\section*{Problem 1 - 031011}

A coil, whose empty mass is \(235 \mathrm{~g}\), is wound with copper wire of 0.70 mm diameter and has a mass of \(4235 \mathrm{~g}\).

How many meters of wire are on the coil? (Density of copper \(\rho=8.93 \mathrm{~g} / \mathrm{cm}^{3}\).)
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The following designations and formulas apply:

\(m_{D}\) mass of copper wire, \(V_{D}\) volume of copper wire, which is a circular cylinder of length \(l_{D}\) with diameter \(d_{D}\), \(\rho_{D}=8.93 \mathrm{~g} / \mathrm{cm}^{3}\) density of copper, \(m_{S}=4235 \mathrm{~g}\) mass of the coil including the wire, \(m_{L}=235 \mathrm{~g}\) empty mass of the coil

\[
\begin{aligned}
m_{D} & =m_{S}-m_{L} \\
V_{D} & =\frac{\pi}{4} d_{D}^{2} \cdot l_{D} \\
\rho_{D} & =\frac{m_{D}}{V_{D}}=\frac{4\left(m_{S}-m_{L}\right)}{\pi d_{D}^{2} l_{D}} \\
l_{D} & =\frac{4\left(m_{S}-m_{L}\right)}{\pi d_{D}^{2} \rho_{D}}=116391.85 \mathrm{~cm} \approx 1.164 \mathrm{~km}
\end{aligned}
\]

There are approximately 1.164 km of copper wire on the coil.