Forces involved in principle of virtual work

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The principle of virtual work indicates that a system can remain in equilibrium if the total virtual work done by weights is zero, allowing for deformation into a parallelogram. However, this assumes that reaction forces at the joints do not contribute to the work done, raising questions about the validity of this assumption. The discussion emphasizes that forces at the joints are internal and consist of action-reaction pairs between bars. Acknowledging these internal forces is crucial for a complete understanding of the system's dynamics. Overall, the equilibrium condition relies heavily on the treatment of internal forces within the system.
phantomvommand
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Homework Statement
See picture below
Relevant Equations
Work done = Fd
Screenshot 2024-05-28 at 12.46.18 AM.png

The answer is as such: There’s only one way for the system to move: the rectangle can deform into a parallelogramso that the left horizontal arm moves up, and the right horizontal arm moves down by thesame amount. Then the total virtual work done on the scale by the weights is zero, so thesystem can be in equilibrium no matter where on the arms the weights are placed.

While I can understand this, this assumes that there is 0 work done by reaction forces at the joints, so the net work done on the system is entirely due to gravity. How fair is this assumption?
 
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The forces in the joints are internal forces of the system. At a joint where two bars meet, the forces that the two bars exert on each other are action-reaction forces.
 
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TSny said:
The forces in the joints are internal forces of the system. At a joint where two bars meet, the forces that the two bars exert on each other are action-reaction forces.
Oh right, forgot about that! Thanks!
 
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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