One of the many fallacious designs for a perpetuum mobile consisted in the following: a shaft is set in a slit in the side of a vessel containing liquid, the shaft's axis lying in the same plane as the vessel's side (Fig.); the shaft completely fills the slit so that no liquid runs out. The shaft can rotate about its own axis. An upthrust acts on the half of the shaft which is immersed in water (according to Archimede's principle) which ought, it would appear, to cause the shaft to rotate in a counter-clockwise direction. This rotation, if it arose, ought to continue perpetually. Where is the fallacy here?
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Step 2: Analyze the forces. When the shaft is partially submerged, it experiences an upward buoyant force on the submerged part. However, this is balanced by the weight of the entire shaft itself which acts downwards.
Step 3: Identify the fallacy. Although the proposed setup suggests a net upward force causing continuous rotation, this neglects the fact that the upthrust on the submerged portion does not create a torque sufficient for perpetual motion; it would only cause rotation until equilibrium is reached.
Step 4: Conclude that no additional energy is supplied into the system to maintain motion. The forces will always lead to a stable equilibrium, thus disproving the concept of a perpetuum mobile.
Therefore, the fault lies in the assumption that the buoyant force can generate continuous motion without an external energy source.
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