\begin{problem*}{1.11}
Kinetic energy $K$ (Chapter 7) has dimensions
$\bareU{kg$\cdot$m$^2$/s$^2$}$.  It can be written in terms of the
momentum $p$ (Chapter 9) and mass $m$ as
\begin{equation}
K = \frac{p^2}{2m}
\end{equation}
\Part{a} Determine the proper units for momentum using dimensional
analysis.  \Part{b} The unit of force is the newton $\bareU{N}$, where
$1\U{N} = 1\U{kg$\cdot$m/s$^2$}$.  What are the units of momentum $p$
in terms of a newton and another fundamental SI unit?
\end{problem*} % Probem 1.11

\begin{solution}
\Part{a}
\begin{align}
  K &= \frac{p^2}{2m} \\
  \bareU{kg$\cdot$m$^2$/s$^2$} &= \frac{p^2}{\bareU{kg}} \\
  p^2 &= \frac{\bareU{kg$^2\cdot$m$^2$}}{\bareU{s$^2$}} \\
  p &= \ans{\bareU{kg$\cdot$m/s}}
\end{align}

\Part{b}
\begin{equation}
  p = \bareU{kg$\cdot$m/s} = \bareU{kg$\cdot$m/s$^2$}\cdot\bareU{s}
    = \ans{\bareU{N$\cdot$s}}
\end{equation}
\end{solution}
