Suppose you pour water into a container until it reaches a depth of 30.2 cm. Next, you carefully pour in a 14.8 cm thickness of olive oil so that it floats on top of the water. What is the pressure at the bottom of the container? Assume 1000 kg/m3 and 901 kg/m3 for the density of water and the oil, respectively.
pressure=weightwater/area + weightoil/area
= densitywater*g*h*area/A +densityoil*g*h*area/A
= 1000*.302*9.8+901*.148*9.8 Pascals
To determine the pressure at the bottom of the container, we need to consider the pressure contribution from both the water and the olive oil.
The pressure at a certain depth in a fluid is given by the formula:
Pressure = Density × Gravity × Height
First, let's calculate the pressure due to the water. The density of water is 1000 kg/m³, and the height at the bottom is 30.2 cm (or 0.302 m). So, the pressure due to the water is:
Pressure_water = Density_water × Gravity × Height_water
= 1000 kg/m³ × 9.8 m/s² × 0.302 m
Next, let's calculate the pressure due to the olive oil. The density of the olive oil is 901 kg/m³, and the height is 14.8 cm (or 0.148 m). So, the pressure due to the olive oil is:
Pressure_oil = Density_oil × Gravity × Height_oil
= 901 kg/m³ × 9.8 m/s² × 0.148 m
To find the total pressure at the bottom of the container, we add the pressure contributions from both the water and the oil:
Total Pressure = Pressure_water + Pressure_oil
Now, let's calculate the total pressure:
Total Pressure = (1000 kg/m³ × 9.8 m/s² × 0.302 m) + (901 kg/m³ × 9.8 m/s² × 0.148 m)
Simplifying this expression will give us the answer to our question.