Buoyant force question: A cylindrically shaped object is placed into a glass of water as shown in the image below. If the radius of the cylinder is 0.2 meter and height of the cylinder is 0.50 meters, what is the magnitude of the buoyant force the object experiences. Give answer in Newton’s.
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.
![### Understanding Buoyant Force in Fluids
In the given image, we see a diagram illustrating the concept of buoyant force acting on an object submerged in a fluid. Here's a detailed explanation:
#### Explanation of Diagram
The diagram shows a cross-sectional view of a cylindrical object (like a block) submerged in a liquid within a container. Several labels and measurements are indicated in the diagram.
1. **h₁ and h₂**: These labels represent the heights of the liquid column at two different points.
- \( h_1 \) is the height from the top surface of the liquid to the upper surface of the submerged object.
- \( h_2 \) is the height from the top surface of the liquid to the bottom surface of the submerged object.
2. **Δh**: The difference in height (\( Δh \)) between \( h_1 \) and \( h_2 \). Mathematically, \( Δh = h_2 - h_1 \).
3. **F₁ and F₂**: These are forces acting on the object due to water pressure.
- \( F₁ \) is the downward force exerted by the fluid pressure at the depth \( h_1 \).
- \( F₂ \) is the upward force exerted by the fluid pressure at the depth \( h_2 \).
4. **ρF**: This symbol represents the density of the fluid.
#### Key Concepts
- **Buoyant Force**: The net upward force exerted by a fluid on a submerged object. This force is what makes objects float or sink.
- **Pressure Difference**: The buoyant force can be calculated using the difference in pressures at the two depths (\( h_1 \) and \( h_2 \)).
- **Force Calculation**: The forces due to pressure are given by \( F_1 = \rho_F \cdot g \cdot h_1 \cdot A \) and \( F_2 = \rho_F \cdot g \cdot h_2 \cdot A \), where \( g \) is the gravitational acceleration, and \( A \) is the area of the object's surface in contact with the fluid.
### Problem to Solve
Using the given values \( h_1 \), \( h_2 \), and \( ρF \), the problem is to calculate the magnitude of the buoyant](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa1a9ff04-dc4c-40e7-a38e-e4d1f42a10d9%2Fff1cc1ec-5fe3-4f38-a1b3-c7d06de4ccf6%2Fxpmui7d_processed.jpeg&w=3840&q=75)
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