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\centerline{\bf Central Forces\qquad Effective Potentials}
\medskip
\centerline{\it Keep in your notebook}
\bigskip

In the Maple worksheet, {\tt http://physics.oregonstate.edu/ph426/veff.mws}, you
will be examining how various parameters affect the shape of the effective
potential.  Experiment with the different parameters and answer the following
questions:

\begin{enumerate}
\item  As you change $\ell$, $k$, and $\mu$, what happens to the shape of the
effective potential?  Make sure to look at both large $r$, small $r$.  Look at
the equation for $V_{\rm eff}$ as you do this.  Can you see how the equation
predicts these changes?
\vfill

\item  For a given constant value of the energy $E$, where are the classical
turning points?  How do the turning points change as you change the parameters
$\ell$, $k$, and $\mu$?
\vfill

\item  How do the energies and radii of possible circular orbits depend on
$\ell$, $k$, and $\mu$?
\vfill

\item  What happens if you choose a repulsive potential instead of an
attractive one, i.e.\ change the sign of $k$.
\end{enumerate}

\vfill
\leftline{\it by Corinne Manogue}
\leftline{\copyright 2000 Corinne A. Manogue}
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