Metacenter Definition | Fluid Mechanics
Magic Marks・3 minutes read
The stability of a floating body is determined by the position of its metacenter in relation to the center of gravity, with different positions leading to stable, unstable, or neutral equilibrium. Stable equilibrium occurs when the metacenter is above the center of gravity, while unstable equilibrium happens when the metacenter is below, and neutral equilibrium is when they coincide.
Insights
- The position of the metacenter relative to the center of gravity determines the stability of a floating body, with stable equilibrium arising when the metacenter is above the center of gravity, unstable equilibrium when it is below, and neutral equilibrium when they coincide.
- The metacentric height (gm) quantifies the stability of a floating body, with a greater distance between the metacenter and center of gravity leading to increased stability, while a smaller distance can result in less stability or potential instability.
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Recent questions
What determines the stability of a floating body?
The stability of a floating body is determined by the position of its metacenter in relation to the center of gravity.
What is the metacenter of a floating body?
The metacenter is the point where the vertical line through the new center of buoyancy intersects the center line bg of the body.
What is the metacentric height?
The metacentric height is the distance between the metacenter and the center of gravity of a floating body.
What is stable equilibrium in floating bodies?
Stable equilibrium occurs when the metacenter is positioned above the center of gravity, creating a restoring couple that brings the body back to its original position.
What is unstable equilibrium in floating bodies?
Unstable equilibrium happens when the metacenter is below the center of gravity, causing an overturning couple that leads to the sinking of the body.
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Summary
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Metacenter Determines Stability of Floating Bodies
- The stability of a floating body is determined by the position of its metacenter, which is the point where the vertical line through the new center of buoyancy intersects the center line bg. The distance between the metacenter and the center of gravity is known as the metacentric height gm, with different positions leading to stable, unstable, or neutral equilibrium.
- In stable equilibrium, the metacenter is above the center of gravity, creating a restoring couple that returns the body to its original position. Unstable equilibrium occurs when the metacenter is below the center of gravity, causing an overturning couple that sinks the body. Neutral equilibrium is when the metacenter coincides with the center of gravity, resulting in no return to the original position or further displacement.
