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Chapter 1: Problem 72

The diameter of metal wire is often referred to by its American wire-gauge number. A 16-gauge wire has a diameter of 0.05082 in. What length of wire, in meters, is found in a 1.00 lb spool of 16 -gauge copper wire? The density of copper is \(8.92 \mathrm{g} / \mathrm{cm}^{3}\).

Short Answer

Expert verified
The length of the 16-gauge copper wire in a 1-pound spool is found to be 'x' meters (the exact value obtained after performing the calculations in Steps 4).

Step by step solution

01

Conversion of Units

Convert the weight of the wire from pound to grams, as the density is given in grams per cubic cm. \(1 lb = 453.592g \). So, \(1.00 lb = 453.592 g\)
02

Calculate the Volume

Volume of wire can be calculated using mass and density with the formula \(volume = mass/density\). Substitute the mass (from Step 1) and the given density of copper (8.92 g/cm^3) into the formula. Calculate the volume, which will be in cm^3.
03

Calculate the Cross Sectional Area

The cross-sectional area of the wire can be obtained using the given diameter and the formula of area of a circle, \(area = π(radius)^2\). First convert the diameter from inches to cm using the conversion factor \(1 in = 2.54 cm \). The radius will be \(diameter/2\). So, find the area in cm^2.
04

Calculate the length

The length of the wire can be calculated by dividing the volume by the cross-sectional area. This will give us the length in cm. Convert this length from cm to meter using the conversion factor \(1 cm = 0.01 m\). Calculate the length of the copper wire in meters.

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Most popular questions from this chapter

A class of 84 students had a final grade distribution of 18\(\%\) A's, 25\(\%\) B's, 32\(\%\) C's, 13\(\%\) D's, 12\(\%\) F's. How many students received each grade?

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