\input{labpreamble}
\begin{document}

\subsubsection*{PHSX 221L\hfill Forces as Vectors\hfill Name:\underline{\hspace*{2in}}}

% \underline{Title:} Forces as Vectors

\underline{Object:} To study how simultaneous forces 
combine together to produce a resultant force.

\underline{Introduction:} A basic concept in the study of physics is 
that forces can be represented theoretically by vectors.  This means 
that when several forces act simultaneously on the same object, they 
combine together into one resultant force.  This resultant force can 
be calculated theoretically using the rules of vector addition by 
either of the following methods:
\begin{enumerate}
\item \underline{By diagram (graphically):} Several vectors 
representing concurrent forces can be added by diagramming the vectors 
head-to-tail using rulers and protractors to measure the magnitude and 
direction of each vector.  The resultant vector is found by drawing 
an arrow from the tail of the first vector in the series to the head 
of the last.

\item \underline{By component (numerically):} The resultant of 
several concurrent vectors can also be found by breaking each vector 
up into its x- and y-components.  

\begin{equation}
x=r\cos\theta\ \ \ \ \ \ \ y=r\sin\theta
\end{equation}

Corresponding components of the 
several forces are then added together separately to obtain the x- and 
y-components of the resultant.  The magnitude $r$ and direction 
$\theta$ of this resultant vector are given by:
\end{enumerate}

\begin{equation}
r = \sqrt{x^{2}+y^{2}}\ \ \ \ \ \ \theta = \arctan{\frac{y}{x}}
\end{equation}

\noindent
\underline{Procedure:} 
Using a force table, three forces will be set up as described in the 
following list.  A fourth force will then be determined by the student 
and adjusted so as to balance the resultant of the other three.  This 
balancing force, which you will find by trial and error, is the 
reverse of the resultant force you are looking for.

\begin{center}
\begin{tabular}{|c|c|c|c|}\hline
	Trial & Force A               & Force B                & Force 	C               \\ \hline
	1     & 150 g at 0$^{\rm o}$  & 130 g at 35$^{\rm o}$  & 150 g at 110$^{\rm o}$ \\
	2     & 110 g at 20$^{\rm o}$ & 110 g at -75$^{\rm o}$ & 150 g at 120$^{\rm o}$ \\ \hline
\end{tabular}
\end{center}

\noindent
\underline{Theoretical Results:} 

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

\item What was the magnitude and direction of each resultant force 
obtained by diagram (graphically)?

\item What was the magnitude and direction of each resultant force 
obtained by the component method (numerically)?

\end{enumerate}

\noindent
\underline{Experimental Results:} 
\vspace{.65in}

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

\item Do your results show that forces combine together the same way 
that vectors do?  That is, do forces really behave as vectors?

\item Calculate the percent difference between theory and experiment 
for the resultant of each trial.

\end{enumerate}


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

\item What is your evaluation of this experiment?

\item What are some possible sources of error?

\item What did you do to reduce your error?

\end{enumerate}


\end{document}
