Show that the total force on a rectangular dam due to the water behind it increases with the square of the water depth. In particular, show that this force is given by F = pgh2 L/2, where is the density of water, is its depth at the dam, and is the length of the dam. You may assume the face of the dam is vertical. (Hint: Calculate the average pressure exerted and multiply this by the area in contact with the water.

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