5. The gate in the figure below is 5 ft wide, is hinged at point B, and rests against a smooth wall at point A. (1) Compute the force on the gate due to water pressure (Must include the magnitude and the center of pressure) (2) Compute the horizontal force exerted by the wall at point A. (3) Compute the reaction force at the hinge B (Must include the magnitude and direction) The image above illustrates a gate submerged in seawater, showcasing several important physical dimensions and parameters for understanding the pressure forces involved. Here's a detailed transcription suitable for an educational context:---**Description:**- The system comprises a gate hinged at point B, which is interacting with seawater on the left side, with a density specified as 64 lb/ft³.- The water level above the hinge is indicated to be 15 ft.- The gate is at an angle represented by $ \theta $, though the exact value is not provided in the diagram.- The gate extends 8 ft from the hinge at B to the wall at A.**Physical Parameters:**- **Seawater density**: 64 lb/ft³- **Vertical water height from free surface to the hinge**: 15 ft- **Length from hinge B to point A where the gate meets the wall**: 8 ft- **Vertical distance from point A to water surface**: 6 ft**Forces:**- **$ P_a $**: Represents the atmospheric pressure force acting directly above the water, affecting all submerged surfaces.- **Gate interaction**: The force exerted by the water, due in part to its depth, which creates torque around the hinge.**Structural Elements:**- **Wall**: A vertical structure on the right side of the gate.- **Hinge (B)**: The pivot point where the gate is attached, allowing it to open or close in response to water pressure and forces.This diagram helps visualize the relationship between the gate, water pressure, and the structure it interacts with, offering a practical application of fluid dynamics and force balance principles.

Answered: The gate in the figure below is 5 ft…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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5. The gate in the figure below is 5 ft wide, is hinged at point B, and rests against a smooth wall at point A. (1) Compute the force on the gate due to water pressure (Must include the magnitude and the center of pressure) (2) Compute the horizontal force exerted by the wall at point A. (3) Compute the reaction force at the hinge B (Must include the magnitude and direction)

The image above illustrates a gate submerged in seawater, showcasing several important physical dimensions and parameters for understanding the pressure forces involved. Here's a detailed transcription suitable for an educational context:

---

**Description:**

- The system comprises a gate hinged at point B, which is interacting with seawater on the left side, with a density specified as 64 lb/ft³.
- The water level above the hinge is indicated to be 15 ft.
- The gate is at an angle represented by $ \theta $, though the exact value is not provided in the diagram.
- The gate extends 8 ft from the hinge at B to the wall at A.

**Physical Parameters:**

- **Seawater density**: 64 lb/ft³
- **Vertical water height from free surface to the hinge**: 15 ft
- **Length from hinge B to point A where the gate meets the wall**: 8 ft
- **Vertical distance from point A to water surface**: 6 ft

**Forces:**

- **$ P_a $**: Represents the atmospheric pressure force acting directly above the water, affecting all submerged surfaces.
- **Gate interaction**: The force exerted by the water, due in part to its depth, which creates torque around the hinge.

**Structural Elements:**

- **Wall**: A vertical structure on the right side of the gate.
- **Hinge (B)**: The pivot point where the gate is attached, allowing it to open or close in response to water pressure and forces.

This diagram helps visualize the relationship between the gate, water pressure, and the structure it interacts with, offering a practical application of fluid dynamics and force balance principles.

Expert Solution

Step 1: Write the given data and what is to find

Given:

$b equals 5 space f t$

To find:

(1) Compute the force on the gate due to water pressure.

(2) Compute the horizontal force exerted by the wall at point A.

(3) Compute the reaction force at the hinge B.

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