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exam2_solnf09

# exam2_solnf09 - Math 116 Second Midterm Name Instructor 1...

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Math 116 / Exam 2 (November 18, 2009) page 2 1 . [12 points] A window is being rated for underwater pressure tests. The window surface is the region bounded by the x -axis, the line x = 4 and the graph of y = x/ 2, where all lengths are measured in feet. (Note that the density of water is 62.4 pounds per cubic foot.) a . [4 points] Suppose the window is lowered under water so that the top of the window is F feet below the surface. Write an expression that estimates the force due to pressure on a thin horizontal strip of the window h i feet below the top of the window, given that the width of the strip is Δ h . Solution: The force due to hydrostatic pressure is approximately given by the product of the density of water, the depth of the slice, and the area of the slice. A slice of width Δ h that is h i feet below the top of the window has depth F + h i . The pressure along this strip is 62 . 4( F + h i ) pounds per square foot. The width of the strip of window h i feet below the top point is given by w i = 2 h i , and so the area of the strip is 2 h i Δ h . The force due to pressure along the strip is then given by Force = Pressure × Area = 62 . 4( F + h i )(2 h i Δ h ) = 124 . 8 h i ( F + h i h b . [5 points] Set up a definite integral that represents the total force due to pressure on the window if the top of the window is F feet under water. Evaluate this integral in order to determine the total force due to pressure on the window. Show appropriate work to support your answer, and include units in your final answer. Your answer may be in terms of F .
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exam2_solnf09 - Math 116 Second Midterm Name Instructor 1...

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