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

In summary, the person has worked out the total force on the gate and the centre of pressure, and has used the equation M=FN*X to calculate the moment about the hinge. They have also tried to calculate the moment due to T, but are unsure if they should equate it to the moment in the downwards direction or not.
  • #1
pressurised
22
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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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  • #2
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

?
 
  • #3
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
 

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

1. How can I find the tension in a rope attached to a gate underwater?

To find the tension in a rope attached to a gate underwater, you can use the equation T = mg + ρVg, where T is the tension, m is the mass of the gate, g is the acceleration due to gravity, ρ is the density of the water, and V is the volume of the gate. This equation takes into account the weight of the gate and the buoyant force acting on it in the water.

2. What factors affect the tension in a rope attached to a gate underwater?

The tension in a rope attached to a gate underwater is affected by several factors, including the weight of the gate, the density of the water, the depth of the gate, and the angle of the rope relative to the gate. These factors all contribute to the overall forces acting on the gate and the rope, which determine the tension.

3. How does the tension in a rope attached to a gate underwater change with depth?

The tension in a rope attached to a gate underwater increases with depth, due to the increase in water pressure. This increase in pressure results in an increase in the buoyant force acting on the gate, which in turn increases the overall tension in the rope.

4. Can the tension in a rope attached to a gate underwater be measured directly?

Yes, the tension in a rope attached to a gate underwater can be measured directly using a tension meter or a load cell. These tools can measure the force being applied to the rope and provide an accurate measurement of the tension.

5. Is it important to find the tension in a rope attached to a gate underwater?

Yes, it is important to find the tension in a rope attached to a gate underwater in order to ensure the stability and safety of the gate. The proper tension is necessary to keep the gate in place and prevent it from floating or sinking. It also helps to prevent damage to the rope and the gate itself.

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