Answer
$$0.661 \space \Omega$$
Work Step by Step
1. We need to find the length of the cable, then calculat the overall resistance.
- In order to find the length, we can use the density of copper, to find the total volume (since we know the mass), then we assume a cylinder shape, and use the radius and the volume to calculate it.
2.
$V_{cylinder} = \pi r^2 h$
$\frac V{\pi r^2} = h$
Now, using the density equation:
$density = \frac{m}{V} \longrightarrow V = \frac m {density}$
Thus:
$\frac {m/density}{\pi r^2} = h$
$\frac {m}{\pi r^2 (density)} = h$
If we multiply the resistance per km by the length of the cable, we will get the overall resistance:
$h \times resistance \space per \space km = overall \space resistance$
$\frac {m}{\pi r^2 (density)} \times resistance \space per \space km = overall \space resistance$
3. Convert the given data to match their units.
$m = 24.0 \space kg \times \frac{1000 \space g}{1 \space kg} = 2.40 \times 10^4 \space g$
$r = 1.63 \space mm \times \frac{1 \space cm}{10 \space mm} = 0.163 \space cm$
$2.061 \space \Omega/km \times \frac{1 \space km}{10^3 \space m} \times \frac{1 \space m}{100 \space cm} = 2.061 \times 10^{-5} \Omega/cm$
4. Calculate it:
$\frac {2.40 \times 10^4 \space g}{\pi (0.163 \space cm)^2 (8.96 \space g/cm^3)} \times 2.061 \times 10^{-5} \space \Omega/cm = 0.661 \space \Omega$
