\begin{problem*}{7.16}
An object of mass $m$ starts from rest and slides a distance $d$ down
a frictionless incline of angle $\theta$.  While sliding, it contacts
an unstressed spring of negligable mass as shown in Figure P7.16.  The
object slides an additional distance $x$ as it is brought momentarily
to rest by the compression of the spring (of force constant $k$).
Find the initial seperation $d$ between the object and the spring.
\end{problem*} % problem 7.16

\begin{solution}
This is just the symbolic form of Chapter 6 Problem 27 from last
week's recitation.

There are no non-conservative forces, so
\begin{align}
 E_i = U_{gi} = mgh &= E_f = U_{sf} = \frac{1}{2} k x^2 \\
 h = (x+d) \cdot \sin\theta &= \frac{k x^2}{mg} \\
 d &= \ans{\frac{k x^2}{mg\sin\theta} - x}
\end{align}
\end{solution}
