The Concept of Stable Equilibrium

Stable equilibrium refers to a state in which a floating body remains in balance without any tendency to tip over or capsize. In this state, any disturbance or external force acting on the body will cause it to oscillate but eventually return to its original position. For a floating body to be in stable equilibrium, the metacentric height must be positive.

Understanding the Metacentric Height

The metacentric height (GM) is a parameter that indicates the stability of a floating body. It is the distance between the center of gravity (G) and the metacenter (M) of the body. The metacenter is the point at which the vertical line passing through the center of buoyancy (B) intersects with the body's centerline.

The Relationship between Metacentric Height and Stability

The metacentric height plays a crucial role in determining the stability of a floating body. It is directly related to the body's ability to resist tipping over when subjected to external forces. The stability of a floating body can be analyzed by considering the position of the center of gravity relative to the metacenter.

Effects of Positive Metacentric Height

When the metacentric height is positive, it indicates that the metacenter is above the center of gravity. This configuration leads to a stable equilibrium for the floating body. Here's why:

1. Restoring Force: When the body is tilted due to an external force, a moment is created between the center of gravity and the center of buoyancy. This moment generates a restoring force that tries to bring the body back to its original position.

2. Increased Stability: A positive metacentric height results in a larger lever arm between the center of gravity and the metacenter. This increased lever arm enhances the stability of the body, making it more resistant to tipping over.

3. Self-Righting Capability: In the event of a disturbance, the body will undergo oscillations, but due to the positive metacentric height, it will eventually return to its original position without capsizing.

Conclusion

In summary, a floating body is in stable equilibrium when its metacentric height is positive. This indicates that the metacenter is located above the center of gravity, providing the body with increased stability and a self-righting capability. Understanding the relationship between the metacentric height and stability is crucial in the design and analysis of floating structures and vessels to ensure their safe operation in various conditions.