How Does Surface Tension Affect Pressure Between Non-Wetting Plates?

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Surface tension plays a crucial role in the interaction between non-wetting plates, affecting the pressure in the liquid between them. The equation F=2*V/(a^2)*σ*cos(180-θ) suggests that the vertical component of surface tension aligns with the force needed to keep the plates together, indicating no additional force is required. The discussion raises questions about the forces that could potentially separate the plates, emphasizing a lack of intuitive understanding of these dynamics. Ultimately, the pressure in the liquid between the plates is influenced by surface tension, which could lead to it being either higher or lower than atmospheric pressure, depending on the specific conditions. Understanding these relationships is essential for solving related fluid dynamics problems.
Aias
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Homework Statement


http://ocw.mit.edu/courses/mechanic...cs-spring-2013/assignments/MIT2_06S13_ps2.pdf
Problem 7[/B]

Homework Equations


##F=2*V/(a^2)*\sigma*cos(180-\theta)##

The Attempt at a Solution


With the problem statement given, it seems like the component of surface tension in the vertical direction on the upper plate would be in the same direction as the proposed required force due to the surface being non-wetting, thus no need for an actual force F to hold the plates together. I don't see what kind of force would want to push the plates apart? I came to that equation after some fiddling around, it seems like it could be correct, but I don't have an intuitive understanding why it would be so.
 
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Aias said:

Homework Statement


http://ocw.mit.edu/courses/mechanic...cs-spring-2013/assignments/MIT2_06S13_ps2.pdf
Problem 7[/B]

Homework Equations


##F=2*V/(a^2)*\sigma*cos(180-\theta)##

The Attempt at a Solution


With the problem statement given, it seems like the component of surface tension in the vertical direction on the upper plate would be in the same direction as the proposed required force due to the surface being non-wetting, thus no need for an actual force F to hold the plates together. I don't see what kind of force would want to push the plates apart? I came to that equation after some fiddling around, it seems like it could be correct, but I don't have an intuitive understanding why it would be so.
As a result of the surface tension effect, is the pressure in the liquid between the plates higher of lower than the pressure of the surrounding atmosphere?

Chet
 
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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