Shear force and bending moment diagrams question

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When analyzing shear force and bending moment diagrams, flipping the beam alters the sign of the shear but not the moment, adhering to established conventions. It is essential to draw these diagrams from left to right to ensure that the area under the shear diagram corresponds to the change in moment between points. The slope of the moment diagram at any point reflects the shear at that point. Additionally, the directions of shears and moments in free body diagrams must remain consistent, regardless of the perspective. Following these guidelines is crucial for accurate analysis in structural engineering.
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Homework Statement


So in my notes we have the following example:
1oNEeJg.png


So I decided to try to solve it another way, this time I flipped the figure and here is my attempt:
aOwzV6o.png


I got the correct moment but then the signs on my shear is flipped. Does anyone know why?
 
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That is correct, when you flip the beam, the shear changes sign but the moment does not. This is the convention used. Always draw shear and moment diagrams from left to right. In this manner, the area under the shear diagram between 2 points will be equal to the change in moment between those 2 points. And the slope of the moment diagram at any point will be equal to the shear at that point. Stick with the convention.
Edit: regardless of convention, some of the directions of the shears and moments in your free body diagrams are shown in the wrong direction. The directions on a cut section are the same no matter from what direction you look at the beam.
 
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The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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