A vertical plate is partially submerged in water and has the indicated shape. 12 m- pg 4 m Express the hydrostatic force (in N) against one side of the plate as an integral (let the positive direction be upwards) and evaluate it. (Round your answer to the nearest whole number. Use 9.8 m/s2 for the acceleration due to gravity. Recall that the weight density of water is 1,000 kg/m³.) x ) dy = D N
A vertical plate is partially submerged in water and has the indicated shape. 12 m- pg 4 m Express the hydrostatic force (in N) against one side of the plate as an integral (let the positive direction be upwards) and evaluate it. (Round your answer to the nearest whole number. Use 9.8 m/s2 for the acceleration due to gravity. Recall that the weight density of water is 1,000 kg/m³.) x ) dy = D N
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![**Title: Calculating Hydrostatic Force on a Partially Submerged Plate**
**Problem Statement:**
A vertical plate is partially submerged in water and has the indicated shape, which is a semicircle. The diameter of the semicircle is 12 meters and the radius is 4 meters.
**Objective:**
Express the hydrostatic force (in Newtons) against one side of the plate as an integral (let the positive direction be upwards) and evaluate it. Round your answer to the nearest whole number. Use \(9.8 \, \text{m/s}^2\) for the acceleration due to gravity. Recall that the weight density of water is \(1,000 \, \text{kg/m}^3\).
**Diagram Explanation:**
- The diagram shows a vertical semicircular plate submerged in water.
- The semicircle has a diameter of 12 meters and a radius of 4 meters.
**Integral Formula:**
The hydrostatic force, \( F \), is given by the integral:
\[
F = \int_{0}^{4} p g \, \left( \text{expression of } y \right) \, dy \approx \text{N}
\]
Where:
- \( p \) is the weight density of water (\(1,000 \, \text{kg/m}^3\)).
- \( g \) is the acceleration due to gravity (\(9.8 \, \text{m/s}^2\)).
- \( y \) is the depth of the horizontal strip of the plate.
**Solution:**
Complete the integration to find the total hydrostatic force on the plate. Enter the final calculated value to complete the expression and obtain the result.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffada2e1a-a9b4-4a48-9f42-6eedf920ed38%2Fd70ffb85-b3c5-4449-a89f-a3aa173de7a2%2Fetk2vf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Calculating Hydrostatic Force on a Partially Submerged Plate**
**Problem Statement:**
A vertical plate is partially submerged in water and has the indicated shape, which is a semicircle. The diameter of the semicircle is 12 meters and the radius is 4 meters.
**Objective:**
Express the hydrostatic force (in Newtons) against one side of the plate as an integral (let the positive direction be upwards) and evaluate it. Round your answer to the nearest whole number. Use \(9.8 \, \text{m/s}^2\) for the acceleration due to gravity. Recall that the weight density of water is \(1,000 \, \text{kg/m}^3\).
**Diagram Explanation:**
- The diagram shows a vertical semicircular plate submerged in water.
- The semicircle has a diameter of 12 meters and a radius of 4 meters.
**Integral Formula:**
The hydrostatic force, \( F \), is given by the integral:
\[
F = \int_{0}^{4} p g \, \left( \text{expression of } y \right) \, dy \approx \text{N}
\]
Where:
- \( p \) is the weight density of water (\(1,000 \, \text{kg/m}^3\)).
- \( g \) is the acceleration due to gravity (\(9.8 \, \text{m/s}^2\)).
- \( y \) is the depth of the horizontal strip of the plate.
**Solution:**
Complete the integration to find the total hydrostatic force on the plate. Enter the final calculated value to complete the expression and obtain the result.
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