An equilateral triangular plate with sides 10 m is submerged vertically in water so that the base is even with the surface. Express the hydrostatic force against one side of the plate as an integral 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 maa density of water is 1000 kg/m3.) „5/3 pg dx
An equilateral triangular plate with sides 10 m is submerged vertically in water so that the base is even with the surface. Express the hydrostatic force against one side of the plate as an integral 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 maa density of water is 1000 kg/m3.) „5/3 pg dx
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![**Problem Statement:**
An equilateral triangular plate with sides \(10 \, \text{m}\) is submerged vertically in water so that the base is even with the surface. Express the hydrostatic force against one side of the plate as an integral 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 mass density of water is \(1000 \, \text{kg/m}^3\).)
**Integral Representation of Hydrostatic Force:**
\[
pg \int_{0}^{5\sqrt{3}} ( \text{[Expression Inside Integral]} ) \, dx \approx \text{[Numeric Answer]} \, \text{N}
\]
**Diagram Description:**
The diagram illustrates an equilateral triangle submerged vertically in water, with the base of the triangle aligned with the water surface. The submerged portion of the triangle is shaded to highlight the section of interest for calculating hydrostatic force.
**Explanation:**
- The integral setup involves calculating the force exerted by the water on one side of the plate.
- \(pg\) represents the product of the density of water (\(1000 \, \text{kg/m}^3\)) and the acceleration due to gravity (\(9.8 \, \text{m/s}^2\)).
- The limits from \(0\) to \(5\sqrt{3}\) indicate the vertical span of the triangle submerged in the water, which corresponds to the height of the equilateral triangle based on its geometry.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffb3b57c0-2cf0-470e-abfa-e04e0f443007%2F0b177141-55ca-44fe-8483-e33cb97aed62%2F03cvhu_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
An equilateral triangular plate with sides \(10 \, \text{m}\) is submerged vertically in water so that the base is even with the surface. Express the hydrostatic force against one side of the plate as an integral 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 mass density of water is \(1000 \, \text{kg/m}^3\).)
**Integral Representation of Hydrostatic Force:**
\[
pg \int_{0}^{5\sqrt{3}} ( \text{[Expression Inside Integral]} ) \, dx \approx \text{[Numeric Answer]} \, \text{N}
\]
**Diagram Description:**
The diagram illustrates an equilateral triangle submerged vertically in water, with the base of the triangle aligned with the water surface. The submerged portion of the triangle is shaded to highlight the section of interest for calculating hydrostatic force.
**Explanation:**
- The integral setup involves calculating the force exerted by the water on one side of the plate.
- \(pg\) represents the product of the density of water (\(1000 \, \text{kg/m}^3\)) and the acceleration due to gravity (\(9.8 \, \text{m/s}^2\)).
- The limits from \(0\) to \(5\sqrt{3}\) indicate the vertical span of the triangle submerged in the water, which corresponds to the height of the equilateral triangle based on its geometry.
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