a physics question about bathysphere from isaac physics

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andy0530
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A bathysphere is a spherical deep-sea submersible which is lowered into the sea on a long cable. Its shell can be made thick enough to withstand depths of over 1000m1000m. It can be modelled as a spherical shell with a small window of very thick glass, which can be considered as a point mass.Before being lowered the bathysphere is floating on the surface, half submerged. By considering the angle, 𝜃θ, of the window to the vertical and the potential energy of the whole system, which of the following is true?There are two points of equilibrium, only one is stable There are no points of equilibrium There is one point of equilibrium, which is stable There are two points of equilibrium, both are stable There is one point of equilibrium, which is unstable
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(Original post by andy0530)
A bathysphere is a spherical deep-sea submersible which is lowered into the sea on a long cable. Its shell can be made thick enough to withstand depths of over 1000m1000m. It can be modelled as a spherical shell with a small window of very thick glass, which can be considered as a point mass.Before being lowered the bathysphere is floating on the surface, half submerged. By considering the angle, 𝜃θ, of the window to the vertical and the potential energy of the whole system, which of the following is true?There are two points of equilibrium, only one is stable There are no points of equilibrium There is one point of equilibrium, which is stable There are two points of equilibrium, both are stable There is one point of equilibrium, which is unstable
There are two points of equilibrium, only one is stable?
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andy0530
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yes
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username5006362
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(Original post by andy0530)
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As the bathysphere is lowered inside, horizontal and vertical forces act on it, hence there are 2 points of equilibrium. The horizontal forces are unaffected/balanced so the equilibrium is stable. The vertical forces (upthrust and weight) are unbalanced due to upthrust not being equal to the weight which means there's an unstable point of equilibrium.
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