Calculating Force & CG of False Mud Gate Made of Steel

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To calculate the required force to lift a false mud gate made of steel, first determine its volume by multiplying its dimensions, which results in a weight of approximately 1,000 lbs using the density of steel (490 lbs/cu ft). The lifting force needed from the hoist must equal the gate's weight for a slow lift. To find the center of gravity, consider the gate's uniform shape and dimensions, which places the center of gravity at its geometric center. The center of gravity for this gate is located at 3'3" from the bottom and 3'3" from either side. Understanding these calculations is essential for effective lifting and safety.
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Homework Statement


A false mud gate made of common steel for a damn is 6'6" wide, 21'1" tall, and 1/2" thick. Assume a constant density throughout. What is the required force to lift this gate if it were laying flat on the ground and a hoist was attached to the center of gravity? also where is its center of gravity?


Homework Equations


Can anyone help me get started on this at least? It would be great if you could, thanks.


The Attempt at a Solution

 
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Calculate the volume of the steel gate in cubic feet. Steel weighs about 490 lbs/cu ft. The lifting force of the hoist must be equal to the gate's weight in order to lift it slowly off the ground.
 
Okay i have the force now, how would i find the center of gravity?
 
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