\documentclass[12pt]{book}
\usepackage{epsfig}

\input{iliheader}



\begin{document}


{\large Names:}
\bigskip

\centerline{\bf \Large How do forces combine?}

\bigskip

The question we want to answer in this exercise is how to add
forces in order to get a net force of zero and no acceleration.

Equipment:  The instructor will demonstrate the force table
which we will use in the following activity.

\begin{enumerate}
\item  For each of the  following three scenarios, make an
experienced guess at which angle you would hang an object to
balance the ring.  What should the mass of that object be? 
Sketch in your answer and verify by pulling the ring that it is
balanced.
\vfill

\psfig{figure=Patsy:Documents:pictures:force.table.1.eps,
height=1.72in,width=1.72in}


\vfill

\psfig{figure=Patsy:Documents:pictures:force.table.2.eps,
height=1.72in,width=1.72in}
\vfill

\psfig{figure=Patsy:Documents:pictures:force.table.3.eps,
height=1.72in,width=1.72in}
\vfill

\item Did increasing the mass of the hanging objects in the $x$
direction change the mass of the hanging object needed in the
$y$ direction?  
\vfill

\clearpage

\item For the  following scenarios, make an reasoned 
guess (based on your answers from the last page) at which angle
you would hang an object to balance the ring.  What should the
mass of that object be?  Hint:  if your could hang {\bf two }
weights in order to balance, where would you hang them and how
big would they be?  How can you combine those two weights into
an equivalent single weight?
 

\vfill

\psfig{figure=Patsy:Documents:pictures:force.table.4.eps,
height=1.72in,width=1.72in}
\vfill

\psfig{figure=Patsy:Documents:pictures:force.table.5.eps,
height=1.72in,width=1.72in}
\vfill


\clearpage

\item Explicitly as you can, describe how you have calculated the
necessary mass and angle needed to balance the given objects.
Be as general as possible.
\vfill

\item Use the method that you just described to find the angle
and mass of a balancing object in the following case:

\psfig{figure=Patsy:Documents:pictures:force.table.6.eps,
height=1.72in,width=1.72in}
 

\vfill

\end{enumerate}

\end{document}

The equipment is a force table (a heavy round table with angles
marked on the edge), moveable pulleys that can attach anywhere
on the edge of the table, strings that hang over the pulleys,
and objects with known masses to hang from the strings.  There
is also a pin at the center of the force table that will hold
all the objects still as long as it is in place.

Instructions: For each of the following situations, predict at
what angle at what mass an object must have in order to balance
the other objects shown with the given masses and locations. 
Then hang the object of the predicted mass and angle, pull the
center pin and see if it does balance.  

If it doesn't balance, reconsider your theory for calculating
the required mass and angle.  Consult an instructor if you are
having troubles.
 
Please show your work, including calculations that didn't give
a zero net force.