \noindent
% \underline{Title:} Acceleration Due to Gravity

\noindent
\underline{Object:} (a) To study the distance-versus-time and 
speed-versus-time relationships for a falling body, and (b) To measure 
experimentally the acceleration of an object in free fall.

\noindent
\underline{Theory:} When a body falls under the influence of gravity 
it moves with a constantly increasing speed---it accelerates.  
Acceleration is defined as the time rate of change of velocity:
\begin{equation}
a = {dv\over dt}.
\end{equation}
When the acceleration is constant this expression can be integrated 
to obtain velocity as a function of time:
\begin{equation}
v(t)  = v_0 + at.
\end{equation}
This is a linear first degree equation.  Therefore, a plot of $v$ 
vs.\ $t$ should be a straight line with slope equal to the 
acceleration $a$.

\noindent
If this equation for velocity is again integrated the result will be 
distance as a function of time:
\begin{equation}
y(t) = y_0 + v_0 t + \frac{1}{2}at^{2}.
\end{equation}
This is a second degree equation, which means that if $y$ 
were plotted against $t$ the result would be a parabolic curve.


\noindent
\underline{Apparatus, Procedure and Results:} 

\vspace{-.25in}
\begin{enumerate}

\item Include a diagram of the apparatus used.

\item Record the steps in your experimental procedure, as explained in 
class.

\item Record the time and position in a ``difference table'' in which 
each column is the difference computed from values in the preceding 
column.  After taking the first difference divide by $\Delta t$ to get 
the velocity.  After taking the second difference divide by $\Delta t$ 
again to get the acceleration.

\item Make a plot of velocity versus time.  The acceleration is the 
slope of this graph.

\item Also, make a plot of position versus time.  Interpret.

\end{enumerate}

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

\item How well do your experimental results agree with theory?

\item How well does your measured acceleration (both methods) agree 
with the accepted value.

\item What is your overall evaluation of this experiment?

\end{enumerate}


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