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Homework Statement
The upper edge of a gate in a dam runs along the water surface. The gate is 2.00 m high and 4.00 m wide and is hinged along a horizontal line through its center (Figure 1)
Calculate the torque about the hinge arising from the force due to the water. (Hint: Calculate the torque on a thin, horizontal strip at a depth h and integrate this over the gate.)
Homework Equations
F = Pressure * Area
M = Density * Volume
Torque = Force * Moment-Arm
Pressure = Density * gravity * depth (edit: I recently found this out)
The Attempt at a Solution
I found out that pressure would be:
1x103 * gravity * depth
And since we want the total pressure we will have to integrate correct?
Therefore our varying variable will be h (height) so pressure would be:
∫ from 0 - 1 (the middle of that gate) of (1x103 * gravity * h) dh correct?
And do I now multiply the answer from that by the area ( 4 * 2 = 8) to get the force?
Then multiply that force by the moment arm? (Not sure how to get this though.)
Any and all help is appreciated.
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