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\title{Math 1b. Applications to Physics and Engineering (Work)}

\date{Spring 2006}

\begin{document}

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\begin{enumerate}

\item
{\em Hooke's Law\/} tells us that the force created by a spring when it is stretched or compressed is proportional to the distance the spring is stretched or compressed,
$$
F(x) = kx.
$$
If a spring stretched 1 foot beyond its natural length requires 10 lbs of force, how much work is done stretching the spring?

\vfill

\clearpage

\item
Is it more work to raise a 70 lb bucket from a 50 ft well or a 50 lb bucket from a 70 ft well if the rope weighs 0.25 lb per foot?

\vfill

\item
A circular swimming pool has a diameter of 24 ft, the sides are 5 ft
high, and the depth of the water is 4 ft.  If the density of water is 62.5~lb/ft$^3$, how much work is required to pump all of the water out over the side?

\vfill

\end{enumerate}


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