Aluminum wire is sold on 10 pound spools (100.00 lbs). The diameter of a 12 gauge aluminum wire sold on these spools is 0.0808 inches. If the density of the aluminum is 2.70 g/ cm3. Wat is the length ( in meters) of the wire on the 10 pound spool of 12 gauge aluminum wire?
How do i go about starting this problem
To find the length of the wire on the 10 pound spool, we need to use the formula:
Length = (Weight / Area) / Density
Let's break down the steps to solve this problem:
Step 1: Convert the weight of the spool from pounds to grams.
Since the weight of the spool is given as 100.00 lbs, we need to convert it to grams. The conversion factor is 1 lb = 453.59 grams.
Weight (in grams) = 100.00 lbs * 453.59 g/lb = 45359 grams.
Step 2: Calculate the cross-sectional area of the wire.
The wire is described as 12 gauge with a diameter of 0.0808 inches. The gauge number of a wire represents its thickness, and for a 12 gauge wire, the radius is 0.0808 inches divided by 2.
Radius = 0.0808 inches / 2 = 0.0404 inches.
Next, we convert the radius to centimeters (1 inch = 2.54 cm).
Radius (in cm) = 0.0404 inches * 2.54 cm/inch = 0.1026 cm.
We can then calculate the cross-sectional area using the formula:
Area = π * radius^2.
Area = 3.1416 * (0.1026 cm)^2 = 0.0331 cm^2.
Step 3: Convert the cross-sectional area to square meters.
To convert the cross-sectional area from square centimeters to square meters, we divide by 10,000 (1 m^2 = 10,000 cm^2).
Area (in m^2) = 0.0331 cm^2 / 10,000 = 0.00000331 m^2.
Step 4: Calculate the length of the wire.
Now we can substitute the values into the formula:
Length = (Weight / Area) / Density.
Length = (45359 grams / 0.00000331 m^2) / 2.70 g/cm^3.
Step 5: Convert the result to meters.
Since the density is given in grams per cubic centimeter (g/cm^3), and we want the length in meters, we need to convert the units.
Length (in meters) = (45359 g / 0.00000331 m^2) / (2.70 g/cm^3 * 1000 cm/m).
After performing the calculation, you will have the length of the 12 gauge aluminum wire on the 10 pound spool in meters.
To solve this problem, you can use the formula to calculate the length of a wire, which is given by:
Length = (mass / density) / (π × radius^2)
Here's how you can proceed with the calculations step-by-step:
Step 1: Convert the weight of the spool from pounds to grams.
- 1 pound = 453.592 grams
- Therefore, the weight of the spool is 100.00 lbs × 453.592 g/lb = 45359.2 g
Step 2: Calculate the volume of the wire on the spool.
- The formula for the volume of a cylinder is: volume = π × radius^2 × height
- Since the wire is wound on a spool, we need to determine the height.
- The diameter of the wire is given as 0.0808 inches, which means the radius is half of this value.
- Radius = 0.0808 inches / 2 = 0.0404 inches = 0.0404 inches × 2.54 cm/inch = 0.102616 cm
- The height is unknown, but we will solve for it using the weight and density of aluminum.
Step 3: Solve for the height in the volume formula.
- volume = π × radius^2 × height
- height = volume / (π × radius^2)
- The volume can be calculated as mass/density: volume = 45359.2 g / 2.70 g/cm^3 = 16829.04 cm^3
- height = 16829.04 cm^3 / (π × (0.102616 cm)^2)
Step 4: Calculate the length of the wire.
- Finally, to get the length, divide the height by the diameter of the wire (0.0808 inches) and convert it to meters:
- Multiply the height in cm by 0.393701 to convert it to inches: height = height (cm) × 0.393701 in/cm
- height (inches) = height (cm) × 0.393701 in/cm
- length = height (inches) / 0.0808 inches
Once you solve for the height and length of the wire, you should have the final answer in meters.