Finding the tension in a rope attached to a gate underwater.

AI Thread Summary
The discussion focuses on calculating the tension in a rope attached to a gate submerged underwater. The total force on the gate and the center of pressure were determined, with the center of pressure calculated to be 10/3m from the hinge. A moment calculation about the hinge resulted in a value of 981,000Nm, leading to an initial tension estimate of 196,200N. However, further analysis suggested that the tension could also be calculated as 117,720N by considering the moments due to the downward force. The calculations indicate a need to clarify the relationship between the moments and the tension in the rope.
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Homework Statement


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2 & 3. The Attempt at a Solution
I've worked out:
The total force on the gate.
I have worked out the centre of pressure which I got a value of 10/3m (from the hinge).
For the moment about the hinge I got a value of 981,000Nm using the equation M=FN*X where X is the centre of pressure and FN is the total force on the gate. Dividing this by 5 (length of gate) I get 196,200N, which I assume must be T?

(Or T*cosθ which gives me 117,720N, which seems to small)
 
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Acutally, if I work out the moment M due to the force dFN * the centre of pressure (metres from hinge), and equate this moment to the moment due to T:

294,300(10/3)=T(5)
T=196,200N

?
 
Sorry, or do I equate the moment 294,300(10/3) in the downwards direction then it will equal T? So 294,300*(10/3)*(3/5)=T(5). So T=117,720N
 
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