1. The problem statement, all variables and given/known data
AB is homogeneous with mass of 180 kg, goes 1.2m in the page and is hinged at A and resting on aa smooth bottom at B. All fluids at 20 C. Find height of water that will result on 0 force at B
2. Relevant equations
[tex] M_s = \int\int_s \ (\vec{r} \times \hat{n} )PdA [/tex]
[tex] \frac{dP}{dy} = \rho \vec{g} [/tex]
3. The attempt at a solution
The approach I am using to solve this problem is that the total moment caused at point is equal to 0. Therefore the moment caused by glycerine must be equal to the moment caused by water. The problem with this approach is that it neglects the weight of the mass. The bigger problem I have is that I can't seem to work with the axes. I know that the origin has to be at A. If I choose to set the positive z axis downwards along AB and the positive x axis perpendicular to AB towards the left, the positive y axis will go into the page. With axes defined the parts of the equation for pressure are [tex]\vec{r} = z\hat{k}[/tex] and [tex]\hat{n} = \hat{i}[/tex] I found [tex]\vec{g} = \ -gcos(60) \vec{i} + gsin(60)\vec{k} [/tex] I am having trouble working out the geometry of the height of the fluid. Can someone check what I already have and help me with the height vector and dA?
AB is homogeneous with mass of 180 kg, goes 1.2m in the page and is hinged at A and resting on aa smooth bottom at B. All fluids at 20 C. Find height of water that will result on 0 force at B
2. Relevant equations
[tex] M_s = \int\int_s \ (\vec{r} \times \hat{n} )PdA [/tex]
[tex] \frac{dP}{dy} = \rho \vec{g} [/tex]
3. The attempt at a solution
The approach I am using to solve this problem is that the total moment caused at point is equal to 0. Therefore the moment caused by glycerine must be equal to the moment caused by water. The problem with this approach is that it neglects the weight of the mass. The bigger problem I have is that I can't seem to work with the axes. I know that the origin has to be at A. If I choose to set the positive z axis downwards along AB and the positive x axis perpendicular to AB towards the left, the positive y axis will go into the page. With axes defined the parts of the equation for pressure are [tex]\vec{r} = z\hat{k}[/tex] and [tex]\hat{n} = \hat{i}[/tex] I found [tex]\vec{g} = \ -gcos(60) \vec{i} + gsin(60)\vec{k} [/tex] I am having trouble working out the geometry of the height of the fluid. Can someone check what I already have and help me with the height vector and dA?
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