An aluminum wire is hung between two towers and has a length of 175 m. A current of 125 A exists in the wire, and the potential difference between the ends of the wire is 0.300 V. The density of aluminum is 2700 kg/m3. Find the mass of the wire
Use the current and voltage to determine that the resistance is R = V/I = 0.0024 ohms
Then use the resistivity of aluminum (which you will need to look up), together with the resistance R and the length L, to determine the cross sectional area, A.
The volume of the wire is L*A. Multiply that by the density for the mass.
A=0.00206
To find the mass of the aluminum wire, we need to know the volume of the wire and its density.
Step 1: Calculate the cross-sectional area of the wire.
The cross-sectional area of the wire can be calculated using the formula:
Area = current / (density * length * potential difference)
Area = 125 A / (2700 kg/m^3 * 175 m * 0.300 V)
Area = 125 A / (141750 kg*m^2/(s^3*A^2))
Area = 0.0008789 m^2
Step 2: Calculate the volume of the wire using the cross-sectional area.
The volume of the wire can be calculated using the formula:
Volume = area * length
Volume = 0.0008789 m^2 * 175 m
Volume = 0.1536 m^3
Step 3: Calculate the mass of the wire using the volume and density.
Mass = volume * density
Mass = 0.1536 m^3 * 2700 kg/m^3
Mass = 414.72 kg
Therefore, the mass of the aluminum wire is 414.72 kg.