Give the answer as a number and in the requested units, rounded to  two
  significant figures. If needed, use a dot / period as a decimal separator.

You were so inspired by the electronics course that you have decided to build your own lab in your basement. You have a coil which has a mass of  0.6000000000000001
  kg. With a Vernier caliper you measure that the diameter of the wire is 0.1 mm. From a data book you check that the density of copper is 8900 kg/m 3
 . Calculate the length of the wire so you can be sure it is long enough for the wiring.
How long is the wire (m)?


To calculate the length of the copper wire, we will first need to determine the volume of the wire based on its mass and the density of copper. From the volume and the diameter, we can find the length of the wire.

### Given dataTo calculate the length of the copper wire, we will first need to determine the volume of the wire based on its mass and the density of copper. From the volume and the diameter, we can find the length of the wire.

### Given 
- Mass of the wire: \( m = 0.600 \, \text{kg} \)
- Density of copper: \( \rho = 8900 \, \text{kg/m}^3 \)
- Diameter of the wire: \( d = 0.1 \, \text{mm} = 0.0001 \, \text{m} \)

### Step 1: Calculate the volume of the wire
Using the formula for mass and density:

\[
V = \frac{m}{\rho}
\]

Substitute the given values:

\[
V = \frac{0.600}{8900} = 6.74 \times 10^{-5} \, \text{m}^3
\]

### Step 2: Calculate the cross-sectional area of the wire
The cross-sectional area of the wire, assuming it's cylindrical, is given by the formula for the area of a circle:

\[
A = \pi \left(\frac{d}{2}\right)^2
\]

Substitute \( d = 0.0001 \, \text{m} \):

\[
A = \pi \left(\frac{0.0001}{2}\right)^2 = 7.854 \times 10^{-9} \, \text{m}^2
\]

### Step 3: Calculate the length of the wire
The length of the wire \( L \) is given by:

\[
L = \frac{V}{A}
\]

Substitute the values for \( V \) and \( A \):

\[
L = \frac{6.74 \times 10^{-5}}{7.854 \times 10^{-9}} = 8585.88 \, \text{m}
\]

### Step 4: Round to two significant figures

\[
L \approx 8600 \, \text{m}
\]

### Final answer:
The length of the wire is approximately **8600 meters**.

Would you like further details or have any questions?

Here are some related questions:
1. How does changing the wire diameter affect the length for the same mass?
2. What is the relationship between wire density and length for a fixed mass?
3. How would using a different material (e.g., aluminum) impact the wire length?
4. What is the impact of measurement precision on calculated wire length?
5. How does the cross-sectional shape of a wire affect its properties?

**Tip**: To improve accuracy, always ensure measurements are taken with precision instruments like Vernier calipers, especially for small dimensions like wire diameters.

You were so inspired by the electronics course that you have decided to build your own lab in your basement. You have a coil which has a mass of 0.6000000000000001 kg. With a Vernier caliper you measure that the diameter of the wire is 0.1 mm. From a data book you check that the density of copper is 8900 kg/m^3. Calculate the length of the wire so you can be sure it is long enough for the wiring. How long is the wire (m)?

Learn how to calculate the length of a copper wire using its mass (0.6 kg), diameter (0.1 mm), and the density of copper (8900 kg/m^3). This problem explores concepts in geometry and physics, including volume, density, and cross-sectional area, suitable for Grades 10-12.

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