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 $F = ρ g h^{2} L /2$ , where $ρ$ 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. (Hint: Calculate the average pressure exerted and multiply this by the area in contact with the water.

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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 = ρ g h^{2} L /2

, where

ρ

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. (Hint: Calculate the average pressure exerted and multiply this by the area in contact with the water.

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Question Text	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 $F = ρ g h^{2} L /2$ , where $ρ$ 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. (Hint: Calculate the average pressure exerted and multiply this by the area in contact with the water.
Topic	All topics
Subject	Physics
Class	Class 11

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