\input{labpreamble}
\begin{document}


\subsubsection*{PHSX 221L\hfill Centripetal Force\hfill Name:\underline{\hspace*{2in}}}

\underline{Object:} To measure the centripetal force which acts on a 
body when it is undergoing uniform circular motion, and to compare with theory.

% \underline{Object:} To measure the force which must act on a body in 
% order for it to travel in a circular path at constant speed, and 
% to compare this measured value with the centipetal force as calculated 
% from Newton's Second Law.

\underline{Theory:} An object moving at constant speed $v$ in a circular 
path experiences an acceleration toward the center of the circle with 
a magnitude of
\begin{equation}
a_{c}={v^{2}\over r}
\end{equation}
where $r$ is the radius of the circle.  Newton's Second Law states 
that such an acceleration is associated with a centripetal (center-seeking) 
force:
\begin{equation}
F_{c}=m{v^{2}\over r}.
\end{equation}
If the moving body makes one revolution in $T$ seconds or $f$ 
revolutions per second, then the velocity $v$ is given by
\begin{equation}
v={2\pi r\over T} = 2\pi rf.
\end{equation}
This can also be expressed in terms of the angular velocity, 
$\omega(=2\pi f)$, as $v=r\omega$, where $\omega$ comes in radians per 
second. 
The centripetal force can now be written as
\begin{equation}
F_{c}=4\pi^{2}f^{2}mr= mr\omega^{2}.\label{force}
\end{equation}

\underline{Procedure:} 
\vspace{-.15in}
\begin{enumerate}

\item Include diagrams of the apparatus used.

\item For each of at least four different spring tension settings,
vary the speed of rotation until the mass moves out and just touches the
pointer, stretching the spring in the process.

\item Use $f$ or $\omega$ (from the counter and from $T$) to obtain 
the computed value of $F_{c}$.

\item The measured value of $F_{c}$ is obtained by removing the 
spring assembly from the rotator and hanging weights on it to stretch 
the spring to the pointer.  The tension in the spring is equal to the 
hanging weight (include the mass of the object that rotated; the 
value should be stamped on it) and is theoretically $F_{c}$.

\item Plot spring tension as a function of either $f^{2}$ or $\omega^{2}$.

\end{enumerate}

\pagebreak

\underline{Analysis:} 
\vspace{-.15in}
\begin{enumerate}

\item Compare the computed centripetal force with the measured 
tension force for each trial.  (Compute percent difference.)

\item Does your graph of spring tension versus $f^{2}$ or $\omega^{2}$
form a straight line?  (A least squares analysis can tell you how well
your data fits a straight line.  Find $r$ or $r^{2}$.)  Should it?  If
so, what should the slope be?  How close is the least squares slope to
the theoretical value of the slope from Equation \ref{force}?

\end{enumerate}


\underline{Conclusions:} 
Summarize and evaluate your experiment.  Include mention of likely sources of 
error and how you dealt with them.

\end{document}
