$\"\"$

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A vertical plate is submerged in water as indicated in the figure.

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Find the hydrostatic force on one end of the aquarium:

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$\"\"$ .

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$\"\"$ , where $\"\"$ is the depth of the aquarium.

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At any time, the plate is $\"\"$ ft depth from the surface.

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Thus, $\"\"$ .

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Strip area of one side of the plate is $\"\"$ , as depth increases then $\"\"$ also increases.

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Thus, consider width as $\"\"$ .

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Find the length of the strip.

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Redraw the figure.

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$\"\"$

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Radius of the semi circle is $\"\"$ .

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If $\"\"$ is the length of the horizontal strip.

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Using Pythagoras theorem:

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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Length of the strip $\"\"$ .

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Area of the strip is $\"\"$ .

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Force acting on that strip is $\"\"$ .

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$\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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Hydrostatic force as a Riemann sum $\"\"$ .

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Set up the integral $\"\"$ .

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Weight density of the water $\"\"$ lb/ft³.

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$\"\"$

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$\"\"$

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$\"\"$

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Substitute $\"\"$ .

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$\"\"$

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$\"\"$ .

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When $\"\"$ , $\"\"$ .

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When $\"\"$ , $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Hydrostatic force on one end of the aquarium is $\"\"$ .

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$\"\"$

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Hydrostatic force on one end of the aquarium is $\"\"$ .