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.

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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.
### 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
Transcribed Image Text:### 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
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