\input{labpreamble}
\begin{document}
\subsubsection*{PHSX 101L\hfill Experiment 6\hfill Name:\underline{\hspace*{2in}}}

\underline{Title:} Centripetal force

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

\underline{Theory:} An object traveling at constant speed in a 
circular path experiences an acceleration which is directed toward the 
center of the circle and has a magnitude given by the formula
\begin{equation}\label{accel}
a_{c} = \frac{v^{2}}{r}
\end{equation}
where $v$ is the speed and $r$ is the radius.

The speed $v$ can be computed from $v = 2\pi r/T$ where $T$ is the 
time for one revolution (known as the period).  This 
acceleration, since it is directed toward the center of the circular 
path, is called centripetal (or center-seeking) acceleration.

By Newton's 2nd Law it is known that a force accompanies
any acceleration.  Thus, a centripetal force must be applied to the 
rotating body in order for it to experience a centripetal 
acceleration.  This force is calculated from Newton's 2nd Law as:
\begin{equation}
\boldsymbol{F}_{c} = m\boldsymbol{a}_{c}
\end{equation}
where $m$ is the mass of the rotating body and $\boldsymbol{a}_{c}$ is the 
centripetal acceleration as computed from the above formula.

\underline{Procedure:} \ The experimental apparatus consists of a 
variable speed rotator which rotates a known mass attached to the 
end of a spring.  As the mass rotates the spring stretches and exerts 
the required centripetal force on the mass.

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

\item\label{weights} Measure the tension in the spring by removing the
spring and mass assembly from the rotator and hanging it from a
support.  With the spring tension adjusted to the desired value,
weights are hung on the spring until it stretches out to the point
where it activates the trigger/pointer.  The spring tension force
(which is the centripetal force when rotating) is then equal to the
combined weights of all the masses hanging on it.

\item The spring and mass assembly is then replaced in the rotator and 
set into rotational motion.  The rotational speed is adjusted until 
the spring stretches out and activates the trigger/pointer.

\item Measure the number of revolutions in a given time.  Also measure 
the radius of the path, the mass of the rotating body and elapsed time.

\item The centripetal force is then calculated using the above 
theoretical formula, and the result is compared with the spring 
tension force found in step \ref{weights}.

\item Now adjust the spring tension to a different value and repeat 
the above procedure.  This will be trial 2.
\vspace{-.2in}

\end{enumerate}

\underline{Apparatus:} \ \ Make a drawing of the rotator and the 
spring-mass assembly.

\vspace{1.1in}

\underline{Results:} \hfill Trial 1 \hspace{.9in} Trial 2 \hspace{.2in}

Total mass of hanging objects: 
\hfill \underline{\hspace{1in}}\hspace{.5in}\underline{\hspace{1in}}

Tension force in spring (weight of hanging objects): 
\hfill \underline{\hspace{1in}}\hspace{.5in}\underline{\hspace{1in}}

Number of revolutions: 
\hfill \underline{\hspace{1in}}\hspace{.5in}\underline{\hspace{1in}}

Elapsed time (total): 
\hfill \underline{\hspace{1in}}\hspace{.5in}\underline{\hspace{1in}}

Radius of path (to center of mass): 
\hfill \underline{\hspace{1in}}\hspace{.5in}\underline{\hspace{1in}}

Circumference of path ($2\pi r$): 
\hfill \underline{\hspace{1in}}\hspace{.5in}\underline{\hspace{1in}}

Speed of rotating body: 
\hfill \underline{\hspace{1in}}\hspace{.5in}\underline{\hspace{1in}}

Acceleration of rotating body (use equation \ref{accel}): 
\hfill \underline{\hspace{1in}}\hspace{.5in}\underline{\hspace{1in}}

Mass of rotating body: 
\hfill \underline{\hspace{1in}}\hspace{.5in}\underline{\hspace{1in}}

Centripetal force calculated from $\boldsymbol{F}_{c} = m\boldsymbol{a}_{c}$: 
\hfill \underline{\hspace{1in}}\hspace{.5in}\underline{\hspace{1in}}

Percent difference between theoretical centripetal force and 
\\ measured spring tension: 
\hfill \underline{\hspace{1in}}\hspace{.5in}\underline{\hspace{1in}}

\vspace{.1in}

\underline{Questions:} \ \ Suppose you tied a 1.5 kg rock to the 
end of a cord 2 m long and swung it around you in a horizontal circle 
so that it made one revolution every 2 seconds.
\vspace{-.2in}
\begin{enumerate}
\item Compute the speed of the rotating rock.
\vspace{.25in}
\item Compute the tension force in the cord.
\vspace{.25in}
\end{enumerate}

\underline{Conclusions:} 

\end{document}
