Question: 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 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 = (gh2 L / 2, where ( is the density of water, h is its depth at the dam, and L is the length of the dam. You may assume the face of the dam is vertical.

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