Statics Problem Submerged Object

[talaroue]

Homework Statement

A 0.5 x 0.8m gate AB is located at the bottomof a ank filled with water. The gate is hinged along its top edge A and rests on a frictionless stop at B. Determine the reactions at A and B when cable BCD is slack.

Homework Equations

Fx=0
Fy=0

The Attempt at a Solution

I thought I would have to find the pressure of the water would be the x component, and then the weght of the water would be for the y component...

Since all of the widths are the same I figured they would null each other out because if they weren't the same water would either over flow under B and A.

Pressure=(1/2)bh*density=(1/2)*.93*.64*1000=297.6 kg (not a force)
Weight=Area of triangle+area of rectangle
=(1/2)bh+bh=((1/2)*.64*.48*1000)+(.64*.93*1000)=748.8 kg(not a force)

I don't understand excatly what the next step is what I tried doing was making Fx and Fy equations and solve for one...but i don't know how to turn kg into N, because when I multiply by gravity I get a huge number which gives me the wrong answer...

Here is my work drawn out on my picture...

Orange triangle is the pressure
The purple square and blue triangle is the weight. Does this make sense? Or am I in the wrong direction

 

[talaroue]

I have a better understanding now I believe is this the correct value for P and W...

P=width*specfic weight*hieght*height*(1/2)
=.5m*(9800N/m^3)*.93 m* .93m *.5m=2119.005 N

W=(area of triangle+area of rectangle)*9800
=(.5*.64*.48)+(.64*.45)=.4416*9800=4327.68 N

 

[Mene]

?


I would first like to clarify that the given information is not enough to solve the problem. We need to know the weight of the gate and the tension in the cable BCD in order to determine the reactions at A and B.

However, based on the information provided, I can provide some general guidance on how to approach this problem.

Firstly, we need to understand that the gate is in static equilibrium, meaning that all the forces acting on it must balance out. This means that the sum of all the forces in the x-direction must be equal to zero, and the sum of all the forces in the y-direction must also be equal to zero.

To solve for the reactions at A and B, we need to consider the forces acting on the gate. These forces include the weight of the gate, the pressure of the water on the gate, and the tension in the cable.

In order to find the weight of the gate, we need to know its mass and the acceleration due to gravity. Once we have the weight, we can determine the reaction at B by taking the component of the weight that is perpendicular to the gate (since it is hinged at A, the reaction at A will be zero).

Next, we need to consider the pressure of the water on the gate. This pressure will act on the entire surface area of the gate and will have a component in the x-direction and in the y-direction. To find the pressure, we can use the formula P = ρgh, where ρ is the density of water, g is the acceleration due to gravity, and h is the depth of the water. We can then find the components of the pressure in the x-direction and y-direction by using trigonometry.

Finally, we need to consider the tension in the cable. Since the cable is slack, we can assume that there is no tension in it.

Once we have all these components, we can set up our equations for the forces in the x-direction and y-direction and solve for the reactions at A and B. Remember to convert all your masses to forces by multiplying them by the acceleration due to gravity.

In summary, the key steps to solving this problem are:
1. Identify all the forces acting on the gate (weight, pressure, and tension in the cable)
2. Set up equations for the forces in the x-direction and y-direction
3. Solve for the