Copper Sheath
Trouble with metric conversions? (Physics) HELP PLEASE?
Ok, I’m not really looking for the answer, I already have it. However, I’m very confused when dealing with these conversions… Here’s an example problem:
Copper has a density of about 8.9 g/cm3. The AAWG 14 (American Wire Gauge 14) copper wire used in 15
amp residential wiring circuits is circular in cross section, with a radius of 0.81 mm. Such wire is usually sold
as A14-2 plus ground meaning that there are actually 3 wires (2 insulated, 1 bare) bundled together inside a
vinyl sheath. Thus a 100 foot spool of A14-2 plus ground actually contains a total of 300 feet (91.4 m) of #14
wire. About how many kg of copper are needed to make this much wire?
I’m confused for when finding the volume of the cylinder of the wire. The length is 91.4 meters, but the radius is .81 mm. If you square a decimal, it gets smaller, but that doesn’t make sense because you’re finding area… I tried converting everything to meters, but I messed everything up.. can anybody PLEASE help me?
There are many ways to do this (basically, you can choose when to convert, but it has to happen at some point). If you look at the units, you’ll know it’s right when the units correctly cancel and yield kg.
Your idea of converting everything to meters is a good one, so let’s go with that:
The equation for volume of a cylinder is pi * r * r * l, where r is the radius and l is the length.
Thus, in this case, V = pi * (0.81 mm)(0.81 mm)(91.4 m) = pi * (0.81 * 10^-3 m)(0.81 * 10^-3 m)(91.4 m) = 1.88 * 10^-4 m^3
Since density = mass / volume, the mass is equal to density * volume
That is, mass = (8.9 g/cm^3)(1.88 * 10^-4 m^3)
We can convert the cm into meters, to obtain:
mass = (8.9 g / cm^3)(100*100*100 cm^3 / m^3) (1.88 * 10^-4 m^3) = (8.9 * 10^6 g / m^3)(1.88 * 10^-4 m^3)
That is, the density is 8.9 * 10^6 g / m^3
Then, just multiplying it out gives mass = 1677 g = 1.677 kg
And I suppose in physics, you’d have to round to the appropriate number of sig figs, but I hate sig figs 
Cable Sheath Cutter
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