\section{M-3~~Static Forces and Moments}

\noindent
OBJECTIVE: 
To check experimentally the conditions for equilibrium of a rigid body. \\

\noindent 
APPARATUS: 
\begin{enumerate}
\item[] \latex{\vspace*{-.05in}}Model of rigid derrick, slotted masses and weight hangers,
knife edge (mounted in wall bracket), vernier caliper, single pan balance. \\
 \end{enumerate}\latex{\vspace*{-.05in}}

\noindent INTRODUCTION:
\begin{enumerate}
\item[] \latex{\vspace*{-.05in}} Equilibrium requires that the 
net linear acceleration and the net angular acceleration be zero.  
Hence $ \sum \vec{F}_{\mbox{\small ext}} = 0  $
and  $ \sum \vec{\tau}_{\mbox{\small ext}} = 0  $.  
We treat the rigid derrick as a two dimensional structure
so the vector equations become:  
$ \sum \vec{F}_{x} = 0 $, $ \sum \vec{F}_y = 0 $
and $ \sum \vec{\tau}= 0 $. 
The choice of the perpendicular axis about which one computes torques is 
arbitrary so in part 4 below we choose an axis which simplifies
calculations. 
 \end{enumerate}\latex{\vspace*{-.05in}}
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<HR> <P>
     <h3><u><font color="ff0000"> Pre-lab Quiz </font></u></h3></a>
<ul><ul>
    <li><a target="_blank" href="../js/q207_m03.html">Expt. M03 Quiz</a>

</ul></ul>
</P>
<HR>
\end{rawhtml}

\noindent SUGGESTED PROCEDURES:

\latex{\hspace*{.18in}\parbox[b]{2.5in}}{
\begin{enumerate}
\item Place a load of about 2 kg for $m_2$.
\item Determine experimentally the force $m_3$ to hold
the derrick in 
equilibrium with the top member level.  Since this is 
an unstable equilibrium, 
adjust $m_3$ so that the derrick will fall either way 
when displaced equally from equilibrium.  
To find the uncertainty in $m_3$ increase
or decrease $m_3$ until you know the smallest force $m_3$ 
which is definitely too large and the largest which 
is definitely too small.  \end{enumerate}} 
\latex{\hspace*{.05in} \includegraphics[width=3.1in]{figs/l103/m03-6r.eps} }
\html{ \begin{figure}[h]
\includegraphics[width=2.8in]{figs/l103/m03-6r.eps} 
       \end{figure} } 

\begin{enumerate} \item[] \latex{\vspace*{-.2in}}\begin{enumerate}
\item[3.] Weigh the derrick (use single pan balance) and find the
horizontal distance between the center of the stirrup and the vertical line 
through the center of gravity (c.g.) of the derrick. (Use the knife edge
mounted in a wall bracket for locating the c.g.)
\item[4.] Calculate how accurately the $ \sum \vec{\tau}_{\mbox{\small ext}} = 0  $ 
condition is 
satisfied about the point where the lower stirrup supports the derrick.  
Note: distance from rotation axis must include stirrup axle radius
(use vernier caliper).
\item[5.]
Calculate the force $\vec{F}$ exerted by the stirrup on the derrick.
\item[6.]
Choose an axis that is {\em not} on the line of action of any force and  
calculate how closely  
is satisfied about that axis. Is the discrepancy reasonable?   
%Make your answer as  \verb|\htmlref| \htmlref{quantitative}{}{}{sec:M2} as you can.  
Make your answer as  \hyperref{quantitative}{quantitative (refer
to Section }{)}{error_top} as you can.  
(Include the uncertainty in $\vec{F}$ and any other measurements). 
\end{enumerate}
\end{enumerate}

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