A cube of unknown material is 0.200 m on each side and has a mass of 17.6 kg. It is suspended in a vat of honey (density h = 1.42 x 103 kg/m3) s0 that its top surface is at a depth of 2.00 m below the surface of the honey (see figure-not to scale). What is the absolute pressure on the top surface of the cube due to the honey and the atmosphere? -h = 0 h = 2.0 m
A cube of unknown material is 0.200 m on each side and has a mass of 17.6 kg. It is suspended in a vat of honey (density h = 1.42 x 103 kg/m3) s0 that its top surface is at a depth of 2.00 m below the surface of the honey (see figure-not to scale). What is the absolute pressure on the top surface of the cube due to the honey and the atmosphere? -h = 0 h = 2.0 m
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Fluid Pressure
The term fluid pressure is coined as, the measurement of the force per unit area of a given surface of a closed container. It is a branch of physics that helps to study the properties of fluid under various conditions of force.
Gauge Pressure
Pressure is the physical force acting per unit area on a body; the applied force is perpendicular to the surface of the object per unit area. The air around us at sea level exerts a pressure (atmospheric pressure) of about 14.7 psi but this doesn’t seem to bother anyone as the bodily fluids are constantly pushing outwards with the same force but if one swims down into the ocean a few feet below the surface one can notice the difference, there is increased pressure on the eardrum, this is due to an increase in hydrostatic pressure.
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![### Pressure on a Submerged Object
**Problem Statement:**
A cube of unknown material has dimensions of 0.200 meters on each side and a mass of 17.6 kg. This cube is suspended in a vat filled with honey, with the honey having a density (\(\rho_h\)) of \(1.42 \times 10^3 \text{kg/m}^3\). The cube is positioned so that its top surface is at a depth (h) of 2.0 meters below the surface of the honey. Given these conditions, the task is to determine the absolute pressure on the top surface of the cube. Choose the correct pressure from the following options:
- 144 kPa
- 110 kPa
- 121 kPa
- 129 kPa
**Explanation of the Diagram:**
The diagram illustrates a tank filled with a liquid (honey), in which a cube is submerged. A vertical distance is marked to highlight the depth of the top surface of the cube, denoted as \(h = 0\) at the surface of the honey and \(h = 2.0 \text{m}\) at the depth of the top surface of the cube.
**Solution:**
The absolute pressure exerted on the cube at depth can be calculated using the principle of fluid statics, which accounts for both the atmospheric pressure and the pressure due to the liquid column above the object.
\[
P_{\text{absolute}} = P_{\text{atmospheric}} + \rho_h \cdot g \cdot h
\]
Where:
- \(P_{\text{atmospheric}}\) represents the atmospheric pressure (approximately \(101.3 \text{kPa}\)).
- \(\rho_h\) is the density of the honey, given as \(1.42 \times 10^3 \text{kg/m}^3\).
- \(g\) is the acceleration due to gravity (\(9.81 \text{m/s}^2\)).
- \(h\) is the depth of the top of the cube (\(2.0 \text{m}\)).
Breaking down the formula:
\[
P_{\text{liquid}} = \rho_h \cdot g \cdot h
\]
\[
P_{\text{liquid}} = (1.42 \times 10^3 \text{kg/m}^](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3fc0f41c-1d8b-41a4-aee9-3a82e03a5afd%2F55609b79-ae63-48a4-838a-91772758768d%2Fzb9wgh.png&w=3840&q=75)
Transcribed Image Text:### Pressure on a Submerged Object
**Problem Statement:**
A cube of unknown material has dimensions of 0.200 meters on each side and a mass of 17.6 kg. This cube is suspended in a vat filled with honey, with the honey having a density (\(\rho_h\)) of \(1.42 \times 10^3 \text{kg/m}^3\). The cube is positioned so that its top surface is at a depth (h) of 2.0 meters below the surface of the honey. Given these conditions, the task is to determine the absolute pressure on the top surface of the cube. Choose the correct pressure from the following options:
- 144 kPa
- 110 kPa
- 121 kPa
- 129 kPa
**Explanation of the Diagram:**
The diagram illustrates a tank filled with a liquid (honey), in which a cube is submerged. A vertical distance is marked to highlight the depth of the top surface of the cube, denoted as \(h = 0\) at the surface of the honey and \(h = 2.0 \text{m}\) at the depth of the top surface of the cube.
**Solution:**
The absolute pressure exerted on the cube at depth can be calculated using the principle of fluid statics, which accounts for both the atmospheric pressure and the pressure due to the liquid column above the object.
\[
P_{\text{absolute}} = P_{\text{atmospheric}} + \rho_h \cdot g \cdot h
\]
Where:
- \(P_{\text{atmospheric}}\) represents the atmospheric pressure (approximately \(101.3 \text{kPa}\)).
- \(\rho_h\) is the density of the honey, given as \(1.42 \times 10^3 \text{kg/m}^3\).
- \(g\) is the acceleration due to gravity (\(9.81 \text{m/s}^2\)).
- \(h\) is the depth of the top of the cube (\(2.0 \text{m}\)).
Breaking down the formula:
\[
P_{\text{liquid}} = \rho_h \cdot g \cdot h
\]
\[
P_{\text{liquid}} = (1.42 \times 10^3 \text{kg/m}^
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