A cube of aluminum is at a depth of 1.00 km under seawater whose density is 1,025 kg/m3. Atmospheric pressure is 101.3 kPa. What is the volume stress on the cube? Use g = 9.80 m/s2.
Question
A cube of aluminum is at a depth of 1.00 km under seawater whose density is 1,025 kg/m3. Atmospheric pressure is 101.3 kPa. What is the volume stress on the cube? Use g = 9.80 m/s2.
Solution
To calculate the volume stress on the cube, we first need to calculate the pressure at the depth of 1.00 km under seawater.
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Calculate the pressure due to the water column above the cube:
Pressure due to water column = Density of water * g * height = 1025 kg/m^3 * 9.80 m/s^2 * 1000 m = 10,045,000 Pa or 10.045 MPa
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Add the atmospheric pressure to the pressure due to the water column to get the total pressure at the depth of the cube:
Total pressure = Pressure due to water column + Atmospheric pressure = 10.045 MPa + 101.3 kPa = 10.1463 MPa
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The volume stress on the cube is equal to the total pressure at the depth of the cube because stress is defined as force per unit area, and pressure is a type of stress that is exerted uniformly in all directions.
So, the volume stress on the cube = 10.1463 MPa.
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